Low temperature resonances in the electron heat capacity and its spectral distribution in finite systems

TL;DR

This paper investigates low-temperature heat capacity resonances in finite 2D and 3D fermionic systems, revealing how spectral distribution peaks relate to single-particle level spacings near the Fermi energy.

Contribution

It introduces the spectral distribution function q to analyze heat capacity contributions, identifying conditions for resonance phenomena linked to level spacings.

Findings

Resonances occur when spectral peaks align with near-Fermi energy levels.

The spectral distribution function q reveals two peaks separated by 2-5T.

Local maxima in heat capacity indicate specific level spacings near the Fermi level.

Abstract

Temperature variations of the heat capacity (C) are studied in a low temperature regime for 2D-, and 3D-systems with N~100-10000 treated as a canonical ensemble of N-noninteracting fermions. The analysis of C is performed by introducing function q, the spectral distribution of C, that gives the contribution of each single-particle state to C. This function has two peaks divided by the energy interval ~(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 Fermi enrgy then C vs T can show a local maximum at Tres. This gives possibility to assess the single-particle level spacings near the Fermi level.