Magnetic Field Effect on an Electron Tunneling out of a Confining Plane

TL;DR

This paper investigates how magnetic fields influence electron tunneling from a confining plane, revealing that parallel fields can suppress tunneling at zero temperature, with explicit formulas matching experimental data.

Contribution

The study introduces a path integral approach to map a 3D tunneling problem onto 1D, providing new insights into magnetic field effects on electron tunneling.

Findings

Parallel magnetic fields can suppress tunneling at zero temperature.

Explicit formulas for tunneling rates are derived.

Theoretical results match recent experimental observations.

Abstract

The influence of a magnetic field on the tunneling of an electron out of a confining plane is studied by a path integral method. We map this 3-d problem on to a 1-d one, and find that the tunneling is strongly affected by the field. Without a perpendicular field the tunneling at zero temperature can be completely suppressed by a large parallel field, but in the small parallel field and low temperature limit the tunneling rate is finite. An explicit formula is obtained in this case. A quantitative explanation without fitting parameter to a recent experiment is provided.