Semiclassical theory of magnetotransport through a chaotic quantum well

TL;DR

This paper presents a semiclassical model linking resonant tunneling current in a quantum well under a magnetic field to periodic orbits, explaining spectral changes via orbit bifurcations.

Contribution

It introduces a quantitative semiclassical formula for magnetotransport that highlights the role of periodic orbits and explains spectral evolution near a specific tilt angle.

Findings

Current depends on periodic orbits within the quantum well.

Spectral evolution near 30° tilt angle explained by orbit bifurcation.

The theory matches experimental observations of tunneling spectra.

Abstract

We develop a quantitative semiclassical formula for the resonant tunneling current through a quantum well in a tilted magnetic field. It is shown that the current depends only on periodic orbits within the quantum well. The theory explains the puzzling evolution of the tunneling spectra near a tilt angle of $30^{\circ}$ as arising from an exchange bifurcation of the relevant periodic orbits.