Reports on Progress in Physics - IOPscience

Reports on Progress in Physics - IOPscience
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1361-6633
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Impact factor
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The following article is
Open access
Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
Mikko Partanen and Jukka Tulkki 2025
Rep. Prog. Phys.
88
057802
View article
, Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
PDF
, Gravity generated by four one-dimensional unitary gauge symmetries and the Standard Model
The Standard Model of particle physics describes electromagnetic, weak, and strong interactions, which are three of the four known fundamental forces of nature. The unification of the fourth interaction, gravity, with the Standard Model has been challenging due to incompatibilities of the underlying theories—general relativity and quantum field theory. While quantum field theory utilizes compact, finite-dimensional symmetries associated with the internal degrees of freedom of quantum fields, general relativity is based on noncompact, infinite-dimensional external space-time symmetries. The present work aims at deriving the gauge theory of gravity using compact, finite-dimensional symmetries in a way that resembles the formulation of the fundamental interactions of the Standard Model. For our eight-spinor representation of the Lagrangian, we define a quantity, called the space-time dimension field, which enables extracting four-dimensional space-time quantities from the eight-dimensional spinors. Four U(1) symmetries of the components of the space-time dimension field are used to derive a gauge theory, called unified gravity. The stress-energy-momentum tensor source term of gravity follows directly from these symmetries. The metric tensor enters in unified gravity through geometric conditions. We show how the teleparallel equivalent of general relativity in the Weitzenböck gauge is obtained from unified gravity by a gravity-gauge-field-dependent geometric condition. Unified gravity also enables a gravity-gauge-field-independent geometric condition that leads to an exact description of gravity in the Minkowski metric. This differs from the use of metric in general relativity, where the metric depends on the gravitational field by definition. Based on the Minkowski metric, unified gravity allows us to describe gravity within a single coherent mathematical framework together with the quantum fields of all fundamental interactions of the Standard Model. We present the Feynman rules for unified gravity and study the renormalizability and radiative corrections of the theory at one-loop order. The equivalence principle is formulated by requiring that the renormalized values of the inertial and gravitational masses are equal. In contrast to previous gauge theories of gravity, all infinities that are encountered in the calculations of loop diagrams can be absorbed by the redefinition of the small number of parameters of the theory in the same way as in the gauge theories of the Standard Model. This result and our observation that unified gravity fulfills the Becchi–Rouet–Stora–Tyutin (BRST) symmetry and its coupling constant is dimensionless suggest that unified gravity can provide the basis for a complete, renormalizable theory of quantum gravity.
Quantum computing
Andrew Steane 1998
Rep. Prog. Phys.
61
117
View article
, Quantum computing
PDF
, Quantum computing
The subject of quantum computing brings together ideas from classical information theory, computer science, and quantum physics. This review aims to summarize not just quantum computing, but the whole subject of quantum information theory. Information can be identified as the most general thing which must propagate from a cause to an effect. It therefore has a fundamentally important role in the science of physics. However, the mathematical treatment of information, especially information processing, is quite recent, dating from the mid-20th century. This has meant that the full significance of information as a basic concept in physics is only now being discovered. This is especially true in quantum mechanics. The theory of quantum information and computing puts this significance on a firm footing, and has led to some profound and exciting new insights into the natural world. Among these are the use of quantum states to permit the secure transmission of classical information (quantum cryptography), the use of quantum entanglement to permit reliable transmission of quantum states (teleportation), the possibility of preserving quantum coherence in the presence of irreversible noise processes (quantum error correction), and the use of controlled quantum evolution for efficient computation (quantum computation). The common theme of all these insights is the use of quantum entanglement as a computational resource.
It turns out that information theory and quantum mechanics fit together very well. In order to explain their relationship, this review begins with an introduction to classical information theory and computer science, including Shannon's theorem, error correcting codes, Turing machines and computational complexity. The principles of quantum mechanics are then outlined, and the Einstein, Podolsky and Rosen (EPR) experiment described. The EPR-Bell correlations, and quantum entanglement in general, form the essential new ingredient which distinguishes quantum from classical information theory and, arguably, quantum from classical physics.
Basic quantum information ideas are next outlined, including qubits and data compression, quantum gates, the `no cloning' property and teleportation. Quantum cryptography is briefly sketched. The universal quantum computer (QC) is described, based on the Church-Turing principle and a network model of computation. Algorithms for such a computer are discussed, especially those for finding the period of a function, and searching a random list. Such algorithms prove that a QC of sufficiently precise construction is not only fundamentally different from any computer which can only manipulate classical information, but can compute a small class of functions with greater efficiency. This implies that some important computational tasks are impossible for any device apart from a QC.
To build a universal QC is well beyond the abilities of current technology. However, the principles of quantum information physics can be tested on smaller devices. The current experimental situation is reviewed, with emphasis on the linear ion trap, high-
optical cavities, and nuclear magnetic resonance methods. These allow coherent control in a Hilbert space of eight dimensions (three qubits) and should be extendable up to a thousand or more dimensions (10 qubits). Among other things, these systems will allow the feasibility of quantum computing to be assessed. In fact such experiments are so difficult that it seemed likely until recently that a practically useful QC (requiring, say, 1000 qubits) was actually ruled out by considerations of experimental imprecision and the unavoidable coupling between any system and its environment. However, a further fundamental part of quantum information physics provides a solution to this impasse. This is quantum error correction (QEC).
An introduction to QEC is provided. The evolution of the QC is restricted to a carefully chosen subspace of its Hilbert space. Errors are almost certain to cause a departure from this subspace. QEC provides a means to detect and undo such departures without upsetting the quantum computation. This achieves the apparently impossible, since the computation preserves quantum coherence even though during its course all the qubits in the computer will have relaxed spontaneously many times.
The review concludes with an outline of the main features of quantum information physics and avenues for future research.
