# Topological Phase Transition

**17:30**Aps.org Editors' Suggestions Classification of $(2+1)$D invertible fermionic topological phases with symmetry

Author(s): Maissam Barkeshli, Yu-An Chen, Po-Shen Hsin, and Naren ManjunathInteger quantum Hall states and their generalization to topological insulators and superconductors are paradigmatic examples of invertible fermionic topological states of matter. Here, the authors develop a comprehensive characterization and classification of invertible fermionic topological phases of matter in two spatial dimensions for general symmetry groups. The results are nonperturbative and apply to strongly interacting systems. In particular, they extend previous classification results to account for the possible chiral nature of invertible phases. [Phys. Rev. B 105, 235143] Published Wed Jun 29, 2022

**16:33**Phys.org The direct detection of a topological phase transition through a sign change in the Berry curvature dipole

The Berry curvature and Chern number are crucial topological qualities of a quantum mechanical origin characterizing the electron wave function of materials. These two elements play a very important role in determining the properties of specific materials.

**16:33**Phys.org Topological phase detected in spin chains

In some materials, there are phases between which a transition is not possible because they are protected by a certain form of symmetry. Physicists refer to these as topological phases. One example of this is the Haldane phase, named after the 2016 Nobel Prize winner in physics Duncan Haldane, which occurs in antiferromagnetic spin-1 chains. A team of researchers at MPQ has now succeeded in realizing this exotic state of matter in a simple system of ultracold atoms. Using a quantum gas microscope, they brought the atomic spins into the desired shape, measured the properties of the system and thus found the hidden internal order typical of the Haldane phase. Their results are published in Nature.

**12:43**Nanowerk.com Topological phase detected in spin chains

In a special arrangement of atomic spins, physicists have measured the properties of the so-called Haldane phase in an experiment. To do so, they used a quantum mechanical trick.

**18:55**Aps.org Editors' Suggestions Topological transitions in arrays of dipoles coupled to a cavity waveguide

Author(s): Charlie-Ray Mann and Eros MarianiThe authors propose a strategy to engineer topological transitions in arrays of dipole emitters by structuring the local photonic environment. [Phys. Rev. Research 4, 013078] Published Tue Feb 01, 2022

**19:57**Aps.org Editors' Suggestions Dissipative Topological Phase Transition with Strong System-Environment Coupling

Author(s): Wei Nie, Mauro Antezza, Yu-xi Liu, and Franco NoriTopological edge states that are modified by an electromagnetic environment are stable and robust in a 1D topological emitter array. [Phys. Rev. Lett. 127, 250402] Published Tue Dec 14, 2021

**17:57**Aps.org Editors' Suggestions Resolving the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XY model with tensor-network-based level spectroscopy

Author(s): Atsushi Ueda and Masaki OshikawaThe discovery of the Berezinskii-Kosterlitz-Thouless transition some fifty years ago was a subject of the 2016 Nobel Prize in Physics. However, quantitative study of the transition in the two-dimensional XY spin model still suffers from significant finite-size effects. The authors implement the level-spectroscopy method, originally developed for quantum systems. They utilize the modern tensor-network renormalization scheme. This allows for an extremely accurate determination of the critical point as well as for a visualization of the celebrated Kosterlitz renormalization-group flow. [Phys. Rev. B 104, 165132] Published Wed Oct 20, 2021

**10:19**Technology.org Physicists find room-temperature, 2D-to-1D topological transition

A Rice University team and its collaborators have discovered a room-temperature transition between 1D and 2D electrical conduction

**22:24**Phys.org Physicists find room-temperature, 2D-to-1D topological transition

A Rice University team and its collaborators have discovered a room-temperature transition between 1D and 2D electrical conduction states in topological crystals of bismuth and iodine.

**22:10**ScienceDaily.com Physicists find room-temperature, 2D-to-1D topological transition

Physicists have discovered a room-temperature transition between 1D and 2D electrical conduction states in the topological insulator bismuth iodide.

**17:58**Aps.org Editors' Suggestions Intrinsically gapless topological phases

Author(s): Ryan Thorngren, Ashvin Vishwanath, and Ruben VerresenMost topological properties of quantum systems, such as the braiding of anyons or protected edge modes, are easiest to define in systems with an energy gap. While some topological phenomena persist in the presence of gapless modes, this paper explores such properties that are only possible without a gap. These systems are here dubbed intrinsically gapless topological phases. The authors study a simple model – a hole-doped one-dimensional antiferromagnet – and describe a mechanism based on anomalies that applies in all dimensions. [Phys. Rev. B 104, 075132] Published Wed Aug 18, 2021

