Topological Anderson insulator in two-dimensional non-Hermitian systems

We study the characterization and realization of higher-order topological Anderson insulator (HOTAI) in non-Hermitian systems, where the non-Hermitian mechanism ensures extra symmetries as well as gain and loss disorder. We illuminate that the quadrupole moment Qxy can be used as the real space topological invariant of non-Hermitian higher-order topological insulator (HOTI). Based on the biorthogonal bases and non-Hermitian symmetries, we prove that Qxy can be quantized to 0 or 0.5. Considering the disorder effect, we find the disorder-induced phase transition from normal insulator to non-Hermitian HOTAI. Furthermore, we elucidate that the real space topological invariant Qxy is also applicable for systems with the non-Hermitian skin effect. Our work enlightens the study of the combination of disorder and non-Hermitian HOTI.

[1]  P. Anderson.  Absence of Diffusion in Certain Random Lattices , 1958 .

[2]  J. Hirsch,et al.  Phase diagram of one-dimensional electron-phonon systems. I. the Su-Schrieffer-Heeger model , 1983 .

[3]  T. V. Ramakrishnan,et al.  Disordered electronic systems , 1985 .

[4]  B. Kramer,et al.  Localization: theory and experiment , 1993 .

[5]  Cha,et al.  Disorder-induced phase transitions in two-dimensional crystals. , 1995, Physical review letters.

[6]  Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures , 1996, cond-mat/9602137.

[7]  E. J. Mele,et al.  Quantum spin Hall effect in graphene. , 2004, Physical review letters.

[8]  E. J. Mele,et al.  Z2 topological order and the quantum spin Hall effect. , 2005, Physical review letters.

[9]  Shou-Cheng Zhang,et al.  Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells , 2006, Science.

[10]  A. Mirlin,et al.  Anderson Transitions , 2007, 0707.4378.

[11]  L. Molenkamp,et al.  Quantum Spin Hall Insulator State in HgTe Quantum Wells , 2007, Science.

[12]  Jian Wang,et al.  Disorder-induced enhancement of transport through graphene p-n junctions. , 2008, Physical review letters.

[13]  Shun-Qing Shen,et al.  Topological Anderson insulator. , 2008, Physical review letters.

[14]  Lei Wang,et al.  Numerical study of the topological Anderson insulator in HgTe/CdTe quantum wells , 2009, Physical Review B.

[15]  Alexei Kitaev,et al.  Periodic table for topological insulators and superconductors , 2009, 0901.2686.

[16]  Joel E Moore,et al.  The birth of topological insulators , 2010, Nature.

[17]  C. Kane,et al.  Topological Insulators , 2019, Electromagnetic Anisotropy and Bianisotropy.

[18]  Liang Fu,et al.  Topological crystalline insulators. , 2010, Physical review letters.

[19]  E. Prodan.  Disordered topological insulators: a non-commutative geometry perspective Disordered topological insulators: a non-commutative geometry perspective , 2011 .

[20]  E. Prodan.  Disordered topological insulators: a non-commutative geometry perspective , 2010, 1010.0595.

[21]  N. Moiseyev.  Non-Hermitian Quantum Mechanics: The properties of the non-Hermitian Hamiltonian , 2011 .

[22]  X. Qi,et al.  Topological insulators and superconductors , 2010, 1008.2026.

[23]  Jason Alicea,et al.  New directions in the pursuit of Majorana fermions in solid state systems , 2012, Reports on progress in physics. Physical Society.

[24]  Hsin Lin,et al.  Topological crystalline insulators in the SnTe material class , 2012, Nature Communications.

[25]  B. M. Wojek,et al.  Topological crystalline insulator states in Pb(1-x)Sn(x)Se. , 2012, Nature materials.

[26]  M. Porta,et al.  Bulk-Edge Correspondence for Two-Dimensional Topological Insulators , 2012, 1207.5989.

[27]  Q. Xue,et al.  Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator , 2013, Science.