Quantum spin liquids: a review
Lucile Savary and Leon Balents 2017
Rep. Prog. Phys.
80
016502
View article
, Quantum spin liquids: a review
PDF
, Quantum spin liquids: a review
Quantum spin liquids may be considered ‘quantum disordered’ ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct
phases
of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.
The following article is
Open access
Granite sliding on granite: friction, wear rates, surface topography, and the scale-dependence of rate–state effects
Sergey V Sukhomlinov
et al
2026
Rep. Prog. Phys.
89
038301
View article
, Granite sliding on granite: friction, wear rates, surface topography, and the scale-dependence of rate–state effects
PDF
, Granite sliding on granite: friction, wear rates, surface topography, and the scale-dependence of rate–state effects
We study tribological granite–granite contacts as a model for tectonic faulting, combining experiments, theory, and molecular dynamics simulations. The high friction in this system is not dominated by particulate wear or plowing, as frequently assumed, but by cold welding within plastically deformed asperity junctions. We base this conclusion on the observation that wear is repeatedly high after cleaning contacts but decreases as gouge accumulates, while friction shows the opposite trend. Moreover, adding water reduces wear by a factor of ten but barely decreases friction. Thermal and rate-dependent effects—central to most earthquake models—are negligible: friction remains unchanged between
C and
C, across abrupt velocity steps, and after hours of stationary contact. The absence of rate–state effects in our macroscopic samples is rationalized by the scale-dependence of pre-slip. The evolution of surface topography shows that quartz grains become locally smooth, with height spectra isotropic for wavelength below 10 microns but anisotropic at longer wavelengths, similar to natural faults. The resulting gouge particles have the usual characteristic sizes near 100 nm. Molecular dynamics simulations of a rigid, amorphous silica tip sliding on
-quartz reproduce not only similar friction coefficients near unity but also other experimentally observed features, including stress-introduced transitions to phases observed in post-mortem faults, as well as theoretical estimates of local flash temperatures. Additionally, they reveal a marked decrease of interfacial shear strength above
C.
The following article is
Open access
Many-body localization in the age of classical computing
Piotr Sierant
et al
2025
Rep. Prog. Phys.
88
026502
View article
, Many-body localization in the age of classical computing
PDF
, Many-body localization in the age of classical computing
Statistical mechanics provides a framework for describing the physics of large, complex many-body systems using only a few macroscopic parameters to determine the state of the system. For isolated quantum many-body systems, such a description is achieved via the eigenstate thermalization hypothesis (ETH), which links thermalization, ergodicity and quantum chaotic behavior. However, tendency towards thermalization is not observed at finite system sizes and evolution times in a robust many-body localization (MBL) regime found numerically and experimentally in the dynamics of interacting many-body systems at strong disorder. Although the phenomenology of the MBL regime is well-established, the central question remains unanswered: under what conditions does the MBL
regime
give rise to an MBL
phase
, in which the thermalization does not occur even in the
asymptotic
limit of infinite system size and evolution time? This review focuses on recent numerical investigations aiming to clarify the status of the MBL phase, and it establishes the critical open questions about the dynamics of disordered many-body systems. The last decades of research have brought an unprecedented new variety of tools and indicators to study the breakdown of ergodicity, ranging from spectral and wave function measures, matrix elements of observables, through quantities probing unitary quantum dynamics, to transport and quantum information measures. We give a comprehensive overview of these approaches and attempt to provide a unified understanding of their main features. We emphasize general trends towards ergodicity with increasing length and time scales, which exclude naive single-parameter scaling hypothesis, necessitate the use of more refined scaling procedures, and prevent unambiguous extrapolations of numerical results to the asymptotic limit. Providing a concise description of numerical methods for studying ETH and MBL, we explore various approaches to tackle the question of the MBL phase. Persistent finite size drifts towards ergodicity consistently emerge in quantities derived from eigenvalues and eigenvectors of disordered many-body systems. The drifts are related to continuous inching towards ergodicity and non-vanishing transport observed in the dynamics of many-body systems, even at strong disorder. These phenomena impede the understanding of microscopic processes at the ETH-MBL crossover. Nevertheless, the abrupt slowdown of dynamics with increasing disorder strength provides premises suggesting the proximity of the MBL phase. This review concludes that the questions about thermalization and its failure in disordered many-body systems remain a captivating area open for further explorations.
The following article is
Open access
Quantum algorithms for scientific computing
R Au-Yeung
et al
2024
Rep. Prog. Phys.
87
116001
View article
, Quantum algorithms for scientific computing
PDF
, Quantum algorithms for scientific computing
Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in real world applications. Areas that are likely to have the greatest impact on high performance computing (HPC) include simulation of quantum systems, optimization, and machine learning. We draw our examples from electronic structure calculations and computational fluid dynamics which account for a large fraction of current scientific and engineering use of HPC. Potential challenges include encoding and decoding classical data for quantum devices, and mismatched clock speeds between classical and quantum processors. Even a modest quantum enhancement to current classical techniques would have far-reaching impacts in areas such as weather forecasting, aerospace engineering, and the design of ‘green’ materials for sustainable development. This requires significant effort from the computational science, engineering and quantum computing communities working together.
Machine learning & artificial intelligence in the quantum domain: a review of recent progress
Vedran Dunjko and Hans J Briegel 2018
Rep. Prog. Phys.
