Gauge Fields, Mode Mixing and Local Density of States in a Quantum Point Contact

TL;DR

This paper introduces a gauge field approach to analyze mode mixing in quantum point contacts, revealing its significant impact on local density of states despite minimal effect on total conductance.

Contribution

It develops an exact method using non-abelian gauge fields to treat mode mixing in waveguides of arbitrary shape, applied specifically to quantum point contacts.

Findings

Mode mixing significantly affects local density of states.

Total conductance remains well-described by adiabatic approximation.

The gauge field approach provides exact treatment of mode interactions.

Abstract

It is shown that the elimination of the discrete transverse motion in a waveguide of arbitrary shape may be described in terms of a non-abelian gauge field for the longitudinal dynamics. This allows for an exact treatment of the scattering between different modes by eliminating the gauge field at the expense of a non-diagonal matrix of local subband energies. The method is applied to calculate the local density of states (LDOS) in a quantum point contact. Contrary to the total conductance which is well described by an adiabatic approximation, mode mixing turns out to play a crucial role for local properties like the LDOS.