[28]  R. Shen,et al.  Coupling-matrix approach to the Chern number calculation in disordered systems , 2012, 1212.6295.

[29]  Z. J. Wang,et al.  Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi , 2013, Science.

[30]  E. Prodan,et al.  AIII and BDI topological systems at strong disorder , 2014, 1402.7116.

[31]  D. Brody.  Biorthogonal quantum mechanics , 2013, 1308.2609.

[32]  Emil Prodan,et al.  Topological criticality in the chiral-symmetric AIII class at strong disorder. , 2013, Physical review letters.

[33]  Y. Ando,et al.  Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials , 2015, 1501.00531.

[34]  Claudia Felser,et al.  Topological Materials: Weyl Semimetals , 2016, 1611.04182.

[35]  L'aszl'o Oroszl'any,et al.  A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions , 2015, 1509.02295.

[36]  Zhijun Wang,et al.  Hourglass fermions , 2016, Nature.

[37]  Z. J. Wang,et al.  Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSb , 2016, 1605.06824.

[38]  Shinsei Ryu,et al.  Classification of topological quantum matter with symmetries , 2015, 1505.03535.

[39]  Y. Xiong.  Why does bulk boundary correspondence fail in some non-hermitian topological models , 2017, 1705.06039.

[40]  H. Panahi,et al.  Solvability of a class of PT-symmetric non-Hermitian Hamiltonians: Bethe ansatz method , 2017 .

[41]  A. Vishwanath,et al.  Symmetry-based indicators of band topology in the 230 space groups , 2017, Nature Communications.

[42]  B. Bernevig,et al.  Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators , 2017, 1708.04230.

[43]  P. Brouwer,et al.  Reflection-Symmetric Second-Order Topological Insulators and Superconductors. , 2017, Physical review letters.

[44]  Luis E. F. Foa Torres,et al.  Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points , 2017, 1711.05235.

[45]  M. I. Aroyo,et al.  Topological quantum chemistry , 2017, Nature.

[46]  Wladimir A. Benalcazar,et al.  Quantized electric multipole insulators , 2016, Science.

[47]  Bin Zhou,et al.  Disorder-induced topological phase transitions on Lieb lattices , 2017, 1708.02121.

[48]  M. Ezawa.  Higher-Order Topological Insulators and Semimetals on the Breathing Kagome and Pyrochlore Lattices. , 2017, Physical review letters.

[49]  Y. Ashida,et al.  Topological Phases of Non-Hermitian Systems , 2018, Physical Review X.

[50]  Liang Fu,et al.  Topological Band Theory for Non-Hermitian Hamiltonians. , 2017, Physical review letters.

[51]  M. Segev,et al.  Photonic topological Anderson insulators , 2018, Nature.

[52]  P. Brouwer,et al.  Second-order topological insulators and superconductors with an order-two crystalline symmetry , 2018, 1801.10053.

[53]  Zhong Wang,et al.  Edge States and Topological Invariants of Non-Hermitian Systems. , 2018, Physical review letters.

[54]  Feng Tang,et al.  Comprehensive search for topological materials using symmetry indicators , 2018, Nature.

[55]  R. Lu,et al.  Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems , 2018, 1802.04169.

[56]  D. Loss,et al.  Majorana Kramers Pairs in Higher-Order Topological Insulators. , 2018, Physical review letters.

[57]  A. Dauphin,et al.  Observation of the topological Anderson insulator in disordered atomic wires , 2018, Science.

[58]  C. Felser,et al.  The (High Quality) Topological Materials In The World , 2018 .

[59]  F. Song,et al.  Non-Hermitian Chern Bands. , 2018, Physical review letters.

[60]  Jan Carl Budich,et al.  Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems. , 2018, Physical review letters.

[61]  M. Vergniory,et al.  Higher-order topological insulators , 2017, Science Advances.

[62]  P. Brouwer,et al.  Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases , 2018, Physical Review X.