**17:59**Aps.org Editors' Suggestions Quantum critical dynamics of a Josephson junction at the topological transition

Author(s): Vladislav D. Kurilovich, Chaitanya Murthy, Pavel D. Kurilovich, Bernard van Heck, Leonid I. Glazman, and Chetan NayakSuppression of conventional superconductivity by a magnetic field closes the gap in electronic excitations and brings back the normal-state conductivity. This simple pattern does not apply to a Majorana wire tuned to the topological phase transition. While the spectral gap also vanishes at the transition in such a wire, the dissipative dynamic response may still be suppressed, showing a strong dependence on frequency and temperature. This unusual behavior is controlled by the symmetries of the wire. [Phys. Rev. B 104, 014509] Published Thu Jul 15, 2021

**20:59**Aps.org Editors' Suggestions Multiple Magnetic Topological Phases in Bulk van der Waals Crystal ${\mathrm{MnSb}}_{4}{\mathrm{Te}}_{7}$

Author(s): Shuchun Huan, Shihao Zhang, Zhicheng Jiang, Hao Su, Hongyuan Wang, Xin Zhang, Yichen Yang, Zhengtai Liu, Xia Wang, Na Yu, Zhiqiang Zou, Dawei Shen, Jianpeng Liu, and Yanfeng GuoThe magnetic van der Waals crystals ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}/{({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})}_{n}$ have drawn significant attention due to their rich topological properties and the tunability by external magnetic field. Although the ${\mathrm{MnBi}}_{2}{\mathrm{Te}}_{4}/{({\mathrm... [Phys. Rev. Lett. 126, 246601] Published Wed Jun 16, 2021

**18:01**Aps.org Editors' Suggestions First-principles design of halide-reduced electrides: Magnetism and topological phases

Author(s): Tonghua Yu, Motoaki Hirayama, José A. Flores-Livas, Marie-Therese Huebsch, Takuya Nomoto, and Ryotaro AritaThe authors demonstrate a computational scheme of systematically designing new magnetic electrides derived from known conventional solids. Intuitively, we think of localized electrons attached to ions in a conventional solid. But there is an exceptional class of solids, where some electrons localize at the empty space in between ions: electrides. These materials can be used as catalysts, or in the case they are magnetic, for spintronic devices. Only few magnetic electrides are confirmed, so the authors have implemented state-of-the-art simulations of many interacting particles to computationally predict new magnetic electrides. The key is to start from known materials and tweak them just enough by removing or substituting

**18:00**Aps.org Editors' Suggestions Network model for higher-order topological phases

Author(s): Hui Liu, Selma Franca, Ali G. Moghaddam, Fabian Hassler, and Ion Cosma FulgaThe network model is a powerful tool in the study of localization-delocalization transitions and has been used to describe a variety of topological systems without crystalline symmetry. Here, the authors show that network models can also realize topological phases protected by point-group symmetries. The latter lead to the formation of a higher-order topological phase characterized by midgap modes present at the corners of the system. [Phys. Rev. B 103, 115428] Published Wed Mar 17, 2021

**18:55**Aps.org Editors' Suggestions Floquet engineering of topological transitions in a twisted transition metal dichalcogenide homobilayer

Author(s): Michael Vogl, Martin Rodriguez-Vega, Benedetta Flebus, Allan H. MacDonald, and Gregory A. FieteMotivated by the recent experimental realization of twisted transition metal dichalcogenide bilayers, the authors study the influence of different forms of monochromatic light on such materials. They consider irradiation with circularly polarized light in free space and longitudinal light, such as the one coming from the waveguide’s TM mode. Unlike irradiated twisted bilayer graphene, they find that the longitudinal light has a more interesting effect on the material and induces topological transitions. [Phys. Rev. B 103, 014310] Published Thu Jan 28, 2021

**05:43**ScienceDaily.com Ecosystem dynamics: Topological phases in biological systems

Physicists have shown that topological phases could exist in biology, and in so doing they have identified a link between solid-state physics and biophysics.

**19:09**Nanowerk.com Topological phases in biological systems

Physicists have shown that topological phases could exist in biology, and in so doing they have identified a link between solid-state physics and biophysics.

**21:06**Phys.org Topological phases in biological systems

LMU physicists have shown that topological phases could exist in biology, and in so doing they have identified a link between solid-state physics and biophysics.

