L\'{e}vy flights in quantum transport in quasi-ballistic wires

TL;DR

This paper investigates how Levy flights influence quantum transport in quasi-ballistic metallic wires, revealing anomalous conductance fluctuation scaling and magnetic field effects on localization and magneto-conductance.

Contribution

It demonstrates the role of Levy flights in quantum transport phenomena and how magnetic fields affect localization and conductance fluctuations in rough metallic wires.

Findings

Correlation energy scales anomalously with sample size

Magnetic field deflects Levy flights, reducing localization length

Magnetic field restores Aharonov-Bohm magneto-conductance fluctuations

Abstract

Conductance fluctuations, localization and statistics of Lyapunov exponents are studied numerically in pure metallic wires with rough boundaries (quasi-ballistic wires). We find that the correlation energy of conductance fluctuations scales anomalously with the sample dimensions, indicating the role of L\'{e}vy flights. Application of a magnetic field deflects the L\'{e}vy flights which reduces the localization length. This deflection also breaks the geometrical flux cancellation and restores the usual Aharonov-Bohm type magneto-conductance fluctuations.