[63]  Masahito Ueda,et al.  Symmetry and Topology in Non-Hermitian Physics , 2018, Physical Review X.

[64]  G. Cho,et al.  Many-body order parameters for multipoles in solids , 2018, Physical Review B.

[65]  T. Hughes,et al.  Many-body electric multipole operators in extended systems , 2018, Physical Review B.

[66]  Feng Tang,et al.  Comprehensive search for topological materials using symmetry indicators , 2019, Nature.

[67]  Franco Nori,et al.  Second-Order Topological Phases in Non-Hermitian Systems. , 2018, Physical review letters.

[68]  Bitan Roy,et al.  Antiunitary symmetry protected higher-order topological phases , 2019, Physical Review Research.

[69]  Flore K. Kunst,et al.  Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence , 2018, Physical Review B.

[70]  Chuanwei Zhang,et al.  Higher-Order Topological Corner States Induced by Gain and Loss. , 2019, Physical review letters.

[71]  J. Christensen,et al.  Non-Hermitian Sonic Second-Order Topological Insulator. , 2019, Physical review letters.

[72]  Hua Jiang,et al.  Topological Anderson insulator in electric circuits , 2019, Physical Review B.

[73]  F. Song,et al.  Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems. , 2019, Physical review letters.

[74]  Hui Jiang,et al.  Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices , 2019, Physical Review B.

[75]  Yuqing He,et al.  Catalogue of topological electronic materials , 2018, Nature.

[76]  F. Song,et al.  Non-Hermitian Topological Invariants in Real Space. , 2019, Physical review letters.

[77]  S. Murakami,et al.  Non-Bloch Band Theory of Non-Hermitian Systems. , 2019, Physical review letters.

[78]  Hua Jiang,et al.  Disorder induced phase transition in magnetic higher-order topological insulator: A machine learning study , 2019, Chinese Physics B.

[79]  A. Arnau,et al.  Unique Thickness-Dependent Properties of the van der Waals Interlayer Antiferromagnet MnBi_{2}Te_{4} Films. , 2018, Physical review letters.

[80]  E. Economou,et al.  Non-Hermitian disorder in two-dimensional optical lattices , 2019, 1909.13816.

[81]  Bo Fu,et al.  Topological Phase Transitions in Disordered Electric Quadrupole Insulators. , 2020, Physical review letters.

[82]  C. Fang,et al.  Correspondence between Winding Numbers and Skin Modes in Non-Hermitian Systems. , 2019, Physical review letters.

[83]  K. Kawabata,et al.  Topological Origin of Non-Hermitian Skin Effects. , 2019, Physical review letters.

[84]  C. Wang,et al.  Level statistics of extended states in random non-Hermitian Hamiltonians , 2020, Physical Review B.

[85]  Qing-feng Sun,et al.  Chiral interface states and related quantized transport in disordered Chern insulators , 2020, 2007.07619.

[86]  Zhesen Yang,et al.  Non-Hermitian Skin Modes Induced by On-Site Dissipations and Chiral Tunneling Effect. , 2020, Physical review letters.

[87]  Ling-Zhi Tang,et al.  Topological Anderson insulators in two-dimensional non-Hermitian disordered systems , 2020, 2005.13205.

[88]  Yong Xu,et al.  Winding numbers and generalized mobility edges in non-Hermitian systems , 2020, Physical Review Research.

[89]  S. Rotter,et al.  Shape-preserving beam transmission through non-Hermitian disordered lattices , 2020, 2005.06414.

[90]  Hui Yan,et al.  Non-Hermitian topological Anderson insulators , 2019, Science China Physics, Mechanics & Astronomy.

[91]  Samit Kumar Gupta,et al.  Photonic non-Hermitian skin effect and non-Bloch bulk-boundary correspondence , 2020 .

[92]  L. Duan,et al.  Higher-order topological Anderson insulators , 2020, 2007.15200.

[93]  Hong Wu,et al.  Floquet second-order topological insulators in non-Hermitian systems , 2020, 2008.06879.