Fermi gas energetics in low-dimensional metals of special geometry

Abstract

Changes in the metal properties caused by periodic indents in the metal surface were studied within the limit of quantum theory of free electrons. The authors show that due to destructive interference of de Broglie waves, some quantum states inside the low-dimensional metal become quantum mechanically forbidden for free electrons. Wave-vector density in k space is reduced dramatically. At the same time the number of free electrons does not change, as the metal remains electrically neutral. Because of the Pauli exclusion principle, some free electrons must occupy quantum states with higher wave numbers. The Fermi vector and Fermi energy of low-dimensional metal increase, and consequently, the work function decreases. In the experiment, the magnitude of the effect is limited by the roughness of the metal surface. A rough surface causes scattering of the de Broglie waves and compromises their interference. Recent experiments demonstrated a reduction of work function in thin metal films having periodic indents in the surface. Experimental results are in good qualitative agreement with the theory. This effect could exist in any quantum system comprising fermions inside a potential-energy box of special geometry.