Pub Date : 2024-06-27DOI: 10.1103/physrevx.14.021053
Weicheng Ye, Liujun Zou
We present a systematic framework to classify symmetry-enriched topological quantum spin liquids in two spatial dimensions. This framework can deal with all topological quantum spin liquids, which may be either Abelian or non-Abelian and chiral or nonchiral. It can systematically treat a general symmetry, which may include both lattice symmetry and internal symmetry, may contain antiunitary symmetry, and may permute anyons. The framework applies to all types of lattices and can systematically distinguish different lattice systems with the same symmetry group using their quantum anomalies, which are sometimes known as Lieb-Schultz-Mattis anomalies. We apply this framework to classify <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mn>2</mn><mi>N</mi></mrow></msub></math> chiral states and non-Abelian <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mrow><mi>Ising</mi></mrow><mrow><mo stretchy="false">(</mo><mi>ν</mi><mo stretchy="false">)</mo></mrow></msup></mrow></math> states enriched by a <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mn>6</mn><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> or <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mn>4</mn><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> symmetry and <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="double-struck">Z</mi><mi>N</mi></msub></math> topological orders and <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mn>2</mn><mi>N</mi></mrow></msub><mo>×</mo><mi mathvariant="normal">U</mi><mo stretchy="false">(</mo><mn>1</mn><msub><mo stretchy="false">)</mo><mrow><mo>−</mo><mn>2</mn><mi>N</mi></mrow></msub></math> topological orders enriched by a <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mn>6</mn><mi>m</mi><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>×</mo><msubsup><mi mathvariant="double-struck">Z</mi><mn>2</mn><mi>T</mi></msubsup></math>, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mn>4</mn><mi>m</mi><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>×</mo><msubsup><mi mathvariant="double-struck">Z</mi><mn>2</mn><mi>T</mi></msubsup></math>, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mn>6</mn><mi>m</mi><mo>×</mo><msubsup><mi mathvariant="double-struck">Z</mi><mn>2</mn><mi>T</mi></msubsup></math>, or <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mn>4</mn><mi>m</mi>
{"title":"Classification of Symmetry-Enriched Topological Quantum Spin Liquids","authors":"Weicheng Ye, Liujun Zou","doi":"10.1103/physrevx.14.021053","DOIUrl":"https://doi.org/10.1103/physrevx.14.021053","url":null,"abstract":"We present a systematic framework to classify symmetry-enriched topological quantum spin liquids in two spatial dimensions. This framework can deal with all topological quantum spin liquids, which may be either Abelian or non-Abelian and chiral or nonchiral. It can systematically treat a general symmetry, which may include both lattice symmetry and internal symmetry, may contain antiunitary symmetry, and may permute anyons. The framework applies to all types of lattices and can systematically distinguish different lattice systems with the same symmetry group using their quantum anomalies, which are sometimes known as Lieb-Schultz-Mattis anomalies. We apply this framework to classify <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"normal\">U</mi><mo stretchy=\"false\">(</mo><mn>1</mn><msub><mo stretchy=\"false\">)</mo><mrow><mn>2</mn><mi>N</mi></mrow></msub></math> chiral states and non-Abelian <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msup><mrow><mi>Ising</mi></mrow><mrow><mo stretchy=\"false\">(</mo><mi>ν</mi><mo stretchy=\"false\">)</mo></mrow></msup></mrow></math> states enriched by a <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>6</mn><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy=\"false\">(</mo><mn>3</mn><mo stretchy=\"false\">)</mo></math> or <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>4</mn><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy=\"false\">(</mo><mn>3</mn><mo stretchy=\"false\">)</mo></math> symmetry and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi mathvariant=\"double-struck\">Z</mi><mi>N</mi></msub></math> topological orders and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi mathvariant=\"normal\">U</mi><mo stretchy=\"false\">(</mo><mn>1</mn><msub><mo stretchy=\"false\">)</mo><mrow><mn>2</mn><mi>N</mi></mrow></msub><mo>×</mo><mi mathvariant=\"normal\">U</mi><mo stretchy=\"false\">(</mo><mn>1</mn><msub><mo stretchy=\"false\">)</mo><mrow><mo>−</mo><mn>2</mn><mi>N</mi></mrow></msub></math> topological orders enriched by a <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>6</mn><mi>m</mi><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy=\"false\">(</mo><mn>3</mn><mo stretchy=\"false\">)</mo><mo>×</mo><msubsup><mi mathvariant=\"double-struck\">Z</mi><mn>2</mn><mi>T</mi></msubsup></math>, <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>4</mn><mi>m</mi><mo>×</mo><mrow><mi>SO</mi></mrow><mo stretchy=\"false\">(</mo><mn>3</mn><mo stretchy=\"false\">)</mo><mo>×</mo><msubsup><mi mathvariant=\"double-struck\">Z</mi><mn>2</mn><mi>T</mi></msubsup></math>, <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>6</mn><mi>m</mi><mo>×</mo><msubsup><mi mathvariant=\"double-struck\">Z</mi><mn>2</mn><mi>T</mi></msubsup></math>, or <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi><mn>4</mn><mi>m</mi>","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"80 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141462640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-26DOI: 10.1103/physrevx.14.021052
Carl Philipp Zelle, Romain Daviet, Achim Rosch, Sebastian Diehl
In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand, the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions they universally either destroy a preexisting static order or give rise to a fluctuation-induced first-order transition. This is demonstrated within a full resummation of loop corrections via Dyson-Schwinger equations for , and a generalization for arbitrary , which can be solved in the long wavelength limit. We show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium.