**19:04**Aps.org Editors' Suggestions Topological Phase Transition in Coupled Rock-Paper-Scissors Cycles

Author(s): Johannes Knebel, Philipp M. Geiger, and Erwin FreyChains of rock-paper-scissors games undergo topological phase transitions. [Phys. Rev. Lett. 125, 258301] Published Thu Dec 17, 2020

**21:01**Physics.Aps.org Viewpoint: Topological Phases Beyond the Hofstadter Butterfly

Author(s): Vidar GudmundssonNew theoretical work explores the phases that may arise when topology intersects with the strong magnetic field effects presented by Hofstadter’s problem. [Physics 13, 187] Published Wed Dec 02, 2020

**20:58**Aps.org Editors' Suggestions Classification of Topological Phase Transitions and van Hove Singularity Steering Mechanism in Graphene Superlattices

Author(s): Jian Wang and Luiz H. SantosNew theoretical work explores the phases that may arise when topology intersects with the strong magnetic field effects presented by Hofstadter’s problem. [Phys. Rev. Lett. 125, 236805] Published Wed Dec 02, 2020

**18:52**Aps.org Editors' Suggestions Bosonic Bott Index and Disorder-Induced Topological Transitions of Magnons

Author(s): X. S. Wang, Arne Brataas, and Roberto E. TroncosoA useful metric for characterizing the topological behavior of fermions can be extended to bosonic systems as well. [Phys. Rev. Lett. 125, 217202] Published Wed Nov 18, 2020

**18:05**Aps.org Editors' Suggestions Circular dichroism in higher-order harmonic generation: Heralding topological phases and transitions in Chern insulators

Author(s): Alexis Chacón, Dasol Kim, Wei Zhu, Shane P. Kelly, Alexandre Dauphin, Emilio Pisanty, Andrew S. Maxwell, Antonio Picón, Marcelo F. Ciappina, Dong Eon Kim, Christopher Ticknor, Avadh Saxena, and Maciej LewensteinThe future technological revolution in the production of ultrafast devices lies in the control of materials that will speed-up transistors. The recent discovery of topological states of matter promises a unique opportunity to address this challenge. However, the control and diagnostics of topological materials remain hard to achieve. Here, the authors show an alternative to distinguish a topological phase by its nonlinear-light circular dichroism (CD): the asymmetry of the material-light emissivity while the topological phase is subjected to right-circularly (RCP) and left-circularly polarized (LCP) mid-infrared lasers. This CD exhibits

**17:59**Aps.org Editors' Suggestions Topological Phase Transitions in Disordered Electric Quadrupole Insulators

Author(s): Chang-An Li, Bo Fu, Zi-Ang Hu, Jian Li, and Shun-Qing ShenThe quantization of electric quadrupole moments is protected by chiral symmetry even in the presence of strong disorder. [Phys. Rev. Lett. 125, 166801] Published Thu Oct 15, 2020

**21:00**Aps.org Editors' Suggestions Floating topological phases

Author(s): Trithep Devakul, S. L. Sondhi, S. A. Kivelson, and Erez BergWhile quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered quantum phases can be asymptotically impervious to interplane couplings. Here, the authors discuss the stability of such “floating topological phases”. Such a phase can produce a divergent ratio of the interlayer to intralayer resistivity at low temperatures. Experimental observation of such a divergence would constitute proof of the existence of a topological (e.g., spin liquid) phase. [Phys. Rev. B 102, 125136] Published Mon Sep 21, 2020

**17:14**Aps.org Editors' Suggestions Symmetry-protected topological phases beyond groups: The $q$-deformed Affleck-Kennedy-Lieb-Tasaki model

Author(s): Thomas QuellaSymmetry-protected topological phases are defined and classified in reference to symmetries that are described by groups. The author argues that there exist such phases that are not captured by this classification. To support this claim a q -deformation of the Affleck-Kennedy-Lieb-Tasaki model is discussed, which exhibits quantum group and duality-type symmetries but breaks all standard group symmetries known to protect the Haldane phase. Its nontrivial topology is linked to a twofold degeneracy in a suitably deformed notion of entanglement spectrum. [Phys. Rev. B 102, 081120(R)] Published Wed Aug 26, 2020

**17:47**Aps.org Editors' Suggestions Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders

Author(s): L. Stenzel, A. L. C. Hayward, U. Schollwöck, and F. Heidrich-MeisnerThe Harper-Hofstadter model for spinful fermions at two-thirds filling is studied using a hybrid-space DMRG approach. Hall conductivity is computed and topological phases, including the appearance of a ferromagnetic ground state between the strongly interacting 1D and 2D models, are identified. [Phys. Rev. A 102, 023315] Published Mon Aug 17, 2020

**18:35**Aps.org Editors' Suggestions The Mott transition as a topological phase transition

Author(s): Sudeshna Sen, Patrick J. Wong, and Andrew K. MitchellThe Mott transition is a classic paradigm in quantum many-body physics, in which electronic interactions can produce an insulating state. By contrast, a nontrivial band-structure topology in condensed matter systems leads to a topological insulator. Here, the authors make a connection between the seemingly disparate physics of these systems, showing that the Mott transition can be understood as a topological transition, and the Mott insulating state manifests a hitherto hidden topology in the interaction self-energy. [Phys. Rev. B 102, 081110(R)] Published Fri Aug 14, 2020

**16:45**Phys.org Study unveils the unstable nature of some topological phases

In recent years, physicists worldwide have been conducting studies exploring the characteristics and dynamics of topological phases of matter that could enable the development of quantum devices and other new technologies. Some of these phases are supported by what is known as the time-reversal symmetry (TRS) of microscopic laws of nature.