81
074001
View article
, Machine learning & artificial intelligence in the quantum domain: a review of recent progress
PDF
, Machine learning & artificial intelligence in the quantum domain: a review of recent progress
Quantum information technologies, on the one hand, and intelligent learning systems, on the other, are both emergent technologies that are likely to have a transformative impact on our society in the future. The respective underlying fields of basic research—quantum information versus machine learning (ML) and artificial intelligence (AI)—have their own specific questions and challenges, which have hitherto been investigated largely independently. However, in a growing body of recent work, researchers have been probing the question of the extent to which these fields can indeed learn and benefit from each other. Quantum ML explores the interaction between quantum computing and ML, investigating how results and techniques from one field can be used to solve the problems of the other. Recently we have witnessed significant breakthroughs in both directions of influence. For instance, quantum computing is finding a vital application in providing speed-ups for ML problems, critical in our ‘big data’ world. Conversely, ML already permeates many cutting-edge technologies and may become instrumental in advanced quantum technologies. Aside from quantum speed-up in data analysis, or classical ML optimization used in quantum experiments, quantum enhancements have also been (theoretically) demonstrated for interactive learning tasks, highlighting the potential of quantum-enhanced learning agents. Finally, works exploring the use of AI for the very design of quantum experiments and for performing parts of genuine research autonomously, have reported their first successes. Beyond the topics of mutual enhancement—exploring what ML/AI can do for quantum physics and vice versa—researchers have also broached the fundamental issue of quantum generalizations of learning and AI concepts. This deals with questions of the very meaning of learning and intelligence in a world that is fully described by quantum mechanics. In this review, we describe the main ideas, recent developments and progress in a broad spectrum of research investigating ML and AI in the quantum domain.
The following article is
Open access
Observation of quantum entanglement in top quark pair production in proton–proton collisions at
TeV
The CMS Collaboration 2024
Rep. Prog. Phys.
87
117801
View article
, Observation of quantum entanglement in top quark pair production in proton–proton collisions at  TeV
PDF
, Observation of quantum entanglement in top quark pair production in proton–proton collisions at  TeV
Entanglement is an intrinsic property of quantum mechanics and is predicted to be exhibited in the particles produced at the Large Hadron Collider. A measurement of the extent of entanglement in top quark-antiquark (
) events produced in proton–proton collisions at a center-of-mass energy of 13 TeV is performed with the data recorded by the CMS experiment at the CERN LHC in 2016, and corresponding to an integrated luminosity of 36.3 fb
−1
. The events are selected based on the presence of two leptons with opposite charges and high transverse momentum. An entanglement-sensitive observable
is derived from the top quark spin-dependent parts of the
production density matrix and measured in the region of the
production threshold. Values of
are evidence of entanglement and
is observed (expected) to be
) at the parton level. With an observed significance of 5.1 standard deviations with respect to the non-entangled hypothesis, this provides observation of quantum mechanical entanglement within
pairs in this phase space. This measurement provides a new probe of quantum mechanics at the highest energies ever produced.
A review of metasurfaces: physics and applications
Hou-Tong Chen
et al
2016
Rep. Prog. Phys.
79
076401
View article
, A review of metasurfaces: physics and applications
PDF
, A review of metasurfaces: physics and applications
Metamaterials are composed of periodic subwavelength metal/dielectric structures that resonantly couple to the electric and/or magnetic components of the incident electromagnetic fields, exhibiting properties that are not found in nature. This class of micro- and nano-structured artificial media have attracted great interest during the past 15 years and yielded ground-breaking electromagnetic and photonic phenomena. However, the high losses and strong dispersion associated with the resonant responses and the use of metallic structures, as well as the difficulty in fabricating the micro- and nanoscale 3D structures, have hindered practical applications of metamaterials. Planar metamaterials with subwavelength thickness, or metasurfaces, consisting of single-layer or few-layer stacks of planar structures, can be readily fabricated using lithography and nanoprinting methods, and the ultrathin thickness in the wave propagation direction can greatly suppress the undesirable losses. Metasurfaces enable a spatially varying optical response (e.g. scattering amplitude, phase, and polarization), mold optical wavefronts into shapes that can be designed at will, and facilitate the integration of functional materials to accomplish active control and greatly enhanced nonlinear response. This paper reviews recent progress in the physics of metasurfaces operating at wavelengths ranging from microwave to visible. We provide an overview of key metasurface concepts such as anomalous reflection and refraction, and introduce metasurfaces based on the Pancharatnam–Berry phase and Huygens’ metasurfaces, as well as their use in wavefront shaping and beam forming applications, followed by a discussion of polarization conversion in few-layer metasurfaces and their related properties. An overview of dielectric metasurfaces reveals their ability to realize unique functionalities coupled with Mie resonances and their low ohmic losses. We also describe metasurfaces for wave guidance and radiation control, as well as active and nonlinear metasurfaces. Finally, we conclude by providing our opinions of opportunities and challenges in this rapidly developing research field.
The following article is
Open access
Heralded generation of entanglement with photons
Imogen Forbes
et al
2025
Rep. Prog. Phys.
88
086002
View article
, Heralded generation of entanglement with photons
PDF
, Heralded generation of entanglement with photons
Entangled states of photons form the backbone of many quantum technologies. Due to the lack of effective photon–photon interactions, the generation of these states is typically probabilistic. In the prevailing but fundamentally limited generation technique, known as postselection, the target photons are measured destructively in the generation process. By contrast, in the alternative approach—heralded state generation—the successful creation of a desired state is verified by the detection of ancillary photons. Heralded state generation is superior to postselection in several critical ways: it enables free usage of the prepared states, allows for the success probability to be arbitrarily increased via multiplexing, and provides a scalable route to quantum information processing using photons. Here, we review theoretical proposals and experimental realisations of heralded entangled photonic state generation, as well as the impact of realistic experimental errors. We then discuss the wide-ranging applications of these states for quantum technologies, including resource states in linear optical quantum computing, entanglement swapping for repeater networks, fundamental physics, and quantum metrology.
The following article is
Open access
Visualizing lattice-mismatch-dependent strain relaxation in epitaxially grown MoS
/WS
and MoS
/WSe
hetero-bilayers
Jinwoo Kim
et al
2026
Rep. Prog. Phys.
