Real-space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems

Liu, Hongfang; Zhou, Ji-Kun; Wu, Bing-Lan; Zhang, Zhiqiang; Jiang, Hua

doi:10.1103/physrevb.103.224203

Cited by 32 publications

(4 citation statements)

References 81 publications

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“…is also referred to as the surrogate Hamiltonian, which is used instead of the original Bloch Hamiltonian H(k) in computing topological invariants (however, the topological eigenenergies themselves fall outside of the purview of our prescription, because they are isolated solutions that are not adiabatically connected to any Bloch solution) [80][81][82] and spectral properties under OBCs.…”

Section: Obc Vs Pbc Spectramentioning

confidence: 99%

Real non-Hermitian energy spectra without any symmetry

Zhang

et al. 2022

Chinese Phys. B

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Non-Hermitian models with real eigenenergies are highly desirable for their stability. Yet, most of the currently known ones are constrained by symmetries such as PT-symmetry, which is incompatible with realizing some of the most exotic non-Hermitian phenomena. In this work, we investigate how the non-Hermitian skin effect provides an alternative route towards enforcing real spectra and system stability. We showcase, for different classes of energy dispersions, various ansatz models that possess large parameter space regions with real spectra, despite not having any obvious symmetry. These minimal local models can be quickly implemented in non-reciprocal experimental setups such as electrical circuits with operational amplifiers.

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Section: Obc Vs Pbc Spectramentioning

confidence: 99%

Real non-Hermitian energy spectra without any symmetry

Zhang

et al. 2022

Chinese Phys. B

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“…Li et al found that strong disorder can destroy the topological insulate state, and a certain strength of disorder can induce the system to transform from a normal insulator to topological non-trivial insulator called topological Anderson insulator (TAI) [65]. After Li et al first proposed this concept [65], TAI and disorder effects have been investigated in various systems [66][67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82][83][84][85], including HgTe/CdTe quantum wells [66], Kane-Mele models [77], electronic circuits [78], photonic crystals [79], quasicrystals [81,83,84]. In experiments, TAIs have been successively realized in a photonic platform [86], an atomic wire [87], and electronic circuits [88].…”

Section: Introductionmentioning

confidence: 99%

Chern insulator in a hyperbolic lattice

Liu,

Hua,

Peng

et al. 2022

Preprint

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Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum electrodynamics and the research interest in the non-Euclidean generalization of topological phenomena, we investigate the Chern insulator phases in a hyperbolic {8, 3} lattice, which is made from regular octagons (8-gons) such that the coordination number of each lattice site is 3. Based on the conformal projection of the hyperbolic lattice into the Euclidean plane, i.e., the Poincaré disk model, by calculating the Bott index (B) and the two-terminal conductance, we reveal two Chern insulator phases (with B = 1 and B = −1, respectively) accompanied with quantized conductance plateaus in the hyperbolic {8, 3} lattice. The numerical calculation results of the nonequilibrium local current distribution further confirm that the quantized conductance plateau originates from the chiral edge states and the two Chern insulator phases exhibit opposite chirality. Moreover, we explore the effect of disorder on topological phases in the hyperbolic lattice. It is demonstrated that the chiral edge states of Chern insulators are robust against weak disorder in the hyperbolic lattice. More fascinating is the discovery of disorder-induced topological non-trivial phases exhibiting chiral edge states in the hyperbolic lattice, realizing a non-Euclidean analog of topological Anderson insulator. Our work provides a route for the exploration of topological non-trivial states in hyperbolic geometric systems.

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“…Such unconventional boundary states have been experimentally observed in a variety of platforms, including electrical circuits 7,[25][26][27] , acoustic 13,14,28,29 and photonic waveguids [30][31][32] , phononic metamaterials 8 , and solid-state materials 16 . Furthermore, the unconventional bulk-boundary correspondence in HOTIs, with the interplay of disorder [33][34][35] , quasicrystal 19,36,37 and amorphous 38,39 structures, many-body interactions [40][41][42] , non-Hermiticity [43][44][45] or periodic driving [46][47][48] , has lead to many intriguing features uncovered in conventional topological insulators.…”

Section: Introductionmentioning

confidence: 99%

Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators

Lu¹,

Zhang²,

Wang³

et al. 2022

Preprint

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We investigate a second-order topological quantum transition of a modified Kane-Mele model driven by electron-phonon interaction. The results show that the system parameters of the bare modified Kane-Mele model are renormalized by the electron-phonon interaction. Starting from the second-order topological phase for the bare model, the increasing electron-phonon coupling strength can drive the second-order topological insulator into a semimetal phase. Such a secondorder topological phase transition is characterized by the band-gap closing, discontinuity of averaged ferminoic number and topological invariant.

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Real-space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems

Cited by 32 publications

References 81 publications

Real non-Hermitian energy spectra without any symmetry

Real non-Hermitian energy spectra without any symmetry

Chern insulator in a hyperbolic lattice

Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators

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