Soft Disorder Effects in the Conductance Quantization in Quantum Point Contacts: Indirect Backscattering Statistics

TL;DR

This paper investigates how indirect backscattering caused by long-range impurities affects conductance quantization in quantum point contacts, revealing a generalized Poisson distribution of conductance fluctuations and factors influencing device performance.

Contribution

It introduces an analytical model for conductance fluctuation distribution and highlights the significant role of indirect backscattering in conductance breakdown.

Findings

Conductance fluctuations follow a generalized Poisson distribution.

Indirect backscattering dominates over direct processes in certain regimes.

Larger intermode distance improves quantum point contact performance.

Abstract

The breakdown of conductance quantization in a quantum point contact in the presence of random long-range impurity potential is discussed. It is shown that in the linear response regime a decisive role is played by the indirect backscattering mechanism via quasilocalized states at the Fermi level; this can provide much higher backscattering rate than any direct backscattering process. For the realistic contact lengths ($\leq 2000$nm) the scattering processes prove to be independent, in spite of coherence of the electron wave. The distribution function of conductance fluctuations is obtained by direct numerical calculations as well as estimated within an analytical model for the first time. It is shown to be a generalized Poisson distribution. Estimates are made for quantum point contact performance at different choice of parameters. In particular, it is the better the larger the intermode distance is compared to the amplitude of the random impurity potential.