# Optimization of edge state velocity in the integer quantum Hall regime

## TL;DR

This paper introduces a simulation method to optimize edge state velocity in the integer quantum Hall regime, aiming to improve quantum interferometry by designing structures with higher edge velocities.

## Contribution

A new simulation approach models edge states near QPCs in the IQHE regime, predicting structures with enhanced edge state velocities.

## Key findings

- High edge state velocity structures identified
- Velocity correlates with electric field expectation value
- Anisotropic trench gated heterostructures perform best

## 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 realistically modeling edge states near QPCs in the integer quantum Hall effect (IQHE) regime. We calculate the filling fraction in the center of the QPC and the velocity of the edge states, and predict structures with high edge state velocity. 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 near the edges, and quantum transport is used to solve for the edge state wavefunctions. The velocity of edge states is found to be $\left< E \right> / B$, where $\left< E \right>$ 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.