**21:17**Aps.org Editors' Suggestions Magnetic-field-induced topological phase transition in Fe-doped ${(\mathrm{Bi},\mathrm{Sb})}_{2}\mathrm{S}{\mathrm{e}}_{3}$ heterostructures

Author(s): Y. Satake, J. Shiogai, G. P. Mazur, S. Kimura, S. Awaji, K. Fujiwara, T. Nojima, K. Nomura, S. Souma, T. Sato, T. Dietl, and A. TsukazakiAlthough Bi 2 Se 3 is one of the most studied topological insulators, it has been difficult so far to observe the quantized anomalous Hall (QAH) effect due to the difficulty in the formation of a gapless chiral state in the gap formed by hybridization of surface states. The authors have developed the molecular beam epitaxial growth of paramagnetic Fe-doped Bi 2 Se

**22:40**Aps.org Editors' Suggestions Superfluid weight and Berezinskii-Kosterlitz-Thouless transition temperature of twisted bilayer graphene

Author(s): A. Julku, T. J. Peltonen, L. Liang, T. T. Heikkilä, and P. TörmäSuperconductivity in twisted bilayer graphene (TBG) has inspired fervent research to explain the origin of the phenomenon and to find whether moiré materials featuring flat bands offer a route to room-temperature superconductivity. Here, the authors show that TBG flat-band superconductivity relies on such quantum geometric properties of the band as its quantum metric and Berry curvature. The authors predict qualitative differences between different pairing potentials, which can be used to reveal the yet unknown pairing symmetry. [Phys. Rev. B 101, 060505(R)] Published Mon Feb 24, 2020

**18:44**Aps.org Editors' Suggestions Magnetoelectric control of topological phases in graphene

Author(s): Hiroyuki Takenaka, Shane Sandhoefner, Alexey A. Kovalev, and Evgeny Y. TsymbalA new paradigm for voltage controlled topological antiferromagnetic spintronics is envisioned via proximity of a magnetoelectric antiferromagnet to a two-dimensional material. Using graphene/chromia as a model system, the authors predict the emergence of unconventional anomalous Hall effects that are electrically controlled by the Néel vector as well as the appearance and transformation of different topological phases and the emergence of chiral edge states. The results advance the research field of topological phenomena and establish connection between the subfields of antiferromagnetism, magnetoelectricity, topology, spintronics, and valleytronics. [Phys. Rev. B 100, 125156] Published Wed Sep 25, 2019

**20:40**Aps.org Editors' Suggestions Symmetry fractionalization, defects, and gauging of topological phases

Author(s): Maissam Barkeshli, Parsa Bonderson, Meng Cheng, and Zhenghan WangThis paper develops a comprehensive theory of symmetry fractionalization together with the properties of symmetry defects in topologically ordered phases of matter in two spatial dimensions. To do this, the authors also introduce the full set of data, consistency conditions, and equivalences for a mathematical theory, known as a G-crossed braided tensor category, that characterizes the algebraic braiding and fusion properties of symmetry defects. This theoretical framework can completely characterize and classify symmetry-enriched topological phases of matter in the presence of arbitrarily strong interactions in quantum many-body systems in two spatial dimensions. [Phys. Rev. B 100, 115147] Published Fri Sep 20, 2019

**16:20**Phys.org Researchers discover new topological phases in a class of optical materials

Optical devices create, guide, and detect electromagnetic waves and include lasers, telescopes, and solar cells. Most of the materials used in these devices are challenging for certain applications because of a phenomenon known as optical reciprocity, an inherent symmetry which forces light to travel bidirectionally. One example of an application-based challenge is a high-powered laser, where back-scattered light caused by optical reciprocity can damage the instrument.

