Surface contribution to electronic density of states, heat capacity, and spin susceptibility

The surface contributions to the electronic heat capacity Cₑₗˢ and spin susceptibility χˢ are, respectively, Cₑₗˢ=(1/3)A[γ(kF)-π4]kB²T and χˢ=(μB²π²)A[γ(kF)-π4] for any semi-infinite free-electron model, where γ(kF) is a phase shift determined by the surface potential. The electronic surface heat capacity thus can provide some information about the surface potential seen by electrons (or with many-body effects included, electron quasiparticles).