Universal Hall conductance scaling in non-Hermitian Chern insulators

Groenendijk, Solofo; Schmidt, Thomas L.; Meng, Tobias

doi:10.1103/physrevresearch.3.023001

Cited by 15 publications

(13 citation statements)

References 59 publications

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“…1(d). In these cases, chiral edge states are non-Hermitian, and the transmission coefficient is nonquantized, qualitatively consistent with previous studies [71][72][73][74].…”

supporting

confidence: 90%

“…This can occur to chiral edge states in twodimensional (2D) CIs, chiral hinge states in three-dimensional second-order topological insulators (3DSOTIs), and topological Anderson insulators (TAIs). Same as those in Hermitian systems, the transmission coefficient of each chiral channel in non-Hermitian topological insulators is precisely 1, in contrast to the non-quantized value of a general non-Hermitian topological insulator [71][72][73][74]. Besides, we verify the robustness of these Hermitian boundary states against impurities.…”

mentioning

confidence: 65%

“…While quantized transport in the quantum Hall effect is one of the fundamental properties of Hermitian CIs, previous works show that Hall conductances of non-Hermitian CIs are non-quantized [71][72][73][74]. The reason for the absence of quantized Hall conductances is that edge states of those CIs are non-Hermitian with certain degrees of loss.…”

mentioning

confidence: 99%

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Hermitian chiral boundary states in non-Hermitian topological insulators

Wang,

Wang

2021

Preprint

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Eigenenergies of a non-Hermitian system without parity-time symmetry are complex in general. Here, we show that the chiral boundary states of non-Hermitian topological insulators without parity-time symmetry can be Hermitian with real eigenenergies under certain conditions. Our finding allows one to construct Hermitian chiral edge and hinge states from non-Hermitian two-dimensional Chern insulators and three-dimensional second-order topological insulators, respectively. Such Hermitian chiral boundary channels have perfect transmission coefficients (quantized values) and are robust against disorders. Furthermore, a non-Hermitian topological insulator can undergo the topological Anderson insulator transition from a topological trivial non-Hermitian metal or insulator to a topological Anderson insulator with quantized transmission coefficients at finite disorders.

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“…1(d). In these cases, chiral edge states are non-Hermitian, and the transmission coefficient is nonquantized, qualitatively consistent with previous studies [71][72][73][74].…”

supporting

confidence: 90%

mentioning

confidence: 65%

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Hermitian chiral boundary states in non-Hermitian topological insulators

Wang,

Wang

2021

Preprint

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“…The interface of junction containing magnetic impurities is placed on the xy -plane. To describe the surface states of topological insulator in the presence of a proximity-coupled ferromagnet, we use the following low-energy effective non-Hermitian Hamiltonian 24 , 55 where M is the proximity-induced exchange field breaking time-reversal symmetry due to the metallic ferromagnet. is the Fermi velocity.…”

Section: Model and Theorymentioning

confidence: 99%

Non-Hermitian indirect exchange interaction in a topological insulator coupled to a ferromagnetic metal

Hosseini

Askari

2021

Sci Rep

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We theoretically demonstrate non-Hermitian indirect interaction between two magnetic impurities placed at the interface between a 3D topological insulator and a ferromagnetic metal. The coupling of topological insulator and the ferromagnet introduces not only Zeeman exchange field on the surface states but also broadening to transfer the charge and spin between the surface states of the topological insulator and the metallic states of the ferromagnet. While the former provides bandgap at the charge neutrality point, the latter causes non-Hermiticity. Using the Green’s function method, we calculate the range functions of magnetic impurity interactions. We show that the charge decay rate provides a coupling between evanescent modes near the bandgap and traveling modes near the band edge. However, the spin decay rate induces a stronger coupling than the charge decay rate so that higher energy traveling modes can be coupled to lower energy evanescent ones. This results in a non-monotonic behavior of the range functions in terms of distance and decay rates in the subgap regime. In the over gap regime, depending on the type of decay rate and on the distance, the amplitude of spatial oscillations would be damped or promoted.

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“…Consequently, disordered Hermitian 3DSOTIs are characterized by the quantized transmission coefficients (equal to the number of chiral channels) and the vanishingly-small fluctuations due to the absence of backward scattering. On the other hand, for non-Hermitian systems, the widely accepted paradigm asserts no quantized transport for chiral edge states in Chern (firstorder topological) insulators [33][34][35]. The effective Hamiltonians of such chiral edge states are non-Hermitian, and the corresponding eigenenergies are complex numbers.…”

Section: Introductionmentioning

confidence: 99%

Chiral Hinge Transport in Disordered Non-Hermitian Second-Order Topological Insulators

Wang¹,

Wang²

2022

Preprint

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The generalized bulk-boundary correspondence predicts the existence of the chiral hinge states in threedimensional second-order topological insulators (3DSOTIs), resulting in a quantized Hall effect in three dimensions. Chiral hinge states in Hermitian 3DSOTIs are characterized by the quantized transmission coefficients with zero fluctuations, even in the presence of disorders. Here, we show that chiral hinge transport in disordered non-Hermitian systems deviates from the paradigm of the Hermitian case. Our numerical calculations prove the robustness of hinge states of disordered non-Hermitian 3DSOTIs. The mean transmission coefficients may or may not equal the number of chiral hinge channels, depending on the Hermiticity of chiral hinge states, while the fluctuations of transmission coefficients are always non-zero. Such fluctuations are not due to the broken chirality of hinge states but the incoherent scatterings of non-Hermitian potentials. The physics revealed here should also be true for one-dimensional chiral channels in topological materials that support chiral boundary states, such as Chern insulators, three-dimensional anomalous Hall insulators, and Weyl semimetals.

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Universal Hall conductance scaling in non-Hermitian Chern insulators

Cited by 15 publications

References 59 publications

Hermitian chiral boundary states in non-Hermitian topological insulators

Hermitian chiral boundary states in non-Hermitian topological insulators

Non-Hermitian indirect exchange interaction in a topological insulator coupled to a ferromagnetic metal

Chiral Hinge Transport in Disordered Non-Hermitian Second-Order Topological Insulators

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