Metrology and microscopic picture of the integer quantum Hall effect

Abstract

Since 1990, the integer quantum Hall effect has provided the electrical resistance standard, and there has been a firm belief that the measured quantum Hall resistances are described only by fundamental physical constants-the elementary charge e and the Planck constant h. The metrological application seems not to rely on detailed knowledge of the microscopic picture of the quantum Hall effect; however, technical guidelines are recommended to confirm the quality of the sample to confirm the exactness of the measured resistance value. In this paper, we give our present understanding of the microscopic picture, derived from systematic scanning force microscopy investigations on GaAs/(AlGa)As quantum Hall samples, and relate these to the technical guidelines.

Observation of finite excess noise in the voltage-biased quantum Hall regime as a precursor for breakdown

“…4 More precisely, the edge channels are regarded as "incompressible strips" owing to the electron screening. [5][6][7] Although the nature of the QHE state is successfully explained by the topological rigidity, details of the state in nonequilibrium are largely unexplored. Recent experiments aimed at quantum information processing by using edge channels, involving phase reversal of electrons in electron interferometers, 8,9 decoherence, 10-15 energy relaxation, [16][17][18] and dynamics of the edge magnetoplasmons in the edge channels, 19,20 have clarified electron behaviors in the nonequilibrium QHE state.…”

Unconventional Correlation between Quantum Hall Transport Quantization and Bulk State Filling in Gated Graphene Devices

“…In particular, graphene's hard wall confining potential has been predicted to result in charge accumulation near physical edges under electrostatic gating [8], which has been used to explain observations in several transport [9][10][11][12] and imaging [13] experiments. In the QH regime where the edges play a crucial role as the connection between bulk state and transport [14][15][16][17][18], how such charge accumulation affects transport quantization remains elusive [11,12,19]. A comprehensive understanding requires a detailed study by both transport and bulk-sensitive techniques on the same gated hall bar.…”

“…Our results can be explained selfconsistently within either model, and our conclusions on how to refine transport-based analysis of QH effect in graphene (which will be discussed later in the paper) do not depend on the model choice. To facilitate our discussion, we work in the incompressible state picture (for a review, see [18] and references therein). The essence of this picture is that the dissipationless transport current flows only in the incompressible regions, hence the transport quantization depends on the spatial structure of such regions.…”

“…Integration of the current density over the entire incompressible region gives rise to a quantized transverse Hall conductance determined by the Landau level filling factor ν in the incompressible region. In a Hall bar geometry, the conditions to measure a quantized conductance νh/e 2 are: 1) the incompressible regions at filling factor ν are able to percolate through the sample and connect to the current leads, and 2) the voltage probes are able to achieve a full equilibration in chemical potential with the boundaries of these incompressible regions [17,18].…”

Mini array of quantum Hall devices based on epitaxial graphene

“…In QHE, the Hall resistance of a two-dimensional (2D) system of charge carriers as a function of magnetic field or charge carrier density shows well-defined quantized plateaus at R H,ν = R K /ν, where R K = h/e 2 is the von Klitzing constant, h is the Planck constant, e is the elementary charge, and ν is an integer [4].…”