89
048005
View article
, Visualizing lattice-mismatch-dependent strain relaxation in epitaxially grown MoS2/WS2 and MoS2/WSe2 hetero-bilayers
PDF
, Visualizing lattice-mismatch-dependent strain relaxation in epitaxially grown MoS2/WS2 and MoS2/WSe2 hetero-bilayers
Strain relaxation at lattice-mismatched interfaces is critical for epitaxial growth and high-quality single-crystal films. While van der Waals (vdW) epitaxy is considered as a promising platform due to its high tolerance to lattice mismatch, its actual response to lattice mismatch remains largely unexplored. Here, we investigate the effect of lattice mismatch on vdW interfaces by epitaxially growing MoS
on WS
or WSe
substrate. annular dark-field scanning transmission electron microscopy reveals that MoS
/WS
with a negligible lattice mismatch of ∼0.22% forms a fully commensurate structure, whereas MoS
/WSe
with a large lattice mismatch of ∼3.96% exhibits non-uniform moiré patterns, characteristic of an incommensurate interface. Detailed analysis shows that the MoS
/WS
hetero-bilayers exhibit perfectly aligned structure through compression of MoS
, whereas the MoS
/WSe
hetero-bilayers show elongation and rotation of moiré orientation driven by tensile strain. Notably, even small twist angles induce significant changes in moiré orientation, resulting in bent fringes that are indicative of local rotational distortions. Large lattice mismatch drives localized lattice distortion, where rotation of the MoS
lattice emerges as an energetically favorable mechanism for strain release, in contrast to commensurate alignment in small-mismatch systems. Our results establish moiré pattern analysis as a powerful framework for directly visualizing spatially varying strain and its relaxation pathways in vdW hetero-bilayers. Our work reveals previously inaccessible interfacial deformation modes in vdW hetero-bilayers and establishes moiré analysis as a powerful platform for strain engineering in 2D electronic and optoelectronic materials.
Probing electron correlations in solids with Auger-photoelectron coincidence spectroscopy
Robert A Bartynski
et al
2026
Rep. Prog. Phys.
89
046502
View article
, Probing electron correlations in solids with Auger-photoelectron coincidence spectroscopy
PDF
, Probing electron correlations in solids with Auger-photoelectron coincidence spectroscopy
Auger photoelectron coincidence spectroscopy (APECS) has emerged as a powerful tool for probing electron–electron correlation in solids. When a photoexcited core hole decays via a core-valence-valence Auger transition, two valence holes are created in the final state. Consequently, the line shape of the Auger electron spectrum is influenced by both Coulomb and exchange interactions between the two holes. By simultaneously detecting the photoelectron and Auger electron emitted from a single photoionization event, APECS measurements place constraints on the two final state holes, enabling one to independently measure Coulomb and exchange correlation energies. This review highlights the key advantages of APECS over other electron spectroscopic techniques including separating overlapping spectral features, removing the background signal from inelastically scattered electrons, enhanced surface sensitivity and site specificity. It also cites examples of how these attributes can be used to investigate the properties of solids in an unprecedented manner. To aid in understanding APECS data and assist in experimental design, a phenomenological model for the probability of electron pair emission as a function of the photo- and Auger electron kinetic energies and emission angles is
presented. The model is applied to a hypothetical
solid, demonstrating how the contribution to APECS spectrum of final states with different spin configurations depends on these experimental parameters. A summary of results obtained by performing one-dimensional (as a function of Auger [
or
photoelectron [
] kinetic energy), two-dimensional (parallel detection of
and
) and angle-resolved (AR) (as a function of
at specific photo- and Auger electron emission angles) APECS measurements is presented. In particular, measurements of ferromagnetic metals and antiferromagnetic transition metal oxides demonstrate how AR-APECS is a powerful tool for independently measuring Coulomb and exchange correlation energies. Finally, potential future applications of APECS and further developments of this experimental technique are discussed.
Observation of custodial chiral symmetry in memristive topological circuits
Wenhao Li
et al
2026
Rep. Prog. Phys.
89
048004
View article
, Observation of custodial chiral symmetry in memristive topological circuits
PDF
, Observation of custodial chiral symmetry in memristive topological circuits
The concept of custodial symmetry, a residual symmetry that protects physical observables from large quantum corrections, has been a cornerstone of high-energy physics. In classical engineered systems, however, experimental realization and observation of its classical analog have remained unexplored. Building on recent theoretical work (2022
Phys. Rev. Lett.
128
097701), we report the first experimental observation of a classical analog of custodial chiral symmetry in a memristive Su–Schrieffer–Heeger (SSH) circuit. We provide direct experimental evidence for custodial symmetry by measuring the correction to the Lagrangian. This Lagrangian correction, which mimics a mass term in field theory, vanishes smoothly as the perturbation is reduced. We also demonstrate that topological edge states in the memristive SSH circuit remain localized at the boundary, consistent with custodial chiral symmetry. This work opens new avenues for emulating field-theoretic symmetries and nonlinear dynamics in memristive platforms.
2D excitonics with atomically thin lateral heterostructures
S Shradha
et al
2026
Rep. Prog. Phys.
89
046501
View article
, 2D excitonics with atomically thin lateral heterostructures
PDF
, 2D excitonics with atomically thin lateral heterostructures
Semiconducting transition metal dichalcogenides (TMDs), such as MoSe
and WSe
, exhibit unique optical and electronic properties. Vertical stacking of layers of one or more TMDs, to create heterostructures, has expanded the fields of moiré physics and twistronics. Bottom-up fabrication techniques, such as chemical vapor deposition, have advanced the creation of heterostructures beyond what was possible with mechanical exfoliation and stacking. These techniques now enable the fabrication of
lateral
heterostructures (LHs), where two or more monolayers are covalently bonded in the plane of their atoms. At their atomically sharp interfaces, lateral heterostructures exhibit additional phenomena, such as the formation of charge-transfer excitons, in which the electron and hole reside on opposite sides of the interface. Due to the energy landscape created by differences in the band structures of the constituent materials, unique effects such as unidirectional exciton transport and excitonic lensing can be observed in LHs. This review outlines recent progress in exciton dynamics and spectroscopy of TMD-based LHs and offers an outlook on future developments in excitonics in this promising system.
