Two dimensional collective electron magnetotransport, oscillations and chaos in a semiconductor superlattice

TL;DR

This paper develops a two-dimensional self-consistent Boltzmann transport theory for semiconductor superlattices, predicting collective chaos and offering a new perspective that challenges previous one-dimensional models linking single-electron chaos to collective transport.

Contribution

It introduces a novel two-dimensional theoretical framework that predicts spontaneous collective chaos in superlattices, diverging from earlier one-dimensional models based on single-electron chaos influence.

Findings

The theory aligns with experimental observations of current self-oscillations.

It predicts spontaneous collective chaos via period doubling.

Potential for experimental validation through electric potential measurements.

Abstract

When quantized, traces of classically chaotic single particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario and it could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.