Fermi gas energetics in low-dimensional metals of spessial geometry
  Changes in the metal properties, caused by periodic indents in the metal surface, have been studied within the limit of quantum theory of free electrons. It was shown 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, reduce dramatically. At the same time, number of free electrons does not change, as metal remains electrically neutral. Because of Pauli exclusion principle some free electrons have to occupy quantum states with higher wave numbers. Fermi vector and Fermi energy of low-dimensional metal increase and consequently its work function decrease. In experiment, magnitude of the effect is limited by the roughness of metal surface. Rough surface causes scattering of the de Broglie waves and compromise their interference. Recent experiments demonstrated 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. 
Avto Tavkhelidze, Vasiko Svanidze and Irakli Noselidze