{"title":"Universal Phenomenology at Critical Exceptional Points of Nonequilibrium O(N) Models","authors":"Carl Philipp Zelle, Romain Daviet, Achim Rosch, Sebastian Diehl","doi":"10.1103/physrevx.14.021052","DOIUrl":"https://doi.org/10.1103/physrevx.14.021052","url":null,"abstract":"In thermal equilibrium the dynamics of phase transitions is largely controlled by fluctuation-dissipation relations: On the one hand, friction suppresses fluctuations, while on the other hand, the thermal noise is proportional to friction constants. Out of equilibrium, this balance dissolves and one can have situations where friction vanishes due to antidamping in the presence of a finite noise level. We study a wide class of <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi mathvariant=\"normal\">O</mi><mo stretchy=\"false\">(</mo><mi>N</mi><mo stretchy=\"false\">)</mo></mrow></math> field theories where this situation is realized at a phase transition, which we identify as a critical exceptional point. In the ordered phase, antidamping induces a continuous limit cycle rotation of the order parameter with an enhanced number of <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mn>2</mn><mi>N</mi><mo>−</mo><mn>3</mn></math> Goldstone modes. Close to the critical exceptional point, however, fluctuations diverge so strongly due to the suppression of friction that in dimensions <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>d</mi><mo><</mo><mn>4</mn></math> they universally either destroy a preexisting static order or give rise to a fluctuation-induced first-order transition. This is demonstrated within a full resummation of loop corrections via Dyson-Schwinger equations for <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi><mo>=</mo><mn>2</mn></math>, and a generalization for arbitrary <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>N</mi></math>, which can be solved in the long wavelength limit. We show that in order to realize this physics it is not necessary to drive a system far out of equilibrium: Using the peculiar protection of Goldstone modes, the transition from an <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>x</mi><mi>y</mi></math> magnet to a ferrimagnet is governed by an exceptional critical point once weakly perturbed away from thermal equilibrium.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"56 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141453027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-21DOI: 10.1103/physrevx.14.021050
Sebastiano Bontorin, Giulia Cencetti, Riccardo Gallotti, Bruno Lepri, Manlio De Domenico
Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral branches, which can appear both in natural and manmade systems, such as subway and railway networks. In this study, we investigate the conditions for the emergence of these nontrivial topological structures in the context of human transportation in cities. We propose a simple model for spatial networks generation, where a network lattice acts as a planar substrate and edge speeds define an effective temporal distance which we aim to optimize and quantifies the efficiency in exploring the urban space. Complex network topologies can be recovered from the optimization of edges’ speeds and we study how the interplay between a flow probability between two nodes in space and the associated travel cost influences the resulting optimal network. In the perspective of urban transportation we simulate these flows by means of human mobility models to obtain origin-destination matrices. We find that when using simple lattices, the obtained optimal topologies transition from treelike structures to more regular networks, depending on the spatial range of flows. Remarkably, we find that branches paired to large loops structures appear as optimal structures when the network is optimized for an interplay between heterogeneous mobility patterns of small range travels and longer-range ones typical of commuting. Moreover, when congestion dynamics in traffic routing is considered, we study the emergence of additional edges from the tree structure to mitigate temporal delays. Finally, we show that our framework is able to recover the statistical spatial properties of the Greater London area subway network.
