Thouless conductances of a three-dimensional quantum Hall system

Zheng, Chao; Yang, Kun; Wan, Xin

doi:10.1103/physrevb.102.064208

Cited by 5 publications

(8 citation statements)

References 51 publications

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“…The effect of bulk disorder on this system has been studied in Refs. 35,36 . Here we consider surface disorder and introduce disorder only for the sites at the outmost sidewalls of the sample.…”

Section: Model and Methodsmentioning

confidence: 99%

“…However, the conductance fluctuations can be much larger in the 2D chiral metal regime, since the system can be effectively broken up into independent parallel strips, whose width is the distance an electron propagates in the chiral direction during the trip 22,25 . We note that to avoid entering into the ballistic regime, the system size needed for the 2D chiral metal regime is rather large for a 3D tight-binding Hamiltonian 26,27,36 . Therefore, we focus on the quasi-1D metal and insulator regimes in this paper.…”

Section: A Localization Lengthmentioning

confidence: 99%

“…In this work, we study the effect of surface disorder on the 2D chiral surface states using a 3D tight-binding lattice model 35,36 . Surface disorder has also been considered in the context of topological insulators [37][38][39][40][41][42] .…”

Section: Introductionmentioning

confidence: 99%

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Effect of surface disorder on the chiral surface states of a three-dimensional quantum Hall system

Zheng,

Yang,

Wan

2020

Preprint

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We investigate the effect of surface disorder on the chiral surface states of a three-dimensional quantum Hall system. Utilizing a transfer matrix method, we find that the localization length of the surface state along the magnetic field decreases with the disorder strength in the weak disorder regime, but increases anomalously in the strong disorder regime. In the strong disorder regime, the surface states mainly locate at the first inward layer to avoid the strong disorder in the outmost layer. The anomalous increase of the localization length can be explained by an effective model, which maps the strong disorder on the surface layer to the weak disorder on the first inward layer. Our work demonstrates that surface disorder can be an effective way to control the transport behavior of the surface states along the magnetic field. We also investigate the effect of surface disorder on the full distribution of conductances P (g) of the surface states in the quasi-one-dimensional (1D) regime. In particular, we find that P (g) is Gaussian in the quasi-1D metal regime and log-normal in the quasi-1D insulator regime. In the crossover regime, P (g) exhibits highly nontrivial forms, whose shapes coincide with the results obtained from the Dorokhov-Mello-Pereyra-Kumar equation of a bulk-disordered quasi-1D wire in the absence of time-reversal symmetry. Our results suggest that P (g) is fully determined by the average conductance, independent of details of the system, in agreement with the single-parameter scaling hypothesis.

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Section: Model and Methodsmentioning

confidence: 99%

Section: A Localization Lengthmentioning

confidence: 99%

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Effect of surface disorder on the chiral surface states of a three-dimensional quantum Hall system

Zheng,

Yang,

Wan

2020

Preprint

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“…We believe that this limited knowledge is related to the fact that, in condensed matter systems, the 3D quantum Hall effect is usually discussed in layered systems. [21][22][23][24][25][26][27][28] Since layered systems have a preferred axis, and since the magnetic field needs to be along this axis, the vectorial nature does not come up. On the contrary, the possibility of orienting Chern vectors in space demonstrated in photonic crystals, [6] open up the possibility of constructing domain walls between different orientations, and thus a definition of a vectorial BBC is required.…”

mentioning

confidence: 99%

Vectorial Bulk‐Boundary Correspondence for 3D Photonic Chern Insulators

Devescovi

García‐Díez

Bradlyn

et al. 2022

Advanced Optical Materials

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The (conserved) component of the group velocity normal to the magnetization axis (i.e., the Chern vector direction) has a welldefined sign and surface states cannot back-scatter along this specific direction.In 2D, the Chern vector is always fixed along the axis of the reduced dimensionality, that is, orthogonal to the plane of the system. Therefore, it can be regarded as a scalar quantity: the Chern number C, which characterizes the bulk topology of 2D CIs. [7][8][9] In this case, a "scalar" version of the bulk-boundary correspondence (sBBC) can be defined, to connect the bulk topology to the number of boundary modes. [10,11] According to sBBC in 2D CIs, an interface between two systems with Chern numbers C 1 , C 2 has n e = |C 1 − C 2 | protected chiral edge states. This means that chiral edge states can only appear in presence of a discontinuity of Chern numbers across the interface, that is, C 1 ≠ C 2 . [12][13][14][15] On the contrary, the interface between two 3D CIs can have Chern vectors C 1 and C 2 that need not be parallel/anti-parallel to each other. [2,16] This leads to vectorial aspects of the bulk boundary correspondance (BBC) which must be taken into account in order to correctly define a "vectorial" BBC (vBBC).In the broader context of topological insulators, the literature has discussed the vectorial aspects of BBC mostly in relation to 3D quantum spin-Hall fermionic insulators. [17][18][19] Such systems are characterized by vectors of 2  invariants and rely on time-reversal symmetry (TRS). However, the photonic 3D CIs studied in this manuscript break TRS and display non-zero Chern vectors, requiring a suited vectorial BBC. While scalar bulk-boundary correspondence is a well-established concept in 2D photonic crystals with broken TRS, [12][13][14][15]20] less is known in photonic 3D CIs, recently demonstrated in ref. [6] which is what motivated our work. We believe that this limited knowledge is related to the fact that, in condensed matter systems, the 3D quantum Hall effect is usually discussed in layered systems. [21][22][23][24][25][26][27][28] Since layered systems have a preferred axis, and since the magnetic field needs to be along this axis, the vectorial nature does not come up. On the contrary, the possibility of orienting Chern vectors in space demonstrated in photonic crystals, [6] open up the possibility of constructing domain walls between different orientations, and thus a definition of a vectorial BBC is required.

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“…[32,33] The model works well in the weak disorder or strong magnetic limits, when the inter-Landau level scattering can be neglected. An alternative model features a tight-binding lattice with on-site disorder, whose Thouless conductance calculation [34] and transfer-matrix study [22] have been reported. The 3D QH system is of great interest due to the rich phases or regimes of the bulk and surface states, which intertwine in the presence of a moderate disorder.…”

mentioning

confidence: 99%

Level Statistics Crossover of Chiral Surface States in a Three-Dimensional Quantum Hall System

Kausar¹,

Zheng²,

Wan³

2021

Chinese Phys. Lett.

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Recent experiments have demonstrated the realization of the three-dimensional quantum Hall effect in highly anisotropic crystalline materials, such as ZrTe5 and BaMnSb2. Such a system supports chiral surface states in the presence of a strong magnetic field, which exhibit a one-dimensional metal-insulator crossover due to suppression of surface diffusion by disorder potential. We study the nontrivial surface states in a lattice model and find a wide crossover of the level-spacing distribution through a semi-Poisson distribution. We also discover a nonmonotonic evolution of the level statistics due to the disorder-induced mixture of surface and bulk states.

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Thouless conductances of a three-dimensional quantum Hall system

Cited by 5 publications

References 51 publications

Effect of surface disorder on the chiral surface states of a three-dimensional quantum Hall system

Effect of surface disorder on the chiral surface states of a three-dimensional quantum Hall system

Vectorial Bulk‐Boundary Correspondence for 3D Photonic Chern Insulators

Level Statistics Crossover of Chiral Surface States in a Three-Dimensional Quantum Hall System

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