Semiclassical description of resonant tunneling

TL;DR

This paper develops a semiclassical formula to describe electron tunneling currents in a quantum well system under a tilted magnetic field, linking quantum tunneling to classical periodic orbits.

Contribution

It introduces a novel semiclassical approach that expresses tunneling current as a sum over specific periodic orbits in a tilted magnetic field scenario.

Findings

Derived a semiclassical tunneling current formula involving periodic orbits.

Applicable to systems with strong magnetic fields and quantum wells.

Provides a new theoretical tool for analyzing resonant tunneling phenomena.

Abstract

We derive a semiclassical formula for the tunneling current of electrons trapped in a potential well which can tunnel into and across a wide quantum well. The calculations idealize an experimental situation where a strong magnetic field tilted with respect to an electric field is used. The resulting semiclassical expression is written as the sum over special periodic orbits which hit both walls of the quantum well and are perpendicular to the first wall.