{"title":"Emergence of Complex Network Topologies from Flow-Weighted Optimization of Network Efficiency","authors":"Sebastiano Bontorin, Giulia Cencetti, Riccardo Gallotti, Bruno Lepri, Manlio De Domenico","doi":"10.1103/physrevx.14.021050","DOIUrl":"https://doi.org/10.1103/physrevx.14.021050","url":null,"abstract":"Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral branches, which can appear both in natural and manmade systems, such as subway and railway networks. In this study, we investigate the conditions for the emergence of these nontrivial topological structures in the context of human transportation in cities. We propose a simple model for spatial networks generation, where a network lattice acts as a planar substrate and edge speeds define an effective temporal distance which we aim to optimize and quantifies the efficiency in exploring the urban space. Complex network topologies can be recovered from the optimization of edges’ speeds and we study how the interplay between a flow probability between two nodes in space and the associated travel cost influences the resulting optimal network. In the perspective of urban transportation we simulate these flows by means of human mobility models to obtain origin-destination matrices. We find that when using simple lattices, the obtained optimal topologies transition from treelike structures to more regular networks, depending on the spatial range of flows. Remarkably, we find that branches paired to large loops structures appear as optimal structures when the network is optimized for an interplay between heterogeneous mobility patterns of small range travels and longer-range ones typical of commuting. Moreover, when congestion dynamics in traffic routing is considered, we study the emergence of additional edges from the tree structure to mitigate temporal delays. Finally, we show that our framework is able to recover the statistical spatial properties of the Greater London area subway network.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"2014 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141435802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-21DOI: 10.1103/physrevx.14.021051
Yanyu Jia, Guo Yu, Tiancheng Song, Fang Yuan, Ayelet J. Uzan, Yue Tang, Pengjie Wang, Ratnadwip Singha, Michael Onyszczak, Zhaoyi Joy Zheng, Kenji Watanabe, Takashi Taniguchi, Leslie M. Schoop, Sanfeng Wu
Two-dimensional (2D) transition metal dichalcogenides (TMDs) is a versatile class of quantum materials of interest to various fields including, e.g., nanoelectronics, optical devices, and topological and correlated quantum matter. Tailoring the electronic properties of TMDs is essential to their applications in many directions. Here, we report that a highly controllable and uniform on-chip 2D metallization process converts a class of atomically thin TMDs into robust superconductors, a property belonging to none of the starting materials. As examples, we demonstrate the introduction of superconductivity into a class of 2D air-sensitive topological TMDs, including monolayers of , , and , as well as their natural and twisted bilayers, metallized with an ultrathin layer of palladium. This class of TMDs is known to exhibit intriguing topological phases ranging from topological insulator, Weyl semimetal to fractional Chern insulator. The unique, high-quality two-dimensional metallization process is based on our recent findings of the long-distance, non-Fickian in-plane mass transport and chemistry in 2D that occur at relatively low temperatures and in devices fully encapsulated with inert insulating layers. Highly compatible with existing nanofabrication techniques for van der Waals stacks, our results offer a route to designing and engineering superconductivity and topological phases in a class of correlated 2D materials.
{"title":"Superconductivity from On-Chip Metallization on 2D Topological Chalcogenides","authors":"Yanyu Jia, Guo Yu, Tiancheng Song, Fang Yuan, Ayelet J. Uzan, Yue Tang, Pengjie Wang, Ratnadwip Singha, Michael Onyszczak, Zhaoyi Joy Zheng, Kenji Watanabe, Takashi Taniguchi, Leslie M. Schoop, Sanfeng Wu","doi":"10.1103/physrevx.14.021051","DOIUrl":"https://doi.org/10.1103/physrevx.14.021051","url":null,"abstract":"Two-dimensional (2D) transition metal dichalcogenides (TMDs) is a versatile class of quantum materials of interest to various fields including, e.g., nanoelectronics, optical devices, and topological and correlated quantum matter. Tailoring the electronic properties of TMDs is essential to their applications in many directions. Here, we report that a highly controllable and uniform on-chip 2D metallization process converts a class of atomically thin TMDs into robust superconductors, a property belonging to none of the starting materials. As examples, we demonstrate the introduction of superconductivity into a class of 2D air-sensitive topological TMDs, including monolayers of <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mrow><mi mathvariant=\"normal\">T</mi></mrow><mrow><mi