Thermodynamics of ultrasmall metallic grains in the presence of pairing and exchange correlations: Mesoscopic fluctuations

TL;DR

This paper investigates how exchange and pairing correlations influence thermodynamic fluctuations in ultrasmall metallic grains, revealing how these interactions shift and modify observable effects like heat capacity and spin susceptibility.

Contribution

It introduces a comprehensive model combining exchange and pairing effects using advanced approximation methods to analyze mesoscopic fluctuations in chaotic metallic grains.

Findings

Exchange shifts parity effects to lower temperatures.

Exchange suppresses parity effects when pairing gap is small.

Large spin susceptibility fluctuations occur with exchange correlations.

Abstract

We study the mesoscopic fluctuations of thermodynamic observables in a nanosized metallic grain in which the single-particle dynamics are chaotic and the dimensionless Thouless conductance is large. Such a grain is modeled by the universal Hamiltonian describing the competition between exchange and pairing correlations. The exchange term is taken into account exactly by a spin-projection method, and the pairing term is treated in the static-path approximation together with small-amplitude quantal fluctuations around each static fluctuation of the pairing field. Odd-even particle-number effects induced by pairing correlations are included using a number-parity projection. We find that the exchange interaction shifts the number-parity effects in the heat capacity and spin susceptibility to lower temperatures. In the regime where the pairing gap is similar to or smaller than the single-particle mean level spacing, these number-parity effects are suppressed by exchange correlations, and the fluctuations of the spin susceptibility may be particularly large. However, for larger values of the pairing gap, the number-parity effects may be enhanced by exchange correlations.