Quantum Tunneling Of Electron Snake States In An Inhomogeneous Magnetic Field

TL;DR

This paper investigates quantum tunneling of electron snake states in a 2DEG with a spatially varying magnetic field, revealing tunneling currents and Rabi oscillations due to parity transitions in a double well potential.

Contribution

It provides a quantum mechanical analysis of electron snake states, computing spectra and wavefunctions, and demonstrates tunneling and resonance phenomena in an inhomogeneous magnetic field.

Findings

Quantum tunneling induces a measurable current between snake states.

Time-dependent perturbations cause Rabi-like oscillations between parity states.

Resonances enable controlled electron transfer across potential barriers.

Abstract

In a two dimensional free electron gas (2DEG) subjected to a perpendicular spatially varying magnetic field, the classical paths of electrons are snake-like trajectories that weave along the line where the field crosses zero. But quantum mechanically this system is described by a symmetric double well potential which, for low excitations, leads to very different electron behavior. We compute the spectrum, as well as the wavefunctions, for states of definite parity in the limit of nearly degenerate states, i.e. for electrons sufficiently far from the $B_z=0$ line. Transitions between the states are shown to give rise to a tunneling current. If the well is made asymmetrical by a time-dependent parity breaking perturbation then Rabi-like oscillations between parity states occur. Resonances can be excited and used to stimulate the transfer of electrons from one side of the potential barrier to the other through quantum tunneling.