mathvariant=\"normal\">d</mi></mrow></msub><mtext>−</mtext><msub><mrow><mi>WTe</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>, <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>1</mn><msup><mrow><mi mathvariant=\"normal\">T</mi></mrow><mrow><mo>′</mo></mrow></msup><mtext>−</mtext><msub><mrow><mi>MoTe</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>, and <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>2</mn><mi mathvariant=\"normal\">H</mi><mtext>−</mtext><msub><mrow><mi>MoTe</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math>, as well as their natural and twisted bilayers, metallized with an ultrathin layer of palladium. This class of TMDs is known to exhibit intriguing topological phases ranging from topological insulator, Weyl semimetal to fractional Chern insulator. The unique, high-quality two-dimensional metallization process is based on our recent findings of the long-distance, non-Fickian in-plane mass transport and chemistry in 2D that occur at relatively low temperatures and in devices fully encapsulated with inert insulating layers. Highly compatible with existing nanofabrication techniques for van der Waals stacks, our results offer a route to designing and engineering superconductivity and topological phases in a class of correlated 2D materials.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"37 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141435809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-20DOI: 10.1103/physrevx.14.021049
Konrad Viebahn, Anne-Sophie Walter, Eric Bertok, Zijie Zhu, Marius Gächter, Armando A. Aligia, Fabian Heidrich-Meisner, Tilman Esslinger
A topological “Thouless” pump represents the quantized motion of particles in response to a slow, cyclic modulation of external control parameters. The Thouless pump, like the quantum Hall effect, is of fundamental interest in physics, because it links physically measurable quantities, such as particle currents, to geometric properties of the experimental system, which can be robust against perturbations and, thus, technologically useful. So far, experiments probing the interplay between topology and interparticle interactions have remained relatively scarce. Here, we observe a Thouless-type charge pump in which the particle current and its directionality inherently rely on the presence of strong interactions. Experimentally, we utilize a two-component Fermi gas in a dynamical superlattice which does not exhibit a sliding motion and remains trivial in the single-particle regime. However, when tuning interparticle interactions from zero to positive values, the system undergoes a transition from being stationary to drifting in one direction, consistent with quantized pumping in the first cycle. Remarkably, the topology of the interacting pump trajectory cannot be adiabatically connected to a noninteracting limit, highlighted by the fact that only one atom is transferred per cycle. Our experiments suggest that Thouless charge pumps are promising platforms to gain insights into interaction-driven topological transitions and topological quantum matter.
{"title":"Interactions Enable Thouless Pumping in a Nonsliding Lattice","authors":"Konrad Viebahn, Anne-Sophie Walter, Eric Bertok, Zijie Zhu, Marius Gächter, Armando A. Aligia, Fabian Heidrich-Meisner, Tilman Esslinger","doi":"10.1103/physrevx.14.021049","DOIUrl":"https://doi.org/10.1103/physrevx.14.021049","url":null,"abstract":"A topological “Thouless” pump represents the quantized motion of particles in response to a slow, cyclic modulation of external control parameters. The Thouless pump, like the quantum Hall effect, is of fundamental interest in physics, because it links physically measurable quantities, such as particle currents, to geometric properties of the experimental system, which can be robust against perturbations and, thus, technologically useful. So far, experiments probing the interplay between topology and interparticle interactions have remained relatively scarce. Here, we observe a Thouless-type charge pump in which the particle current and its directionality inherently rely on the presence of strong interactions. Experimentally, we utilize a two-component Fermi gas in a dynamical superlattice which does not exhibit a sliding motion and remains trivial in the single-particle regime. However, when tuning interparticle interactions from zero to positive values, the system undergoes a transition from being stationary to drifting in one direction, consistent with quantized pumping in the first cycle. Remarkably, the topology of the interacting pump trajectory cannot be adiabatically connected to a noninteracting limit, highlighted by the fact that only one atom is transferred per cycle. Our experiments suggest that Thouless charge pumps are promising platforms to gain insights into interaction-driven topological transitions and topological quantum matter.