Quantum conductance fluctuations in 3D ballistic adiabatic wires.

TL;DR

This paper investigates quantum conductance fluctuations in 3D ballistic wires, revealing how their amplitude and magnetic field sensitivity depend on the wire's cross-sectional shape and integrability, differing from universal conductance fluctuation behavior.

Contribution

It provides a detailed analysis of conductance fluctuations in 3D ballistic wires, highlighting the dependence on cross-sectional shape and distinguishing between integrable and non-integrable geometries.

Findings

Conductance fluctuation amplitude varies with cross-sectional shape.

Correlation field depends on Fermi wavelength and cross-sectional area.

Non-integrable shapes exhibit fluctuations at the scale of e^2/h.

Abstract

Quantum conductance of 3D ballistic wires with idealy flat boundaries obeys fluctuations with the properties quite distinguishable from those of universal conductance fluctuations: Both their amplitude and the sensitivity to the magnetic field flux $\Phi =HS$ penetrated into the sample cross-sectional area $S$ are different and depend on details of the cross-sectioanl shape of the wire. When the latter is integrable, conductance fluctuations have the enlarged amplitude $\delta G\sim\left[(e^2/h)^3G\right]^{1/4}$. When the cross-sectional shape of a wire is non-integrable, the irregular part of a conductance has the $e^ 2/h$ scale, whereas the correlation field is reduced to the value of $H_S\sim (\lambda_F/\sqrt S)^{1/2}(\Phi_0/S)$ and the correlation voltage of the nonlinear conductance fluctuations has the scale of $eV_c\sim\hbar^2/mS\sim E_F/(S/\lambda_F)$, where $\lambda_F=1/p_F$ is the Fermi wavelength.