**12:54**Technology.org Researchers discover new topological phases in a class of optical materials

Optical devices create, guide, and detect electromagnetic waves and include lasers, telescopes, and solar cells. Most of the

**17:35**Aps.org Editors' Suggestions Higher-order Floquet topological phases with corner and bulk bound states

Author(s): Martin Rodriguez-Vega, Abhishek Kumar, and Babak SeradjehPeriodically driven systems can be quite different from those in equilibrium. For example, vortices stirred in a fluid can trap nearby objects, such as bubbles. The authors report their theoretical discovery of new phases of a two-dimensional quantum system under periodic drive, in which nonequilibrium states are stabilized at the corners as well as within stirred vortices in the bulk. These are higher-order topological phases, exhibiting the intimate connection between corner and bulk vortex structures generated by spatiotemporal modulations. [Phys. Rev. B 100, 085138] Published Mon Aug 26, 2019

**20:52**Phys.org Researchers propose new topological phase of atomic matter hosting 'photonic skyrmions'

The field of topology or the study of how surfaces behave in different dimensions has profoundly influenced the current understanding of matter. The prime example is the topological insulator, which conducts electricity only on the surface while being completely insulating inside the bulk. Topological insulators behave like a metal, i.e., silver on the surface, but inside, it would behave like glass. These properties are defined using the conductivity or flow of electrons depicting whether there is a highway or a road-block for their motion. One major driver of future applications for topological insulators is in the field of spin-electronic devices since these electrons spin in unison, all aligned with each other while flowing on the surface.

**18:29**Aps.org Editors' Suggestions Universal driving protocol for symmetry-protected Floquet topological phases

Author(s): Bastian Höckendorf, Andreas Alvermann, and Holger FehskeTopological systems can exhibit different types of bulk and boundary transport, which are regularly associated with fundamental, nonunitarily realized symmetries. Here, the authors introduce a universal driving protocol for Floquet topological phases with time-reversal, particle-hole, or chiral symmetry. By selectively enforcing or breaking the individual symmetries, the driving protocol manages to implement various topological phases in the same system. Depending on the specific combination of symmetries, these phases feature copropagating as well as symmetry-protected counterpropagating topological boundary states. [Phys. Rev. B 99, 245102] Published Mon Jun 03, 2019

**18:27**Aps.org Editors' Suggestions Crystalline topological phases as defect networks

Author(s): Dominic V. Else and Ryan ThorngrenIn order to understand topological phases of matter that exist in crystalline solids, it is necessary to take into account their spatial symmetries, which gives a notion of crystalline topological phases. Here, the authors give a general picture for understanding such phases. The idea is that ground states in such phases can be schematically represented by a crystalline network of defects imprinted on a topological substrate. Equivalence classes of such defect networks under symmetric deformations correspond precisely to crystalline topological phases. [Phys. Rev. B 99, 115116] Published Thu Mar 14, 2019

**17:06**Aps.org Editors' Suggestions Multiple topological transitions in twisted bilayer graphene near the first magic angle

Author(s): Kasra Hejazi, Chunxiao Liu, Hassan Shapourian, Xiao Chen, and Leon BalentsThe noninteracting physics of electrons in twisted bilayer graphene is considered by varying the twist angle close to the magic angle using a continuum model. The magic angle is known to occur when the dispersion at the two Dirac cones of the two bands close to neutrality become quadratic. These are topological transitions, in which three moving Dirac points pass through each of the two immobile ones as the angle varies. Indeed, the motion of Dirac points is not limited to this and their participation in several topological transitions is very rich, which is the main subject of this study. [Phys. Rev. B 99, 035111] Published Mon Jan 07, 2019

**17:05**Aps.org Editors' Suggestions Higher-order topological phases: A general principle of construction

Author(s): Dumitru Călugăru, Vladimir Juričić, and Bitan RoyThe surface states of a d -dimensional conventional or first-order topological state of matter reside on a ( d -1) dimensional boundary. However, its n th order incarnation, commonly known as a higher-order topological (HOT) phase, accommodates ( d - n ) dimensional boundary states, with corner and hinge modes standing as their representatives. Here, the authors introduce a general principle of

**18:10**Aps.org Editors' Suggestions Paradoxical extension of the edge states across the topological phase transition due to emergent approximate chiral symmetry in a quantum anomalous Hall system

Author(s): Denis R. Candido, Maxim Kharitonov, J. Carlos Egues, and Ewelina M. HankiewiczIn quantum anomalous Hall systems (Chern insulators) the topological Chern number defines, via bulk-boundary correspondence, the number of the edge-state bands that connect the valence and conduction bulk bands. This is the only characteristic of the edge states required by quantum Hall topology. Here, the authors present a paradoxical finding that, in the vicinity of a topological phase transition in a quantum anomalous Hall system, topology nearly always results in a significant extension of the edge-state structure beyond the minimal one required to satisfy the Chern numbers. [Phys. Rev. B 98, 161111(R)] Published Mon Oct 15, 2018