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"80 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141435798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quantum many-body systems, particularly, the ones with large near-<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>F</mi></mrow></msub></mrow></math> density states, are well known for exhibiting rich phase diagrams as a result of enhanced electron correlations. The recently discovered locally noncentrosymmetric heavy fermion superconductor <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>CeRh</mi><mn>2</mn></msub><msub><mi>As</mi><mn>2</mn></msub></mrow></math> has stimulated extensive attention due to its unusual <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>H</mi><mtext>−</mtext><mi>T</mi></mrow></math> phase diagram consisting of two-phase superconductivity, antiferromagnetic order, and possible quadrupole-density wave orders. However, the critical near-<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>F</mi></mrow></msub></mrow></math> electronic structure remains experimentally elusive. Here, we provide this key information by combining soft-x-ray and vacuum ultraviolet (VUV) angle-resolved-photoemission-spectroscopy measurements and atom-resolved density-functional-theory <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo stretchy="false">(</mo><mi>DFT</mi><mo stretchy="false">)</mo><mo>+</mo><mi>U</mi></mrow></math> calculations. With bulk-sensitive soft x ray, we reveal quasi-2D hole and electron pockets near the <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>F</mi></mrow></msub></mrow></math>. On the other hand, under VUV light, the Ce flat bands are resolved with the <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>c</mi><mtext>−</mtext><mi>f</mi></mrow></math> hybridization persisting up to well above the Kondo temperature. Most importantly, we observe a symmetry-protected fourfold Van Hove singularity (VHS) coexisting with the <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Ce</mi><mtext> </mtext><mtext> </mtext><mtext> </mtext><mn>4</mn><msubsup><mrow><mi>f</mi></mrow><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow><mrow><mn>1</mn></mrow></msubsup></mrow></math> flat bands at the <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi></math> point, which, to the best of our knowledge, has never been reported before. Such a rare coexistence is expected to lead to a large density of states at the zone edge, a large upper critical field of the odd-parity phase, as well as spin and/or charge instabilities with a vector of (<math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>, <math display="inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>, 0). Uniquely, it will also result in a new
众所周知，量子多体系统，尤其是具有大的近 EF 密度态的量子多体系统，由于电子相关性的增强而表现出丰富的相图。最近发现的局部非中心对称重费米子超导体 CeRh2As2 因其不同寻常的 H-T 相图（包括两相超导性、反铁磁秩序和可能的四极密度波秩序）而引起了广泛关注。然而，临界近 EF 电子结构在实验中仍然难以捉摸。在这里，我们将软 X 射线和真空紫外线（VUV）角度分辨光电发射光谱测量与原子分辨密度函数理论（DFT）+U 计算相结合，提供了这一关键信息。通过体敏软 X 射线，我们揭示了 EF 附近的准二维空穴和电子袋。另一方面，在紫外光下，Ce 平带被解析，c-f 杂化持续到远远高于 Kondo 温度。最重要的是，我们在 X 点观察到一个对称保护的四倍范霍夫奇点（VHS）与铈 4f5/21 平面带共存，据我们所知，这是以前从未报道过的。这种罕见的共存现象预计会导致区域边缘的大状态密度、奇偶相的大上临界场以及矢量为（1/2, 1/2, 0）的自旋和/或电荷不稳定性。独特的是，它还会导致一种新型的 f-VHS 杂化，改变 VHS 和平面带的有序和精细电子结构。我们的发现不仅为了解 CeRh2As2 中多相的性质提供了重要见解，而且为探索具有 f-VHS 杂化的多体系统的新特性开辟了新的前景。
{"title":"Coexistence of near-EF Flat Band and Van Hove Singularity in a Two-Phase Superconductor","authors":"Xuezhi Chen, Le Wang, Jun Ishizuka, Renjie Zhang, Kosuke Nogaki, Yiwei Cheng, Fazhi Yang, Zhenhua Chen, Fangyuan Zhu, Zhengtai Liu, Jiawei Mei, Youichi Yanase, Baiqing Lv, Yaobo Huang","doi":"10.1103/physrevx.14.021048","DOIUrl":"https://doi.org/10.1103/physrevx.14.021048","url":null,"abstract":"Quantum many-body systems, particularly, the ones with large near-<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>F</mi></mrow></msub></mrow></math> density states, are well known for exhibiting rich phase diagrams as a result of enhanced electron correlations. The recently discovered locally noncentrosymmetric heavy fermion superconductor <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mi>CeRh</mi><mn>2</mn></msub><msub><mi>As</mi><mn>2</mn></msub></mrow></math> has stimulated extensive attention due to its unusual <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>H</mi><mtext>−</mtext><mi>T</mi></mrow></math> phase diagram consisting of two-phase superconductivity, antiferromagnetic order, and possible quadrupole-density wave orders. However, the critical near-<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>F</mi></mrow></msub></mrow></math> electronic structure remains experimentally elusive. Here, we provide this key information by combining soft-x-ray and vacuum ultraviolet (VUV) angle-resolved-photoemission-spectroscopy measurements and atom-resolved density-functional-theory <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mo stretchy=\"false\">(</mo><mi>DFT</mi><mo stretchy=\"false\">)</mo><mo>+</mo><mi>U</mi></mrow></math> calculations. With bulk-sensitive soft x ray, we reveal quasi-2D hole and electron pockets near the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>F</mi></mrow></msub></mrow></math>. On the other hand, under VUV light, the Ce flat bands are resolved with