Non-Hermitian Topological Invariants in Real Space

Song, Fei; Yao, Shunyu; Wang, Zhong

doi:10.48550/arxiv.1905.02211

Cited by 12 publications

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“…( 4)]. Note that the system recovers to the Hermitian disordered SSH chain when γ = 0 [26,27,32] and to the non-Hermitian clean chain when W 1 = W 2 = 0 [47][48][49][50], respectively. In the clean limit, the topological invariant of the nonreciprocal SSH model can be a non-Bloch winding number in complex momentum space [48] or a dual open-bulk winding number in real space [49].…”

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confidence: 99%

“…On the other hand, recent advances in non-Hermitian physics show that non-Hermitian systems have many intriguing features and applications [34][35][36][37]. Particularly, growing efforts have been made to reveal topological properties in non-Hermitian systems , which include new topological invariants [65], the non-Hermitian skin effect [48], the revised bulk-edge correspondence [47][48][49][50][51][52], and gain-and-loss induced topological phases [56]. In addition, non-Hermitian systems can exhibit unique localization properties in the presence of disorders [70][71][72][73][74][75][76][77].…”

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confidence: 99%

“…Here the summing takes over the eigenstates in the bulk continuum spectrum without the discrete edge modes. The winding number in real space is then defined as [49] where X is the coordinate operator of the lattice cell, L = L + 2l is the chain length with three intervals of lengthes l, L , l, and Tr denotes the trace over the middle interval of length L (with l sufficiently large to avoid boundary effects). This real-space winding number does not require the translation invariance and thus serves well for disordered systems.…”

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confidence: 99%

“…(3) correctly corresponds to the topological edge modes only under OBCs, due to the unconventional bulk-edge correspondence in the non-Hermitian cases [47][48][49][50][51][52].…”

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confidence: 99%

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Non-Hermitian topological Anderson insulators

Zhang

Tang

Lang

et al. 2020

Sci. China Phys. Mech. Astron.

114

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Non-Hermitian systems can exhibit exotic topological and localization properties. Here we elucidate the non-Hermitian effects on disordered topological systems by studying a nonreciprocal disordered Su-Schrieffer-Heeger model. We show that the non-Hermiticity can enhance the topological phase against disorders by increasing energy gaps. Moreover, we uncover a topological phase which emerges only under both moderate non-Hermiticity and disorders, and is characterized by localized insulating bulk states with a disorder-averaged winding number and zero-energy edge modes. Such topological phases induced by the combination of non-Hermiticity and disorders are dubbed non-Hermitian topological Anderson insulators. We also find that the system has unique non-monotonous localization behaviour and the topological transition is accompanied by an Anderson transition.Topological states of matter have been widely explored in condensed-matter materials [1-5] and various engineered systems, which include ultracold atoms [6-8], photonic lattices [9, 10], mechanic systems [11], classic electronic circuits [12][13][14][15], and superconducting circuits [16][17][18][19][20]. One hallmark of topological insulators is the robustness of nontrivial boundary states against certain types of weak disorders, since the topological band gap (topological invariants) preserves under these perturbations [1][2][3]. However, the band gap closes for sufficiently strong disorders and the system becomes trivial as all states are localized according to the Anderson localization [21]. Surprisingly, there is a topological phase driven from a trivial phase by disorders, known as topological Anderson insulator (TAI) [22]. The TAI was first predicted in two-dimensional (2D) quantum wells and then shown to exhibit in a wide range of systems [22][23][24][25][26][27][28][29][30], such as Su-Schrieffer-Heeger (SSH) chains [31]. Recently, the TAI has been observed in one-dimensional (1D) cold atomic wires and 2D photonic waveguide arrays [32,33].

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confidence: 99%

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confidence: 99%

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confidence: 99%

“…(3) correctly corresponds to the topological edge modes only under OBCs, due to the unconventional bulk-edge correspondence in the non-Hermitian cases [47][48][49][50][51][52].…”

mentioning

confidence: 99%

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Non-Hermitian topological Anderson insulators

Zhang

Tang

Lang

et al. 2020

Sci. China Phys. Mech. Astron.

114

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“…Topological states of matter in non-Hermitian systems have attracted great attention in recent years [1][2][3][4][5][6][7][8][9][10]. Theoretically, the presence of gain and loss or nonreciprocal effects induce rich static/Floquet topological phases and exotic phenomena like the non-Hermitian skin effect [39][40][41][42][43][44][45][46][47][48][49] and unique entanglement properties [50][51][52], resulting in the reformulation of topological classification schemes [53][54][55][56][57][58][59][60][61][62] and principle of bulk-edge correspondence [63][64][65][66][67][68][69][70][71][72][73] for their description. Experimentally, non-Hermitian topological phases have been observed in optical [74,75], ...…”

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confidence: 99%

Dynamical characterization of non-Hermitian Floquet topological phases in one dimension

Zhou

2019

Phys. Rev. B

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Non-Hermitian topological phases in static and periodically driven systems have attracted great attention in recent years. Finding dynamical probes for these exotic phases would be of great importance in the detection and application of their topological properties. In this work, we propose a systematic approach to dynamically characterize non-Hermitian Floquet topological phases in one-dimension with chiral symmetry. We show that the topological invariants of a chiral symmetric Floquet system can be fully determined by measuring the winding angles of its time-averaged spin textures. We further purpose a piecewise quenched lattice model with rich non-Hermitian Floquet topological phases, in which our theoretical predictions are numerically demonstrated and compared with another approach utilizing the mean chiral displacement of a wavepacket.

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Non-Hermitian anomalous skin effect

Yüce

2020

Physics Letters A

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A non-Hermitian topological insulator is fundamentally different from conventional topological insulators. The non-Hermitian skin effect arises in a nonreciprocal tight binding lattice with open edges. In this case, not only topological states but also bulk states are localized around the edges of the nonreciprocal system. We discuss that controllable switching from topological edge states into topological extended states in a chiral symmetric non-Hermitian system is possible. We show that the skin depth decreases with non-reciprocity for bulk states but increases with it for topological zero energy states.

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Non-Hermitian Topological Invariants in Real Space

Cited by 12 publications

References 0 publications

Non-Hermitian topological Anderson insulators

Non-Hermitian topological Anderson insulators

Dynamical characterization of non-Hermitian Floquet topological phases in one dimension

Non-Hermitian anomalous skin effect

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