**18:04**Aps.org Editors' Suggestions Avoided level crossing at the magnetic field induced topological phase transition due to spin-orbital mixing

Author(s): G. Krizman, B. A. Assaf, M. Orlita, T. Phuphachong, G. Bauer, G. Springholz, G. Bastard, R. Ferreira, L. A. de Vaulchier, and Y. GuldnerA three-dimensional gapless Dirac state is expected to occur at the critical point between a topological and a trivial phase. By applying a strong magnetic field or increasing temperature, a transition from topological to trivial can be induced in the topological crystalline insulator Pb 1 − x Sn x Se ( x >0.16). Using magneto-optical spectroscopy, the authors show

**18:14**Aps.org Editors' Suggestions Topological Phases of Non-Hermitian Systems

Author(s): Zongping Gong, Yuto Ashida, Kohei Kawabata, Kazuaki Takasan, Sho Higashikawa, and Masahito UedaA new theoretical framework for topological phases provides the first systematic classification of non-Hermitian systems, those that exchange matter and energy with their environment. [Phys. Rev. X 8, 031079] Published Mon Sep 24, 2018

**19:09**Aps.org Editors' Suggestions Dyonic Lieb-Schultz-Mattis theorem and symmetry protected topological phases in decorated dimer models

Author(s): Xu Yang, Shenghan Jiang, Ashvin Vishwanath, and Ying RanLieb-Schultz-Mattis (LSM) theorem and its various generalizations provide powerful guidance towards the search for novel phases of matter. Here, the authors propose and prove a generalized LSM theorem suitable for 2+1D lattice models of interacting bosons or spins, with both magnetic flux and fractional spin in the unit cell. One outcome of this theorem is that, under certain conditions, the gapped ground states preserving all symmetries must be a nontrivial symmetry-protected topological (SPT) phase. Such symmetry-enforced SPTs display a dyonic character in that they associate charge with symmetry flux, which is demonstrated using quasiexactly solvable models constructed by decorating quantum dimer models. [Phys. Rev. B 98, 125120] Published Mon Sep 10, 2018

**23:03**Aps.org Editors' Suggestions Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries

Author(s): Ken Shiozaki, Hassan Shapourian, Kiyonori Gomi, and Shinsei RyuHere, the authors introduce a set of quantities to diagnose symmetry-protected topological phases of fermions protected by antiunitary symmetries. These quantities, which can be written as expectation values of nonlocal operators, effectively simulate the partition function on nonorientable spacetime manifolds in the operator formalism. The important observation is that the proposed quantities are complex valued for topological states, where the complex phase is the many-body topological invariant. Numerous symmetry classes and dimensionalities are studied in detail. The key ingredient of all quantities is the “fermionic partial transpose”. For example, the Z 2 topological

**18:11**Aps.org Editors' Suggestions Chiral topological phases from artificial neural networks

Author(s): Raphael Kaubruegger, Lorenzo Pastori, and Jan Carl BudichArtificial neural networks and machine learning tools have become ubiquitous far beyond the field of computer science. They already smartly assist us in our daily lives in various ways. Recently, these concepts have been adopted and applied in the realm of quantum physics, for example as a computational Ansatz for the state of a quantum many-body system. In this work, the authors harness the enormous flexibility of artificial neural networks to study exotic phases of quantum matter, known as chiral topological phases, that are particularly hard to investigate microscopically with more conventional computational methods. [Phys. Rev. B 97, 195136] Published Fri May 18, 2018

**18:06**Aps.org Editors' Suggestions Learning disordered topological phases by statistical recovery of symmetry

Author(s): Nobuyuki Yoshioka, Yutaka Akagi, and Hosho KatsuraUnderstanding the phases of a model usually requires knowledge of their characteristic features, which are nonlocal in topologically ordered systems. Here, the authors reframe the phase classification problem in disordered topological superconductors as a data-driven task, motivated by the recent surge of interest in the application of machine-learning techniques including deep learning. It is demonstrated that an artificial neural network learns to extract the essence of the clean system and successfully distinguishes phases even under disorder by statistical recovery of translational symmetry. [Phys. Rev. B 97, 205110] Published Wed May 09, 2018

**23:16**Aps.org Editors' Suggestions Temperature-Induced Topological Phase Transition in HgTe Quantum Wells

Author(s): A. M. Kadykov, S. S. Krishtopenko, B. Jouault, W. Desrat, W. Knap, S. Ruffenach, C. Consejo, J. Torres, S. V. Morozov, N. N. Mikhailov, S. A. Dvoretskii, and F. TeppeThe visualization of the Landau levels in HgTe/CdTe quantum wells at different temperatures allows the exploration of the phase diagram as a function of magnetic field and temperature. [Phys. Rev. Lett. 120, 086401] Published Thu Feb 22, 2018