the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>c</mi><mtext>−</mtext><mi>f</mi></mrow></math> hybridization persisting up to well above the Kondo temperature. Most importantly, we observe a symmetry-protected fourfold Van Hove singularity (VHS) coexisting with the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>Ce</mi><mtext> </mtext><mtext> </mtext><mtext> </mtext><mn>4</mn><msubsup><mrow><mi>f</mi></mrow><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow><mrow><mn>1</mn></mrow></msubsup></mrow></math> flat bands at the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>X</mi></math> point, which, to the best of our knowledge, has never been reported before. Such a rare coexistence is expected to lead to a large density of states at the zone edge, a large upper critical field of the odd-parity phase, as well as spin and/or charge instabilities with a vector of (<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>, <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math>, 0). Uniquely, it will also result in a new ","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"14 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141435772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-18DOI: 10.1103/physrevx.14.021047
Yuelin Shao, Xi Dai
We propose a new electrical breakdown mechanism for exciton insulators in the BCS limit, which differs fundamentally from the Zener breakdown mechanism observed in traditional band insulators. Our new mechanism results from the instability of the many-body ground state for exciton condensation, caused by the strong competition between the polarization and condensation energies in the presence of an electric field. We refer to this mechanism as “many-body breakdown.” To investigate this new mechanism, we propose a BCS-type trial wave function under finite electric fields and use it to study the many-body breakdown numerically. Our results reveal two different types of electric breakdown behavior. If the system size is larger than a critical value, the Zener tunneling process is first turned on when an electrical field is applied, but the excitonic gap remains until the field strength reaches the critical value of the many-body breakdown, after which the excitonic gap disappears and the system becomes a highly conductive metallic state. However, if the system size is much smaller than the critical value, the intermediate tunneling phase disappears since the many-body breakdown happens before the onset of Zener tunneling. The sudden disappearance of the local gap leads to an “off-on” feature in the current-voltage () curve, providing a straightforward way to distinguish excitonic insulators from normal insulators.
{"title":"Electrical Breakdown of Excitonic Insulators","authors":"Yuelin Shao, Xi Dai","doi":"10.1103/physrevx.14.021047","DOIUrl":"https://doi.org/10.1103/physrevx.14.021047","url":null,"abstract":"We propose a new electrical breakdown mechanism for exciton insulators in the BCS limit, which differs fundamentally from the Zener breakdown mechanism observed in traditional band insulators. Our new mechanism results from the instability of the many-body ground state for exciton condensation, caused by the strong competition between the polarization and condensation energies in the presence of an electric field. We refer to this mechanism as “many-body breakdown.” To investigate this new mechanism, we propose a BCS-type trial wave function under finite electric fields and use it to study the many-body breakdown numerically. Our results reveal two different types of electric breakdown behavior. If the system size is larger than a critical value, the Zener tunneling process is first turned on when an electrical field is applied, but the excitonic gap remains until the field strength reaches the critical value of the many-body breakdown, after which the excitonic gap disappears and the system becomes a highly conductive metallic state. However, if the system size is much smaller than the critical value, the intermediate tunneling phase disappears since the many-body breakdown happens before the onset of Zener tunneling. The sudden disappearance of the local gap leads to an “off-on” feature in the current-voltage (<math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>I</mi><mtext>−</mtext><mi>V</mi></mrow></math>) curve, providing a straightforward way to distinguish excitonic insulators from normal insulators.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"32 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141425174","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-17DOI: 10.1103/physrevx.14.021046
Soumya Sankar, Ruizi Liu, Cheng-Ping Zhang, Qi-Fang Li, Caiyun Chen, Xue-Jian Gao, Jiangchang Zheng, Yi-Hsin Lin, Kun Qian, Ruo-Peng Yu, Xu Zhang, Zi Yang Meng, Kam Tuen Law, Qiming Shao, Berthold Jäck
