Field Emission in a Magnetic Field

Abstract

An expression for the field-emission current in a longitudinal magnetic field is derived in the zero-temperature limit. Two cases are considered, corresponding to constant Fermi energy (A) and constant electron density (B). In both cases the calculated current density contains an oscillatory contribution periodic in $\frac{1}{H}$, as well as a term which decreases as the square of the magnetic field. In case B, however, an oscillatory contribution appears that is absent in case A. Since the two oscillatory terms in case B differ in phase and their amplitudes depend on different powers of $H$, it should be possible to distinguish between cases A and B. The current-decrease quadratic in $H$ has its origin in the steady diamagnetism of the electron gas. Using accepted values of effective mass, Fermi energy, and work function, we find that for bismuth the predicted variations of the emission current with magnetic field should be readily observable.