**23:14**Aps.org Editors' Suggestions Fracton Topological Phases from Strongly Coupled Spin Chains

Author(s): Gábor B. Halász, Timothy H. Hsieh, and Leon BalentsA realistic model of fracton topological phases using only two spins brings their experimental realization a step closer. [Phys. Rev. Lett. 119, 257202] Published Wed Dec 20, 2017

**19:21**Aps.org Editors' Suggestions Building crystalline topological phases from lower-dimensional states

Author(s): Sheng-Jie Huang, Hao Song, Yi-Ping Huang, and Michael HermeleTopological phases protected by the geometrical symmetries of crystal lattices turn out to be surprisingly simple. They can be built from simpler lower-dimensional states, arranged in a crystalline pattern. [Phys. Rev. B 96, 205106] Published Mon Nov 06, 2017

**16:50**ScienceDaily.com Missing link between new topological phases of matter discovered

Physicists have investigated a class of materials that exhibit characteristics of topological insulators. During these studies they discovered a transition between two different topological phases, one of which is ferroelectric.

**13:03**Phys.org Missing link between new topological phases of matter discovered

Physicists at BESSY II have investigated a class of materials that exhibit characteristics of topological insulators. During these studies, they discovered a transition between two different topological phases, one of which is ferroelectric, meaning a phase in the material that exhibits spontaneous electric polarisation and can be reversed by an external electric field. This could also lead to new applications such as switching between differing conductivities.

**20:08**Aps.org Editors' Suggestions One-dimensional symmetry protected topological phases and their transitions

Author(s): Ruben Verresen, Roderich Moessner, and Frank PollmannThe authors present a unified perspective on a large class of one-dimensional symmetry-protected topological phases. Characterizing critical points between such phases leads to a conjecture of a topological lower bound on the central charge in terms of the phase-specific edge mode dimension. [Phys. Rev. B 96, 165124] Published Thu Oct 12, 2017

**00:07**Aps.org Editors' Suggestions Exactly solvable models for symmetry-enriched topological phases

Author(s): Meng Cheng, Zheng-Cheng Gu, Shenghan Jiang, and Yang QiSymmetry-enriched topological phases (SET) exhibit both long-range entanglement and intricate interplay with global symmetries, such as anyon permutation symmetry or fractionalization of quantum numbers, going beyond the Landau paradigm of symmetry breaking. Here, the authors study two-dimensional SET phases based on the novel concept of symmetric local unitary transformations. Using the fixed-point structure of wave functions, they construct systematically exactly solvable models that can describe generic nonchiral SET phases. The technique applies to on-site as well as spatial symmetries and, furthermore, to anomalous symmetries that can only be realized on the surface of three-dimensional symmetry-protected phases. [Phys. Rev. B 96, 115107] Published Wed Sep 06, 2017

**19:28**Aps.org Editors' Suggestions Cheshire charge in (3+1)-dimensional topological phases

Author(s): Dominic V. Else and Chetan NayakThe authors examine the phenomenon of “Cheshire charge” in topological phases of matter in three spatial dimensions. A looplike excitation is said to carry Cheshire charge if the charge is not locally detectable, that is, it can only be observed by a nonlocal process such as shrinking the loop to a point. The authors show that “Cheshire charge” is a generic feature of three-dimensional topological phases. They relate it to other features of these phases, such as three-loop braiding, as well as to higher-category theory that is hypothesized to be the general mathematical framework describing three-dimensional topological phases. [Phys. Rev. B 96, 045136] Published Tue Jul 25, 2017

**18:38**Aps.org Editors' Suggestions Floquet topological phases protected by time glide symmetry

Author(s): Takahiro Morimoto, Hoi Chun Po, and Ashvin VishwanathNonequilibrium systems under periodic driving realize novel topological phases that cannot be achieved in equilibrium systems. One unique feature of periodically driven systems is that they can host a purely dynamical symmetry that involves time translation. This work explores a new class of Floquet topological phases protected by one realization of such dynamical symmetry, i.e., “time glide symmetry”, which is defined by a combination of reflection and time translation. Lattice models with time glide symmetric driving that are introduced show stable gapless surface states along with nontrivial topological numbers defined with time glide symmetry. In addition, a general classification theory of time glide symmetric topological phases is obtained by using a Clifford algebra

**21:36**Aps.org Editors' Suggestions Many-body topological invariants in fermionic symmetry-protected topological phases: Cases of point group symmetries