Fractionalized Fermi liquids and the cuprate phase diagram
Pietro M Bonetti
et al
2026
Rep. Prog. Phys.
89
044501
View article
, Fractionalized Fermi liquids and the cuprate phase diagram
PDF
, Fractionalized Fermi liquids and the cuprate phase diagram
We review a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area
at hole doping
, in contrast to the area
in spin density wave theory. Magnetotransport measurements, including observation of the Yamaji angle, show clear evidence of hole pocket quasiparticles which can tunnel coherently between square lattice layers, and are consistent with the FL* description. The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site: the Ancilla layer model (ALM). Its mean field theory yields hole pockets of area
, and matches the gapped photoemission spectrum in the anti-nodal region of the Brillouin zone. Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields a
-wave superconductor via a Kosterlitz–Thouless transition of
vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. An alternative route yields a charge-ordered metallic state that has quantum oscillations consistent with observations. These confinement transitions are driven by the condensation of a SU(2) fundamental Higgs field, which also provides a fractionalized description of intertwined orders. Increasing doping from the FL* phase in the ALM drives a transition to a conventional FL at large doping, passing through an intermediate strange metal regime. We formulate a theory of the FL*-FL metal-metal transition without a symmetry-breaking order parameter, using a critical quantum ‘charge’ liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev–Ye–Kitaev model to two spatial dimensions. At low temperatures, and across optimal and over doping, we address the regimes of extended non-FL behavior by Griffiths effects near quantum phase transitions in disordered metals.
Partly based on lectures by S S at
Boulder School 2025, Dynamics of Strongly Correlated Electrons
, 14–18 July.
Lecture videos
Joint ICTP-WE Heraeus School and Workshop on Advances in Quantum Matter: Pushing the Boundaries
, ICTP, Trieste, 4, 6 August 2025.
Lecture videos
School on Quantum Dynamics of Matter, Light and Information
, ICTP, Trieste, 18, 19 August 2025.
Lecture videos
Croucher Advanced Study Institute for Fractional Chern Insulators
, University of Hong Kong, 4, 5 September 2025.
Lecture slides
Advanced School and Conference on Quantum Matter
, ICTP Trieste, 1–12 December 2025.
Lecture Notes
Lecture videos
Probing electron correlations in solids with Auger-photoelectron coincidence spectroscopy
Robert A Bartynski
et al
2026
Rep. Prog. Phys.
89
046502
View article
, Probing electron correlations in solids with Auger-photoelectron coincidence spectroscopy
PDF
, Probing electron correlations in solids with Auger-photoelectron coincidence spectroscopy
Auger photoelectron coincidence spectroscopy (APECS) has emerged as a powerful tool for probing electron–electron correlation in solids. When a photoexcited core hole decays via a core-valence-valence Auger transition, two valence holes are created in the final state. Consequently, the line shape of the Auger electron spectrum is influenced by both Coulomb and exchange interactions between the two holes. By simultaneously detecting the photoelectron and Auger electron emitted from a single photoionization event, APECS measurements place constraints on the two final state holes, enabling one to independently measure Coulomb and exchange correlation energies. This review highlights the key advantages of APECS over other electron spectroscopic techniques including separating overlapping spectral features, removing the background signal from inelastically scattered electrons, enhanced surface sensitivity and site specificity. It also cites examples of how these attributes can be used to investigate the properties of solids in an unprecedented manner. To aid in understanding APECS data and assist in experimental design, a phenomenological model for the probability of electron pair emission as a function of the photo- and Auger electron kinetic energies and emission angles is
presented. The model is applied to a hypothetical
solid, demonstrating how the contribution to APECS spectrum of final states with different spin configurations depends on these experimental parameters. A summary of results obtained by performing one-dimensional (as a function of Auger [
or
photoelectron [
] kinetic energy), two-dimensional (parallel detection of
and
) and angle-resolved (AR) (as a function of
at specific photo- and Auger electron emission angles) APECS measurements is presented. In particular, measurements of ferromagnetic metals and antiferromagnetic transition metal oxides demonstrate how AR-APECS is a powerful tool for independently measuring Coulomb and exchange correlation energies. Finally, potential future applications of APECS and further developments of this experimental technique are discussed.
2D excitonics with atomically thin lateral heterostructures
S Shradha
et al
2026
Rep. Prog. Phys.
89
046501
View article
, 2D excitonics with atomically thin lateral heterostructures
PDF
, 2D excitonics with atomically thin lateral heterostructures
Semiconducting transition metal dichalcogenides (TMDs), such as MoSe
and WSe
, exhibit unique optical and electronic properties. Vertical stacking of layers of one or more TMDs, to create heterostructures, has expanded the fields of moiré physics and twistronics. Bottom-up fabrication techniques, such as chemical vapor deposition, have advanced the creation of heterostructures beyond what was possible with mechanical exfoliation and stacking. These techniques now enable the fabrication of
lateral
heterostructures (LHs), where two or more monolayers are covalently bonded in the plane of their atoms. At their atomically sharp interfaces, lateral heterostructures exhibit additional phenomena, such as the formation of charge-transfer excitons, in which the electron and hole reside on opposite sides of the interface. Due to the energy landscape created by differences in the band structures of the constituent materials, unique effects such as unidirectional exciton transport and excitonic lensing can be observed in LHs. This review outlines recent progress in exciton dynamics and spectroscopy of TMD-based LHs and offers an outlook on future developments in excitonics in this promising system.
Fractionalized Fermi liquids and the cuprate phase diagram
Pietro M Bonetti
et al
2026
Rep. Prog. Phys.
