Integer quantum Hall transition in a $\text{fraction}$ of a Landau level

Abstract

We investigate the quantum Hall problem in the lowest Landau level in two dimensions, in the presence of an arbitrary number of $\delta$-function potentials arranged in different geometric configurations. When the number of delta functions $N_{\delta }$ is smaller than the number of flux quanta through the system ($N_{\varphi }$), there is a manifold of $(N_{\varphi }-N_{\delta })$ degenerate states at the original Landau level energy. We prove that the total Chern number of this set of states is +1 regardless of the number or position of the $\delta$ functions. Furthermore, we find numerically that, upon the addition of disorder, this subspace includes a quantum Hall transition which is (in a well-defined sense) $\text{quantitatively}$ the same as that for the lowest Landau level without $\delta$-function impurities, but with a reduced number $N_{\varphi }^{\prime }\equiv N_{\varphi }-N_{\delta }$ of magnetic flux quanta. We discuss the implications of these results for studies of the integer plateau transitions, as well as for the many-body problem in the presence of electron-electron interactions.

11 pages (including appendix and references), 7 figures

References in corpus (5)

• Critical exponent for the quantum Hall transition
• Observation of a Nematic Quantum Hall Liquid on the Surface of Bismuth
• Finite Size Effects and Irrelevant Corrections to Scaling near the Integer Quantum Hall Transition
• Marginal Anderson localization and many body delocalization
• Absence of Many-Body Localization in a Single Landau Level

Cited by in corpus (11)

• Criticality of two-dimensional disordered Dirac fermions in the unitary class and universality of the integer quantum Hall transition
• Fractional Chern insulators with a non-Landau level continuum limit
• Disorder in dissipation-induced topological states: Evidence for a different type of localization transition
• Numerical Study of a Dual Representation of the Integer Quantum Hall Transition
• The integer quantum Hall transition: an $S$-matrix approach to random networks
• Topology and many-body localization
• Anisotropic quantum Hall states in the presence of interactions with fourfold rotational symmetry
• Superlattice induced electron percolation within a single Landau level
• Quantum Hall criticality in an amorphous Chern insulator
• Quasi-quantized Hall response in bulk InAs
• The impact of dimensionality on universality of quantum Hall transitions