Author(s): Ken Shiozaki, Hassan Shapourian, and Shinsei RyuFinding suitable nonlocal order parameters that distinguish various symmetry-protected topological (SPT) phases is an important subject in view of experimental and numerical detection of SPT phases. By “simulating” the generating manifold of cobordism group in the operator formalism, the authors here propose nonlocal operations as diagnoses for SPT phases protected by point group symmetries. The nonlocal operations involve “partial point group transformations”, which are obtained by point group transformations restricted to a spatial subregion on a given ground-state wave function. Through analytical and numerical calculations, the authors show that the complex U

**19:09**Physics.Aps.org Viewpoint: Neural Networks Identify Topological Phases

Author(s): Juan CarrasquillaA new machine-learning algorithm based on a neural network can tell a topological phase of matter from a conventional one. [Physics 10, 56] Published Mon May 22, 2017

**19:06**Aps.org Editors' Suggestions Interacting fermionic symmetry-protected topological phases in two dimensions

Author(s): Chenjie Wang, Chien-Hung Lin, and Zheng-Cheng GuSymmetry-protected topological (SPT) phases (e.g., the well known topological insulators) are a class of energetically gapped condensed matter systems that exhibit interesting topological properties only in the presence of certain global symmetries. While a great understanding of noninteracting fermionic SPT phases has been achieved recently, interacting SPT phases, in particular those that exist only in strongly interacting systems, are much less understood in general. Here, the authors study strongly interacting fermionic SPT phases in two spatial dimensions with finite Abelian unitary symmetries and provide a potentially complete classification of them. [Phys. Rev. B 95, 195147] Published Mon May 22, 2017

**18:01**Aps.org Editors' Suggestions Floquet topological phases with symmetry in all dimensions

Author(s): Rahul Roy and Fenner HarperPeriodically driven Floquet systems can host dynamical phases, including a range of exotic topological phases that have no static analogs. This work presents a homotopy approach to the study of driven systems, which treats unitary evolutions as paths in the space of unitary operators. By considering loop evolutions in this space, the authors obtain a topological classification, free of uncertainties and ambiguities about the long-time robustness of of behavior in specific physical models. Two classes of Floquet symmetry-protected topological phase are identified, characterized by unitary evolutions that act trivially in the bulk but nontrivially at the boundary of an open system. The first class is captured by an explicit group cohomology construction; it has the remarkable property of converting a trivial

**21:15**Aps.org Editors' Suggestions Anyon condensation and a generic tensor-network construction for symmetry-protected topological phases

Author(s): Shenghan Jiang and Ying RanBosonic symmetry protected topological (SPT) phases are bosonic analogs of free-fermion topological insulators and superconductors, but require interactions to be realized. Previously, a wide range of bosonic SPT phases protected by on-site symmetries has been systematically investigated, which are found to be related to group cohomology theory. However, a systematic understanding of SPT phases protected by spatial symmetries is still lacking. Here, the authors present systematic constructions of tensor-network wave functions for bosonic SPT phases protected by a general symmetry group SG involving both on-site and spatial symmetries. They find, in spatial dimension d = 1

**17:19**Physics.Aps.org Focus: Nobel Prize—Topological Phases of Matter

Author(s): Michael SchirberThe 2016 Nobel Prize in Physics was awarded to theoretical physicists whose work established the role of topology in understanding exotic forms of matter. [Physics 9, 116] Published Fri Oct 07, 2016

**13:13**Washington Post Nobel jury praises physics winners for ‘discoveries of topological phase transitions and topological phases of matter’

Nobel jury praises physics winners for ‘discoveries of topological phase transitions and topological phases of matter’

**22:59**Aps.org Editors' Suggestions Anomalous Topological Phases and Unpaired Dirac Cones in Photonic Floquet Topological Insulators

Author(s): Daniel Leykam, M. C. Rechtsman, and Y. D. ChongThe design for a photonic lattice that can realize a previously unobserved anomalous Floquet phase is proposed. [Phys. Rev. Lett. 117, 013902] Published Wed Jun 29, 2016

**16:24**Aps.org Editors' Suggestions Phase structure of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases

Author(s): C. W. von Keyserlingk and S. L. SondhiPhases of matter are traditionally seen as families of static systems exhibiting the same long-distance and low-energy correlations. In this work, the authors propose and classify a new family of phases of matter. They are novel insofar as they are intrinsically driven and out of equilibrium — they can only be realized in systems with time-dependent Hamiltonians. The phases we consider arise in 1D periodically driven systems, in the presence of strong disorder and interactions, and are similar to but qualitatively distinct from the symmetry-protected topological phases now well known in the equilibrium setting. In a companion paper, the authors examine similar intrinsically driven families of states with long-range order, and an order parameter that oscillates at a frequency that is robustly an integer

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