89
044501
View article
, Fractionalized Fermi liquids and the cuprate phase diagram
PDF
, Fractionalized Fermi liquids and the cuprate phase diagram
We review a theoretical framework for the cuprate superconductors, rooted in a fractionalized Fermi liquid (FL*) description of the intermediate-temperature pseudogap phase at low doping. The FL* theory predicted hole pockets each of fractional area
at hole doping
, in contrast to the area
in spin density wave theory. Magnetotransport measurements, including observation of the Yamaji angle, show clear evidence of hole pocket quasiparticles which can tunnel coherently between square lattice layers, and are consistent with the FL* description. The FL* phase of a single-band model is described using a layer construction with a pair of ancilla qubits on each site: the Ancilla layer model (ALM). Its mean field theory yields hole pockets of area
, and matches the gapped photoemission spectrum in the anti-nodal region of the Brillouin zone. Fluctuations are described by the SU(2) gauge theory of a background spin liquid with critical Dirac spinons. A Monte Carlo study of the thermal SU(2) gauge theory transforms the hole pockets into Fermi arcs in photoemission. One route to confinement of FL* upon lowering temperature yields a
-wave superconductor via a Kosterlitz–Thouless transition of
vortices, with nodal Bogoliubov quasiparticles featuring anisotropic velocities and vortices surrounded by charge order halos. An alternative route yields a charge-ordered metallic state that has quantum oscillations consistent with observations. These confinement transitions are driven by the condensation of a SU(2) fundamental Higgs field, which also provides a fractionalized description of intertwined orders. Increasing doping from the FL* phase in the ALM drives a transition to a conventional FL at large doping, passing through an intermediate strange metal regime. We formulate a theory of the FL*-FL metal-metal transition without a symmetry-breaking order parameter, using a critical quantum ‘charge’ liquid of mobile electrons in the presence of disorder, developed via an extension of the Sachdev–Ye–Kitaev model to two spatial dimensions. At low temperatures, and across optimal and over doping, we address the regimes of extended non-FL behavior by Griffiths effects near quantum phase transitions in disordered metals.
Partly based on lectures by S S at
Boulder School 2025, Dynamics of Strongly Correlated Electrons
, 14–18 July.
Lecture videos
Joint ICTP-WE Heraeus School and Workshop on Advances in Quantum Matter: Pushing the Boundaries
, ICTP, Trieste, 4, 6 August 2025.
Lecture videos
School on Quantum Dynamics of Matter, Light and Information
, ICTP, Trieste, 18, 19 August 2025.
Lecture videos
Croucher Advanced Study Institute for Fractional Chern Insulators
, University of Hong Kong, 4, 5 September 2025.
Lecture slides
Advanced School and Conference on Quantum Matter
, ICTP Trieste, 1–12 December 2025.
Lecture Notes
Lecture videos
The following article is
Open access
High energy resolution x-ray spectroscopy at the actinide M
4,5
edges: experimental challenges and theoretical advances
Clara L Silva
et al
2026
Rep. Prog. Phys.
89
047101
View article
, High energy resolution x-ray spectroscopy at the actinide M4,5 edges: experimental challenges and theoretical advances
PDF
, High energy resolution x-ray spectroscopy at the actinide M4,5 edges: experimental challenges and theoretical advances
Actinide systems continue to raise many unanswered questions on topics involving the number of electrons in valence states, the degree of f-electron localization, and the character of their chemical bonding. Their partially filled 6d and 5f valence shells are responsible for most of their complex behaviour. Understanding the intricate electronic structure of actinides requires the use of advanced experimental and theoretical techniques. Among the experimental approaches, resonant inelastic x-ray scattering and x-ray absorption near edge structure in the high energy resolution fluorescence detection mode at the actinide M
4,5
edges have proven to be powerful techniques for investigating their electronic structure. Here, we review the fundamentals of these x-ray spectroscopies and the theoretical advances in electronic structure calculations using data recorded on 5f electron systems at the An M
4,5
edges (An = Th, U, Np, Pu).
Magnetoactive soft elastomers-materials design, processing and applications
Somashree Mondal
et al
2026
Rep. Prog. Phys.
89
036502
View article
, Magnetoactive soft elastomers-materials design, processing and applications
PDF
, Magnetoactive soft elastomers-materials design, processing and applications
Magnetoactive soft elastomers (MSEs) have garnered considerable attention in various fields of application. Their ability to reversibly change stiffness in the presence of an external magnetic field makes them applicable as dampers and shock absorbers, in soft robotics as actuators and shape-morphing structures and in the biomedical field for minimally invasive tools and devices. Significant progress has been made in the development of MSE in recent years. This review provides a comprehensive overview of the fundamental concepts, material formulation, processing and characterization of MSEs, including their applications in different fields. Emphasis is placed on various aspects such as particle concentration, size and shape, which influence the magneto-mechanical properties of MSEs. Additionally, this review highlights the various characterization methods, both conventional and innovative, that are used to investigate the magneto-mechanical properties. Finally, the authors have addressed the limitations in the field of MSEs, as well as the future directions for MSEs in terms of their composition and shaping techniques.