Berry curvature multipoles appearing in topological quantum materials have recently attracted much attention. Their presence can manifest in novel phenomena, such as nonlinear anomalous Hall effects (NLAHE). The notion of Berry curvature multipoles extends our understanding of Berry curvature effects on the material properties. Hence, research on this subject is of fundamental importance and may also enable future applications in energy harvesting and high-frequency technology. It was shown that a Berry curvature dipole can give rise to a second-order NLAHE in materials of low crystalline symmetry. Here, we demonstrate a fundamentally new mechanism for Berry curvature multipoles in antiferromagnets that are supported by the underlying magnetic symmetries. Carrying out electric transport measurements on the kagome antiferromagnet FeSn, we observe a third-order NLAHE, which appears as a transverse voltage response at the third harmonic frequency when a longitudinal ac drive is applied. Interestingly, this NLAHE is strongest at and above room temperature. We combine these measurements with a scaling law analysis, a symmetry analysis, model calculations, first-principle calculations, and magnetic Monte Carlo simulations to show that the observed NLAHE is induced by a Berry curvature quadrupole appearing in the spin-canted state of FeSn. At a practical level, our study establishes NLAHE as a sensitive probe of antiferromagnetic phase transitions in other materials—such as moiré superlattices, two-dimensional van der Waal magnets, and quantum spin liquid candidates, which remain poorly understood to date. More broadly, Berry curvature multipole effects are predicted to exist for 90 magnetic point groups. Hence, our work opens a new research area to study a variety of topological magnetic materials through nonlinear measurement protocols.
{"title":"Experimental Evidence for a Berry Curvature Quadrupole in an Antiferromagnet","authors":"Soumya Sankar, Ruizi Liu, Cheng-Ping Zhang, Qi-Fang Li, Caiyun Chen, Xue-Jian Gao, Jiangchang Zheng, Yi-Hsin Lin, Kun Qian, Ruo-Peng Yu, Xu Zhang, Zi Yang Meng, Kam Tuen Law, Qiming Shao, Berthold Jäck","doi":"10.1103/physrevx.14.021046","DOIUrl":"https://doi.org/10.1103/physrevx.14.021046","url":null,"abstract":"Berry curvature multipoles appearing in topological quantum materials have recently attracted much attention. Their presence can manifest in novel phenomena, such as nonlinear anomalous Hall effects (NLAHE). The notion of Berry curvature multipoles extends our understanding of Berry curvature effects on the material properties. Hence, research on this subject is of fundamental importance and may also enable future applications in energy harvesting and high-frequency technology. It was shown that a Berry curvature dipole can give rise to a second-order NLAHE in materials of low crystalline symmetry. Here, we demonstrate a fundamentally new mechanism for Berry curvature multipoles in antiferromagnets that are supported by the underlying magnetic symmetries. Carrying out electric transport measurements on the kagome antiferromagnet FeSn, we observe a third-order NLAHE, which appears as a transverse voltage response at the third harmonic frequency when a longitudinal ac drive is applied. Interestingly, this NLAHE is strongest at and above room temperature. We combine these measurements with a scaling law analysis, a symmetry analysis, model calculations, first-principle calculations, and magnetic Monte Carlo simulations to show that the observed NLAHE is induced by a Berry curvature quadrupole appearing in the spin-canted state of FeSn. At a practical level, our study establishes NLAHE as a sensitive probe of antiferromagnetic phase transitions in other materials—such as moiré superlattices, two-dimensional van der Waal magnets, and quantum spin liquid candidates, which remain poorly understood to date. More broadly, Berry curvature multipole effects are predicted to exist for 90 magnetic point groups. Hence, our work opens a new research area to study a variety of topological magnetic materials through nonlinear measurement protocols.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"3 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141333699","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-14DOI: 10.1103/physrevx.14.021045
Mengyao Du, Huiqian Min, Ke Xia, Dazhi Hou, Lei Wang, Zhiyong Qiu
Spin current is a crucial element in spintronics, and its diffusion in materials is typically characterized by monotonic decay. However, when the material hosting the spin current is also a magnet, the spin current is expected to exhibit spatial oscillations, the observation of which remains elusive. Here, we demonstrate the spatial oscillation of a spin current in a nickel film by measuring the thickness-dependent inverse spin Hall effect in bilayers. The inverse spin Hall current in nickel is found to oscillate with its film thickness, in contrast to nonmagnetic materials, and that the oscillation period quantitatively agrees with theoretical predictions based on differences in the Fermi wave vector between majority and minority carriers. Our findings reveal a previously hidden behavior of spin-transport dynamics and identify a new degree of freedom for manipulating spin current, with potential implications for future spintronic devices.
