Majorana zero modes, unconventional real–complex transition, and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice

Cheng, Shujie; Xianlong, Gao

doi:10.1088/1674-1056/ac3222

Cited by 8 publications

(3 citation statements)

References 78 publications

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“…For example recently, plenty of interesting localization properties have been found in one-dimensional (1D) lattices with a quasi-periodic potential, such as well-defined mobility edges [22,23], and a critical region consisting of critical states [24]. Insightful predictions on other rich physics in 1D quasi-periodic lattices are proposed, for example, topology, non-Hermeticity, superconductivity and superfluidity [25][26][27][28]. Some interesting experimental realizations of quasicrystalline physics have also been discussed recently [29,30].…”

Section: Introductionmentioning

confidence: 99%

Transport through quantum anomalous Hall bilayers with lattice mismatch

Zhang

Wang

et al. 2022

New J. Phys.

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We theoretically investigate quantum transport properties of quantum anomalous Hall bilayers, with arbitrary ratio of lattice constants, i.e., with lattice mismatch. In the simplest case of ratio 1 (but with different model parameters in two layers), the inter-layer coupling results in resonant traversing between forward propagating waves in two layers. In the case of generic ratios, there is a quantized conductance plateau originated from two Chern numbers associated with two layers. However, the phase boundary of this quantization plateau consists of a fractal transitional region (instead of a clear transition line) of interpenetrating edge states (with quantized conductance) and bulk states (with unquantized conductance). We attribute these bulk states as mismatch induced in-gap bulk states. Different from in-gap localized states induced by random disorder, these in-gap bulk states are extended in the limit of vanishing random disorder. However, the detailed fine structure of this transitional region is sensitive to disorder, lattice structure, sample size, and even the configuration of leads connecting to it, due to the bulk and topologically trivial nature of these in-gap bulk states.

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Section: Introductionmentioning

confidence: 99%

Transport through quantum anomalous Hall bilayers with lattice mismatch

Zhang

Wang

et al. 2022

New J. Phys.

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“…It was shown that an intermediate regime characterized by the coexistence of localized and extended states at different energies may occur 3,4 . The theoretical findings were confirmed in an experimental realization of a system with a single-particle mobility edge 5 .Recently, in non-Hermitian systems mobility edges have been explored for various 1D tight-binding models [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] . In non-Hermitian systems, in comparison to the Hermitian ones, the mobility edges not only separate localized states from the extended states but also indicate the coexistence of complex and real energies.…”

mentioning

confidence: 68%

“…Recently, in non-Hermitian systems mobility edges have been explored for various 1D tight-binding models [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] . In non-Hermitian systems, in comparison to the Hermitian ones, the mobility edges not only separate localized states from the extended states but also indicate the coexistence of complex and real energies.…”

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confidence: 99%

Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model

Yuce,

Ramezani

2022

Preprint

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In one-dimensional Hermitian tight-binding models, mobility edges separating extended and localized states can appear in the presence of properly engineered quasi-periodical potentials and coupling constants. On the other hand, mobility edges don't exist in a one-dimensional Anderson lattice since localization occurs whenever a diagonal disorder through random numbers is introduced. Here, we consider a nonreciprocal non-Hermitian lattice and show that the coexistence of extended and localized states appears with or without diagonal disorder in the topologically nontrivial region. We discuss that the mobility edges appear basically due to the boundary condition sensitivity of the nonreciprocal non-Hermitian lattice.Introduction-Anderson localization (AL), a wellunderstood fundamental problem in condensed matter, is the absence of diffusion of waves in a disordered medium due to interference of waves 1 . Specifically in AL, all states are exponentially localized in the presence of any disorder in one and two-dimensional Anderson model at which a random disordered on-site potential is introduced. On the other hand for weak disorder if the localization length is bigger than the system size then the system behaves as it is delocalized. In three dimensions, we would have a mobility edge separating localized and extended states. On contrary to the one dimensional (1D) Anderson model, in the Aubry-André model in which its disorder is modeled as a quasi-periodic on-site potential depending on the strength of incommensurate potential, all states are localized or delocalized 2 . This means that the system can undergo a metal-insulator transition even in 1D. However, this transition is sharp, i.e. all singleparticle eigenstates in the spectrum suddenly become exponentially localized above a threshold level of disorder. In both cases, localized and extended states generally do not coexist since non of these models possess a mobility edge in 1D, i.e., critical energy separates localized and delocalized energy eigenstates. Recent studies show that the transition is not sharp beyond the one-dimensional Aubry-André model with correlated disorder and hopping amplitudes. It was shown that an intermediate regime characterized by the coexistence of localized and extended states at different energies may occur 3,4 . The theoretical findings were confirmed in an experimental realization of a system with a single-particle mobility edge 5 .Recently, in non-Hermitian systems mobility edges have been explored for various 1D tight-binding models [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] . In non-Hermitian systems, in comparison to the Hermitian ones, the mobility edges not only separate localized states from the extended states but also indicate the coexistence of complex and real energies. The latter allows us to come out with a topological characterization of mobility edges 7 . Apart from these models, extended and localized states can coexist in some other Hermitian lattices with inhomogeneous trap 24,25 and wi...

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Universal characteristics of one-dimensional non-Hermitian superconductors

Cao¹,

Li²,

Chen³

et al. 2022

J. Phys.: Condens. Matter

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We establish a non-Bloch band theory for one-dimensional(1D) non-Hermitian topological superconductors. The universal physical properties of non-Hermitian topological superconductors are revealed based on the theory. According to the particle-hole symmetry, there exist reciprocal particle and hole loops of generalized Brillouin zone (GBZ). The critical point of quantum phase transition, where the energy gap closes, appears when the particle and hole loops intersect at Bloch points.If the non-Hermitian system has non-Hermitian skin effects, the non-Hermitian skin effect should be the Z_{2} skin effect: the corresponding eigenstates of particle and hole localize at opposite ends of an open chain, respectively. The non-Bloch band theory is applied to two examples, non-Hermitian p- and s-wave topological superconductors. In terms of Majorana Pfaffian, a Z_{2} non-Bloch topological invariant is defined to establish the non-Hermitian bulk-boundary correspondence in non-Hermitian superconductors.

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Majorana zero modes, unconventional real–complex transition, and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice

Abstract: A one-dimensional non-Hermitian quasiperiodic p-wave superconductor without P T -symmetry is studied. By analyzing the spectrum, we discovered that there still exists real–complex energy transition even if the inexistence of P T … Show more

Cited by 8 publications

References 78 publications

Transport through quantum anomalous Hall bilayers with lattice mismatch

Transport through quantum anomalous Hall bilayers with lattice mismatch

Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model

Universal characteristics of one-dimensional non-Hermitian superconductors

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