Transport between edge states in multilayer integer quantum Hall systems: Exact treatment of Coulomb interactions and disorder

Tomlinson, Jeremy; Caux, Jean-Sébastien; Chalker, J. T.

doi:10.1103/physrevb.72.235307

Cited by 6 publications

(2 citation statements)

References 34 publications

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“…On the experimental side, a number of experiments on 3D semiconductor multilayers have explored the behavior of stacked integer quantum Hall states [5,6,7], including the novel vertical transport due to the conducting surface sheath. [1,8,9,10,11,12,13,14] More recently, experiments on bismuth crystals in high magnetic fields have revealed intriguing anomalies in the ultra quantum limit -the limit where the magnetic field is sufficiently large that only the lowest Landau level is (partially) occupied. [15] It has been suggested that a novel 3D fractional quantum Hall type state might be present.…”

Section: Introductionmentioning

confidence: 99%

Gapless layered three-dimensional fractional quantum Hall states

Levin¹,

Fisher²

2009

Phys. Rev. B

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Using the parton construction, we build a three-dimensional (3D) multilayer fractional quantum Hall state with average filling \nu = 1/3 per layer that is qualitatively distinct from a stacking of weakly coupled Laughlin states. The state supports gapped charge e/3 fermionic quasiparticles that can propagate both within and between the layers, in contrast to the quasiparticles in a multilayer Laughlin state which are confined within each layer. Moreover, the state has gapless neutral collective modes, a manifestation of an emergent "photon", which is minimally coupled to the fermionic quasiparticles. The surface sheath of the multilayer state resembles a chiral analog of the Halperin-Lee-Read state, which is protected against gap forming instabilities by the topological character of the bulk 3D phase. We propose that this state might be present in multilayer systems in the "intermediate tunneling regime", where the interlayer tunneling strength is on the same order as the Coulomb energy scale. We also find that the parton construction leads to a candidate state for a bilayer \nu = 1/3 system in the intermediate tunneling regime. The candidate state is distinct from both a bilayer of \nu=1/3 Laughlin states and the single layer \nu = 2/3 state, but is nonetheless a fully gapped fractional quantum Hall state with charge e/3 anyonic quasiparticles.Comment: 11 pages, 1 figur

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Section: Introductionmentioning

confidence: 99%

Gapless layered three-dimensional fractional quantum Hall states

Levin¹,

Fisher²

2009

Phys. Rev. B

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“…Therefore, it is important to investigate the effect of surface disorder on the 2D chiral surface states. Theoretically, the disordered surface states have been mainly investigated using a 2D directed network model 4,[24][25][26][27]29 and a 2D continuum model [21][22][23][30][31][32] . However, we note that the scattering strength of an adatom on a sample surface can easily be the order of magnitude of 1 eV 33,34 , which can be much larger than the 3D quantum Hall gap 6 .…”

Section: Introductionmentioning

confidence: 99%

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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