Theory of magnetostriction of electron-hole drops in Ge

Abstract

A large mass of electron-hole liquid ($\ensuremath{\gamma}$ drop) formed in a strain-induced potential well in Ge is known to distort its shape significantly in a magnetic field $B\ensuremath{\gtrsim}1$ kG. It is shown in this paper that the shape change can be understood in detail as due to a "recombination current" of electron-hole pairs needed to replace those pairs which recombine in the drop volume. The Lorentz force deflects this current and produces a macroscopic dipole current loop inside the drop. The drop then changes shape to minimize its total energy, including magnetic, strain, and surface energies. While the drop usually flattens along the field direction, both para- and diamagnetic effects (elongated drops) are found to be possible, depending on excitation conditions, in accord with experiment. Similar effects are predicted to occur in small drops in unstrained Ge. This paper presents a magnetohydrodynamic theory of the magnetostriction which takes into account density variations which occur in the strain well and in high magnetic fields. A simpler theory is given for the special case in which the drop may be considered incompressible (small drops and moderate fields). Effects of carrier mass anisotropy and fluid viscosity are taken into consideration.