Low temperature resonances in the fermion heat capacity of finite systems

Abstract

Temperature variations of the heat capacity (C) are studied in a low temperature regime T < ϵf/N (ϵf is the Fermi energy) for 2D-, and 3D-systems with N∼ 102 ÷ 104 treated as a canonical ensemble of N-noninteracting fermions. The analysis of C is performed by introducing a function ρ(ϵ), the spectral distribution of C that gives the contribution of each single-particle state to C. The function ρ(ϵ) has two peaks divided by the energy interval Δ ϵ ≈ (2 ÷ 5) T. If at some temperature Tres there takes place a resonance i.e. the positions of these peaks coincide with energies of two levels nearest to ϵF then C vs T shows a local maximum i.e. Tres is determined by single-particle level spacings near the Fermi level.