{"title":"Direct Observation of Spin Current Oscillation in a Ferromagnet","authors":"Mengyao Du, Huiqian Min, Ke Xia, Dazhi Hou, Lei Wang, Zhiyong Qiu","doi":"10.1103/physrevx.14.021045","DOIUrl":"https://doi.org/10.1103/physrevx.14.021045","url":null,"abstract":"Spin current is a crucial element in spintronics, and its diffusion in materials is typically characterized by monotonic decay. However, when the material hosting the spin current is also a magnet, the spin current is expected to exhibit spatial oscillations, the observation of which remains elusive. Here, we demonstrate the spatial oscillation of a spin current in a nickel film by measuring the thickness-dependent inverse spin Hall effect in <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow><mi>Ni</mi><mo>/</mo><mi>YIG</mi></mrow></math> bilayers. The inverse spin Hall current in nickel is found to oscillate with its film thickness, in contrast to nonmagnetic materials, and that the oscillation period quantitatively agrees with theoretical predictions based on differences in the Fermi wave vector between majority and minority carriers. Our findings reveal a previously hidden behavior of spin-transport dynamics and identify a new degree of freedom for manipulating spin current, with potential implications for future spintronic devices.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"65 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141326841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-06-13DOI: 10.1103/physrevx.14.021044
Zheng Zhou (周正), Liangdong Hu, W. Zhu, Yin-Chen He
The deconfined quantum critical point (DQCP) is an example of phase transitions beyond the Landau symmetry-breaking paradigm that attracts wide interest. However, its nature has not been settled after decades of study. In this paper, we apply the recently proposed fuzzy-sphere regularization to study the SO(5) nonlinear sigma model with a topological Wess-Zumino-Witten term, which serves as a dual description of the DQCP with an exact SO(5) symmetry. We demonstrate that the fuzzy sphere functions as a powerful microscope, magnifying and revealing a wealth of crucial information about the DQCP, ultimately paving the way toward its final answer. In particular, through exact diagonalization, we provide clear evidence that the DQCP exhibits approximate conformal symmetry. The evidence includes the existence of a conserved SO(5) symmetry current, a stress tensor, and integer-spaced levels between conformal primaries and their descendants. Most remarkably, we identify 23 primaries and 76 conformal descendants. Furthermore, by examining the renormalization group flow of the lowest symmetry singlet as well as other primaries, we provide numerical evidence in favor of DQCP being pseudo-critical, with the approximate conformal symmetry plausibly emerging from nearby complex fixed points. The primary spectrum we compute also has important implications, including the conclusion that the SO(5) DQCP cannot describe a direct transition from the Néel to valence bond solid phase on the honeycomb lattice.
{"title":"SO(5) Deconfined Phase Transition under the Fuzzy-Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum","authors":"Zheng Zhou (周正), Liangdong Hu, W. Zhu, Yin-Chen He","doi":"10.1103/physrevx.14.021044","DOIUrl":"https://doi.org/10.1103/physrevx.14.021044","url":null,"abstract":"The deconfined quantum critical point (DQCP) is an example of phase transitions beyond the Landau symmetry-breaking paradigm that attracts wide interest. However, its nature has not been settled after decades of study. In this paper, we apply the recently proposed fuzzy-sphere regularization to study the SO(5) nonlinear sigma model with a topological Wess-Zumino-Witten term, which serves as a dual description of the DQCP with an exact SO(5) symmetry. We demonstrate that the fuzzy sphere functions as a powerful microscope, magnifying and revealing a wealth of crucial information about the DQCP, ultimately paving the way toward its final answer. In particular, through exact diagonalization, we provide clear evidence that the DQCP exhibits approximate conformal symmetry. The evidence includes the existence of a conserved SO(5) symmetry current, a stress tensor, and integer-spaced levels between conformal primaries and their descendants. Most remarkably, we identify 23 primaries and 76 conformal descendants. Furthermore, by examining the renormalization group flow of the lowest symmetry singlet as well as other primaries, we provide numerical evidence in favor of DQCP being pseudo-critical, with the approximate conformal symmetry plausibly emerging from nearby complex fixed points. The primary spectrum we compute also has important implications, including the conclusion that the SO(5) DQCP cannot describe a direct transition from the Néel to valence bond solid phase on the honeycomb lattice.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":"37 1","pages":""},"PeriodicalIF":12.5,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141319992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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