The following article is
Open access
Observation of a cross-section enhancement near the $t\bar{t}$ production threshold in √s=13 TeV
pp
collisions with the ATLAS detector
Collaboration
View accepted manuscript
, Observation of a cross-section enhancement near the $t\bar{t}$ production threshold in √s=13 TeV pp collisions with the ATLAS detector
PDF
, Observation of a cross-section enhancement near the $t\bar{t}$ production threshold in √s=13 TeV pp collisions with the ATLAS detector
A measurement of $t\bar{t}$ production is presented in the invariant-mass region near the pair production threshold, $m_{t\bar{t}} \sim 345$~GeV, in final states with two charged leptons and multiple jets. The measurement is based on $140\,\mathrm{fb}^{-1}$ of proton-proton collision data collected at $\sqrt{s} = 13$~TeV with the ATLAS detector at the Large Hadron Collider. The data are compared to two models of $t\bar{t}$ production: a baseline model including only perturbative QCD predictions for the hard process at approximate next-to-next-to leading order accuracy in the strong coupling, and an extended model that, in addition, incorporates non-relativistic QCD simulations that also include the formation of colour-singlet quasi-bound-states near the $t\bar{t}$ threshold. The agreement between the data and the models is quantified via a profile-likelihood fit to the reconstructed $m_{t\bar{t}}$ distributions, in bins of two angular observables sensitive to spin-correlations in the $t\bar{t}$ system. An excess of events is observed over the baseline perturbative QCD prediction, with an observed significance over $8$ standard deviations. This excess is consistent with the formation of colour-singlet and spin-singlet $S$-wave quasi-bound $t\bar{t}$ states, as predicted by non-relativistic QCD, and corresponds to an observed cross-section of $9.3^{+1.4}_{-1.3}$~pb.
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A review of metasurfaces: physics and applications
Hou-Tong Chen
et al
2016
Rep. Prog. Phys.
79
076401
View article
, A review of metasurfaces: physics and applications
PDF
, A review of metasurfaces: physics and applications
Metamaterials are composed of periodic subwavelength metal/dielectric structures that resonantly couple to the electric and/or magnetic components of the incident electromagnetic fields, exhibiting properties that are not found in nature. This class of micro- and nano-structured artificial media have attracted great interest during the past 15 years and yielded ground-breaking electromagnetic and photonic phenomena. However, the high losses and strong dispersion associated with the resonant responses and the use of metallic structures, as well as the difficulty in fabricating the micro- and nanoscale 3D structures, have hindered practical applications of metamaterials. Planar metamaterials with subwavelength thickness, or metasurfaces, consisting of single-layer or few-layer stacks of planar structures, can be readily fabricated using lithography and nanoprinting methods, and the ultrathin thickness in the wave propagation direction can greatly suppress the undesirable losses. Metasurfaces enable a spatially varying optical response (e.g. scattering amplitude, phase, and polarization), mold optical wavefronts into shapes that can be designed at will, and facilitate the integration of functional materials to accomplish active control and greatly enhanced nonlinear response. This paper reviews recent progress in the physics of metasurfaces operating at wavelengths ranging from microwave to visible. We provide an overview of key metasurface concepts such as anomalous reflection and refraction, and introduce metasurfaces based on the Pancharatnam–Berry phase and Huygens’ metasurfaces, as well as their use in wavefront shaping and beam forming applications, followed by a discussion of polarization conversion in few-layer metasurfaces and their related properties. An overview of dielectric metasurfaces reveals their ability to realize unique functionalities coupled with Mie resonances and their low ohmic losses. We also describe metasurfaces for wave guidance and radiation control, as well as active and nonlinear metasurfaces. Finally, we conclude by providing our opinions of opportunities and challenges in this rapidly developing research field.
) teleparallel gravity and cosmology
Yi-Fu Cai
et al
2016
Rep. Prog. Phys.
79
106901
View article
, f(T) teleparallel gravity and cosmology
PDF
, f(T) teleparallel gravity and cosmology
Over recent decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein–Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of
) gravity, where
) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from
) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The
gravity construction can provide a theoretical interpretation of the late-time universe acceleration, alternative to a cosmological constant, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, for a certain class of
models, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations—or, alternatively, the Big Bang singularity can be avoided at even earlier moments due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of
cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the
paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like
) gravity, trying to illuminate the subject of which formulation, or combination of formulations, might be more suitable for quantization ventures and cosmological applications.
Quantum spin liquids: a review
Lucile Savary and Leon Balents 2017
Rep. Prog. Phys.
80
016502
View article
, Quantum spin liquids: a review
PDF
, Quantum spin liquids: a review
Quantum spin liquids may be considered ‘quantum disordered’ ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct
phases
of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.
Stochastic thermodynamics, fluctuation theorems and molecular machines
Udo Seifert 2012
Rep. Prog. Phys.
75
126001
View article
, Stochastic thermodynamics, fluctuation theorems and molecular machines
PDF
, Stochastic thermodynamics, fluctuation theorems and molecular machines
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Constraints on primordial black holes
Bernard Carr
et al
2021
Rep. Prog. Phys.
84
116902
View article
, Constraints on primordial black holes
PDF
, Constraints on primordial black holes
We update the constraints on the fraction of the Universe that may have gone into primordial black holes (PBHs) over the mass range 10
−5
to 10
50
g. Those smaller than ∼10
15
g would have evaporated by now due to Hawking radiation, so their abundance at formation is constrained by the effects of evaporated particles on big bang nucleosynthesis, the cosmic microwave background (CMB), the Galactic and extragalactic
-ray and cosmic ray backgrounds and the possible generation of stable Planck mass relics. PBHs larger than ∼10
15
g are subject to a variety of constraints associated with gravitational lensing, dynamical effects, influence on large-scale structure, accretion and gravitational waves. We discuss the constraints on both the initial collapse fraction and the current fraction of the dark matter (DM) in PBHs at each mass scale but stress that many of the constraints are associated with observational or theoretical uncertainties. We also consider indirect constraints associated with the amplitude of the primordial density fluctuations, such as second-order tensor perturbations and
-distortions arising from the effect of acoustic reheating on the CMB, if PBHs are created from the high-
peaks of nearly Gaussian fluctuations. Finally we discuss how the constraints are modified if the PBHs have an extended mass function, this being relevant if PBHs provide some combination of the DM, the LIGO/Virgo coalescences and the seeds for cosmic structure. Even if PBHs make a small contribution to the DM, they could play an important cosmological role and provide a unique probe of the early Universe.
Topological superconductors: a review
Masatoshi Sato and Yoichi Ando 2017
Rep. Prog. Phys.
