Incompressible strips in dissipative Hall bars as origin of quantized Hall plateaus

Abstract

We study the current and charge distribution in a two dimensional electron system, under the conditions of the integer quantized Hall effect, on the basis of a quasi-local transport model, that includes non-linear screening effects on the conductivity via the self-consistently calculated density profile. The existence of "incompressible strips" with integer Landau level filling factor is investigated within a Hartree-type approximation, and non-local effects on the conductivity along those strips are simulated by a suitable averaging procedure. This allows us to calculate the Hall and the longitudinal resistance as continuous functions of the magnetic field B, with plateaus of finite widths and the well-known, exactly quantized values. We emphasize the close relation between these plateaus and the existence of incompressible strips, and we show that for B values within these plateaus the potential variation across the Hall bar is very different from that for B values between adjacent plateaus, in agreement with recent experiments.

Metrology and microscopic picture of the integer quantum Hall effect

“…Theoretical work, inspired by our experiments, could reproduce the types of Hall potential profiles and predict the occurrence of quantum Hall plateaus even without localization [37].…”

“…However, incompressible strips become narrower the closer they are positioned to the edge, as there the confining potential becomes steeper: the Thomas-Fermi approximation breaks down, and actually these outer incompressible strips do not exist owing to the finite extension of the wave function. In our sample where the edges of the 2DES are defined by an etched mesa, we can expect-before entering a quantum Hall plateau from lower magnetic field values-at most one or two incompressible strips to exist along such edges [37]. Defining the edges of the 2DES by gate electrodes on top of the GaAs/(AlGa)As heterostructures leads at large negative voltages to a smooth edge depletion where indeed more incompressible strips are expected.…”

Spin and Charge Ordering in the Quantum Hall Regime

“…As a result, the current can flow dissipationless inside of the incompressible stripes, and any externally injected current will preferentially distribute to flow in the incompressible stripes. Moreover, the current will favor the innermost incompressible stripe on either side of the sample because it is the most stable one and can sustain the highest currents [48][49][50]. If these incompressible stripes become too narrow (on the order of ), scattering into the central compressible regions is possible and dissipation occurs.…”

Formation of spin droplet atν=52in an asymmetric quantum dot under quantum Hall conditions

“…To calculate electron and potential profiles within the TFA the computational effort is much simpler than other quantum mechanical calculations and yields compatible results. The spatial distrubition of the electron density is calculated within the TFA 23,24 ,…”