{"title":"次对称保护拓扑相的非布洛克带理论","authors":"Sonu Verma, Moon Jip Park","doi":"10.1103/physrevb.110.035424","DOIUrl":null,"url":null,"abstract":"Bulk-boundary correspondence (BBC) of symmetry-protected topological (SPT) phases relates the nontrivial topological invariant of the bulk to the number of topologically protected boundary states. Recently, a finer classification of SPT phases in Hermitian systems has been discovered, known as subsymmetry-protected topological (sub-SPT) phases [Wang <i>et al.</i>, <span>Nat. Phys.</span> <b>19</b>, 992 (2023)]. In sub-SPT phases, a fraction of the boundary states is protected by the subsymmetry of the system, even when the full symmetry is broken. While the conventional topological invariant derived from the Bloch band is not applicable to describe the BBC in these systems, we propose to use the non-Bloch topological band theory to describe the BBC of sub-SPT phases. Using the concept of the generalized Brillouin zone (GBZ), where Bloch momenta are generalized to take complex values, we show that the non-Bloch band theory naturally gives rise to a non-Bloch topological invariant, establishing the BBC in both SPT and sub-SPT phases. In a one-dimensional system, we define the winding number, whose physical meaning corresponds to the reflection amplitude in the scattering matrix. Furthermore, the non-Bloch topological invariant characterizes the hidden intrinsic topology of the GBZ under translation symmetry-breaking boundary conditions. The topological phase transitions are characterized by the generalized momenta touching the GBZ, which accompanies the emergence of diabolic or band-touching points. Additionally, we discuss the BBCs in the presence of local or global full-symmetry or subsymmetry-breaking deformations.","PeriodicalId":20082,"journal":{"name":"Physical Review B","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Non-Bloch band theory of subsymmetry-protected topological phases\",\"authors\":\"Sonu Verma, Moon Jip Park\",\"doi\":\"10.1103/physrevb.110.035424\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Bulk-boundary correspondence (BBC) of symmetry-protected topological (SPT) phases relates the nontrivial topological invariant of the bulk to the number of topologically protected boundary states. Recently, a finer classification of SPT phases in Hermitian systems has been discovered, known as subsymmetry-protected topological (sub-SPT) phases [Wang <i>et al.</i>, <span>Nat. Phys.</span> <b>19</b>, 992 (2023)]. In sub-SPT phases, a fraction of the boundary states is protected by the subsymmetry of the system, even when the full symmetry is broken. While the conventional topological invariant derived from the Bloch band is not applicable to describe the BBC in these systems, we propose to use the non-Bloch topological band theory to describe the BBC of sub-SPT phases. Using the concept of the generalized Brillouin zone (GBZ), where Bloch momenta are generalized to take complex values, we show that the non-Bloch band theory naturally gives rise to a non-Bloch topological invariant, establishing the BBC in both SPT and sub-SPT phases. In a one-dimensional system, we define the winding number, whose physical meaning corresponds to the reflection amplitude in the scattering matrix. Furthermore, the non-Bloch topological invariant characterizes the hidden intrinsic topology of the GBZ under translation symmetry-breaking boundary conditions. The topological phase transitions are characterized by the generalized momenta touching the GBZ, which accompanies the emergence of diabolic or band-touching points. Additionally, we discuss the BBCs in the presence of local or global full-symmetry or subsymmetry-breaking deformations.\",\"PeriodicalId\":20082,\"journal\":{\"name\":\"Physical Review B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physical Review B\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1103/physrevb.110.035424\",\"RegionNum\":2,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Physics and Astronomy\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review B","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevb.110.035424","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Physics and Astronomy","Score":null,"Total":0}
Non-Bloch band theory of subsymmetry-protected topological phases
Bulk-boundary correspondence (BBC) of symmetry-protected topological (SPT) phases relates the nontrivial topological invariant of the bulk to the number of topologically protected boundary states. Recently, a finer classification of SPT phases in Hermitian systems has been discovered, known as subsymmetry-protected topological (sub-SPT) phases [Wang et al., Nat. Phys.19, 992 (2023)]. In sub-SPT phases, a fraction of the boundary states is protected by the subsymmetry of the system, even when the full symmetry is broken. While the conventional topological invariant derived from the Bloch band is not applicable to describe the BBC in these systems, we propose to use the non-Bloch topological band theory to describe the BBC of sub-SPT phases. Using the concept of the generalized Brillouin zone (GBZ), where Bloch momenta are generalized to take complex values, we show that the non-Bloch band theory naturally gives rise to a non-Bloch topological invariant, establishing the BBC in both SPT and sub-SPT phases. In a one-dimensional system, we define the winding number, whose physical meaning corresponds to the reflection amplitude in the scattering matrix. Furthermore, the non-Bloch topological invariant characterizes the hidden intrinsic topology of the GBZ under translation symmetry-breaking boundary conditions. The topological phase transitions are characterized by the generalized momenta touching the GBZ, which accompanies the emergence of diabolic or band-touching points. Additionally, we discuss the BBCs in the presence of local or global full-symmetry or subsymmetry-breaking deformations.
期刊介绍:
Physical Review B (PRB) is the world’s largest dedicated physics journal, publishing approximately 100 new, high-quality papers each week. The most highly cited journal in condensed matter physics, PRB provides outstanding depth and breadth of coverage, combined with unrivaled context and background for ongoing research by scientists worldwide.
PRB covers the full range of condensed matter, materials physics, and related subfields, including:
-Structure and phase transitions
-Ferroelectrics and multiferroics
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-Magnetism
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-Semiconductors and mesoscopic systems
-Surfaces, nanoscience, and two-dimensional materials
-Topological states of matter