Surface statistical thermodynamics and magnetic susceptibility in the infinite-barrier model.

Abstract

The effects of a planar bounding surface on the statistical thermodynamics of a semi-infinite solid-state electron gas in a magnetic field normal to the surface are examined. The boundary condition of specular reflection for an infinite-barrier model is employed. Contributions proportional to surface area are determined for particle number ${\mathit{N}}_{\mathit{s}}$, grand thermodynamic potential ${\mathit{W}}_{\mathit{s}}$, internal energy ${\mathit{E}}_{\mathit{s}}$, magnetization ${\mathit{M}}_{\mathit{s}}$, and specific heat ${\mathit{C}}_{\mathit{s}}$. Surface Landau diamagnetic effects are studied in all regimes of magnetic field strength: Low monotonic magnetic field effects and surface de Haas--van Alphen oscillations are treated at low to intermediate field strengths. We also examine the surface statistical thermodynamic functions in the quantum high-field limit (all electrons in the lowest Landau level). All are analyzed in the degenerate regime, including finite-temperature corrections to the exact zero-temperature results. Nondegenerate quantum magnetic-field effects in ${\mathit{N}}_{\mathit{s}}$, ${\mathit{W}}_{\mathit{s}}$, ${\mathit{E}}_{\mathit{s}}$, ${\mathit{M}}_{\mathit{s}}$, and ${\mathit{C}}_{\mathit{s}}$ are also treated in this study.