80
076501
View article
, Topological superconductors: a review
PDF
, Topological superconductors: a review
This review elaborates pedagogically on the fundamental concept, basic theory, expected properties, and materials realizations of topological superconductors. The relation between topological superconductivity and Majorana fermions are explained, and the difference between dispersive Majorana fermions and a localized Majorana zero mode is emphasized. A variety of routes to topological superconductivity are explained with an emphasis on the roles of spin–orbit coupling. Present experimental situations and possible signatures of topological superconductivity are summarized with an emphasis on intrinsic topological superconductors.
Fundamentals of zinc oxide as a semiconductor
Anderson Janotti and Chris G Van de Walle 2009
Rep. Prog. Phys.
72
126501
View article
, Fundamentals of zinc oxide as a semiconductor
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, Fundamentals of zinc oxide as a semiconductor
In the past ten years we have witnessed a revival of, and subsequent rapid expansion in, the research on zinc oxide (ZnO) as a semiconductor. Being initially considered as a substrate for GaN and related alloys, the availability of high-quality large bulk single crystals, the strong luminescence demonstrated in optically pumped lasers and the prospects of gaining control over its electrical conductivity have led a large number of groups to turn their research for electronic and photonic devices to ZnO in its own right. The high electron mobility, high thermal conductivity, wide and direct band gap and large exciton binding energy make ZnO suitable for a wide range of devices, including transparent thin-film transistors, photodetectors, light-emitting diodes and laser diodes that operate in the blue and ultraviolet region of the spectrum. In spite of the recent rapid developments, controlling the electrical conductivity of ZnO has remained a major challenge. While a number of research groups have reported achieving p-type ZnO, there are still problems concerning the reproducibility of the results and the stability of the p-type conductivity. Even the cause of the commonly observed unintentional n-type conductivity in as-grown ZnO is still under debate. One approach to address these issues consists of growing high-quality single crystalline bulk and thin films in which the concentrations of impurities and intrinsic defects are controlled. In this review we discuss the status of ZnO as a semiconductor. We first discuss the growth of bulk and epitaxial films, growth conditions and their influence on the incorporation of native defects and impurities. We then present the theory of doping and native defects in ZnO based on density-functional calculations, discussing the stability and electronic structure of native point defects and impurities and their influence on the electrical conductivity and optical properties of ZnO. We pay special attention to the possible causes of the unintentional n-type conductivity, emphasize the role of impurities, critically review the current status of p-type doping and address possible routes to controlling the electrical conductivity in ZnO. Finally, we discuss band-gap engineering using MgZnO and CdZnO alloys.
Making sense of non-Hermitian Hamiltonians
Carl M Bender 2007
Rep. Prog. Phys.
70
947
View article
, Making sense of non-Hermitian Hamiltonians
PDF
, Making sense of non-Hermitian Hamiltonians
The Hamiltonian
specifies the energy levels and time evolution of a quantum theory. A standard axiom of quantum mechanics requires that
be Hermitian because Hermiticity guarantees that the energy spectrum is real and that time evolution is unitary (probability-preserving). This paper describes an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose +complex conjugate) is replaced by the physically transparent condition of space–time reflection (
) symmetry. If
has an unbroken
symmetry, then the spectrum is real. Examples of
-symmetric non-Hermitian quantum-mechanical Hamiltonians are
and
. Amazingly, the energy levels of these Hamiltonians are all real and positive!
Does a
-symmetric Hamiltonian
specify a physical quantum theory in which the norms of states are positive and time evolution is unitary? The answer is that if
has an unbroken
symmetry, then it has another symmetry represented by a linear operator
. In terms of
, one can construct a time-independent inner product with a positive-definite norm. Thus,
-symmetric Hamiltonians describe a new class of complex quantum theories having positive probabilities and unitary time evolution.
The Lee model provides an excellent example of a
-symmetric Hamiltonian. The renormalized Lee-model Hamiltonian has a negative-norm ‘ghost’ state because renormalization causes the Hamiltonian to become non-Hermitian. For the past 50 years there have been many attempts to find a physical interpretation for the ghost, but all such attempts failed. The correct interpretation of the ghost is simply that the non-Hermitian Lee-model Hamiltonian is
-symmetric. The
operator for the Lee model is calculated exactly and in closed form and the ghost is shown to be a physical state having a positive norm. The ideas of
symmetry are illustrated by using many quantum-mechanical and quantum-field-theoretic models.
New directions in the pursuit of Majorana fermions in solid state systems
Jason Alicea 2012
Rep. Prog. Phys.
75
076501
View article
, New directions in the pursuit of Majorana fermions in solid state systems
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, New directions in the pursuit of Majorana fermions in solid state systems
The 1937 theoretical discovery of Majorana fermions—whose defining property is that they are their own anti-particles—has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review paper highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic ‘topological’ one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to ‘engineer’ such exotic superconductors in the laboratory by forming appropriate heterostructures with
ordinary
s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions—the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.
An updated review of the new hadron states
Hua-Xing Chen
et al
2023
Rep. Prog. Phys.
86
026201
View article
, An updated review of the new hadron states
PDF
, An updated review of the new hadron states
The past decades witnessed the golden era of hadron physics. Many excited open heavy flavor mesons and baryons have been observed since 2017. We shall provide an updated review of the recent experimental and theoretical progresses in this active field. Besides the conventional heavy hadrons, we shall also review the recently observed open heavy flavor tetraquark states
(2900) and
as well as the hidden heavy flavor multiquark states
(6900),
, and
. We will also cover the recent progresses on the glueballs and light hybrid mesons, which are the direct manifestations of the non-Abelian
SU
(3) gauge interaction of the Quantum Chromodynamics in the low-energy region.
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Reports on Progress in Physics
doi: 10.1088/issn.0034-4885
Online ISSN: 1361-6633
Print ISSN: 0034-4885