Optimization of edge state velocity in the integer quantum Hall regime

Abstract

Observation of interference in the quantum Hall regime may be hampered by a small edge state velocity due to finite phase coherence time. Therefore designing two quantum point contact (QPCs) interferometers having a high edge state velocity is desirable. Here we present a new simulation method for designing heterostructures with high edge state velocity by realistically modeling edge states near QPCs in the integer quantum Hall effect (IQHE) regime. Using this simulation method, we also predict the filling factor at the center of QPCs and their conductance at different gate voltages. The 3D Schr\"odinger equation is split into 1D and 2D parts. Quasi-1D Schr\"odinger and Poisson equations are solved self-consistently in the IQHE regime to obtain the potential profile, and quantum transport is used to solve for the edge state wave functions. The velocity of edge states is found to be $\ensuremath{\langle}E\ensuremath{\rangle}/B$, where $\ensuremath{\langle}E\ensuremath{\rangle}$ is the expectation value of the electric field for the edge state. Anisotropically etched trench gated heterostructures with double-sided delta doping have the highest edge state velocity among the structures considered.