Loss of Hall conductivity quantization in a non-Hermitian quantum anomalous Hall insulator

A non-Hermitian extension of a Chern insulator and its bulk-boundary correspondence are investigated. It is shown that in addition to the robust chiral edge states that reflect the nontrivial topology of the bulk (nonzero Chern number), anomalous helical edge states localized only at one edge can appear, which are unique to the non-Hermitian Chern insulator. I. INTRODUCTIONOver the past decade, remarkable progress has been achieved in phases of matter characterized by the topology of their wave functions [1][2][3][4][5]. Such topological phases were explored in solid-state systems including insulators [6][7][8][9][10][11][12][13], superconductors [14-18], and semimetals [19][20][21], as well as in photonic [22][23][24][25][26] and atomic [27][28][29][30][31][32][33] systems, all of which are classified according to spatial dimension and symmetry [34][35][36][37][38][39][40][41]. A hallmark of these topological phases is the bulk-boundary correspondence: the topologically protected gapless boundary states appear as a consequence of the nontrivial topology of the gapped bulk. Examples include chiral edge states in Chern insulators [7], helical edge states in quantum spin Hall insulators [8][9][10][11], and Majorana zero modes in topological superconducting wires [15].Recently, there has been growing interest in non-Hermitian topological phases of matter both in theory and experiment [73][74][75][76][77][78][79][80]. In general, non-Hermiticity arises from the exchange of energy and/or particles with the environment [81-84], and several phenomena unique to the nonconservative systems have been theoretically proposed and experimentally observed [114][115][116][117][118][119][120][121][122][123][124][125][126]. A key feature of non-Hermitian systems is the presence of a level degeneracy called an exceptional point [127][128][129], at which eigenstates coalesce to render the Hamiltonian nondiagonalizable. The exceptional point brings about novel functionalities with no Hermitian counterparts such as unidirectional invisibility [95,[116][117][118] and enhanced sensitivity [98,102,125,126]. Recent studies have also revealed that non-Hermiticity alters the nature of the bulk-boundary correspondence in topological systems [43,46,47,49,51,59,60,67]. Non-Hermiticity was shown to amplify the topologically protected edge states [46], which were experimentally observed in one dimension [75,78] and two dimensions [79]. Furthermore, the presence of exceptional points makes edge states anomalous, so that they are localized only at one edge in a non-Hermitian extension of the Su-Schrieffer-Heeger model (i.e., a non-Hermitian

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“…Moreover, Refs. [144,145], which appeared after the present work was submitted, study the Hall conductance of a non-Hermitian Chern insulator.…”

Section: Discussionmentioning

confidence: 99%

Anomalous helical edge states in a non-Hermitian Chern insulator

2018

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“…Recent theoretical studies have been focusing on topological systems in solid-state physics [70][71][72][73][74][75][76][77][78][79][80][81][82]. The bulk-edge correspondence has been notably under debate since it seems to be violated in contrast to Hermitian systems.…”

Section: Introductionmentioning

confidence: 99%

Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems

Yokomizo

Murakami

2020

Phys. Rev. Research

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Energy bands of non-Hermitian crystalline systems are described in terms of the generalized Brillouin zone (GBZ) having unique features which are absent in Hermitian systems. In this paper, we show that in one-dimensional non-Hermitian systems with both sublattice symmetry and time-reversal symmetry such as the non-Hermitian Su-Schrieffer-Heeger model, a topological semimetal phase with exceptional points is stabilized by the unique features of the GBZ. Namely, under a change of a system parameter, the GBZ is deformed so that the system remains gapless. It is also shown that each energy band is divided into three regions, depending on the symmetry of the eigenstates, and the regions are separated by the cusps and the exceptional points in the GBZ.

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“…Open systems ubiquitously exist in physics [8][9][10], particularly, the optical and photonic systems; these are mostly non-Hermitian because they interact with the environment [11][12][13][14][15][16]. Currently, topological systems extend into the non-Hermitian region , and the nontrivial topological properties are studied in one-dimensional (1D), twodimensional (2D), and three-dimensional (3D) systems, including the Su-Schrieffer-Heeger (SSH) model [45][46][47][48][49], Aubry-André-Harper (AAH) model [50][51][52][53][54][55], Rice-Mele (RM) model [56,57], Chern insulator [58][59][60][61][62], and Weyl semimetal [63,64].…”

Section: Introductionmentioning

confidence: 99%

Inversion symmetric non-Hermitian Chern insulator

Jin

Song

2019

Phys. Rev. B

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We propose a two-dimensional non-Hermitian Chern insulator with inversion symmetry, which is anisotropic and has staggered gain and loss in both x and y directions. In this system, conventional bulk-boundary correspondence holds. The Chern number is a topological invariant that accurately predicts the topological phase transition and the existence of helical edge states in the topologically nontrivial phase. The band touching points are isolated and protected by the symmetry. The band touching affects the existence of helical edge states. Moreover, topologically protected helical edge states exist in the gapless phase for the system under open boundary condition in one direction. The detaching points between the edge states and the bulk states are predicted by the winding number associated with the vector field of average values of Pauli matrices. The non-Hermiticity also supports a topological phase with zero Chern number, where a pair of in-gap helical edge states exists. Our findings provide insights into the symmetry protected non-Hermitian topological insulators.

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Loss of Hall conductivity quantization in a non-Hermitian quantum anomalous Hall insulator

Cited by 68 publications

References 33 publications

Anomalous helical edge states in a non-Hermitian Chern insulator

Anomalous helical edge states in a non-Hermitian Chern insulator

Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems

Inversion symmetric non-Hermitian Chern insulator

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