Electronic correlations on a metallic nanosphere

TL;DR

This paper derives explicit formulas for electron correlation functions on a nanoscale spherical surface, highlighting how spherical geometry influences quantum correlations and coherence effects.

Contribution

It provides closed-form expressions for key electron correlations on a nanosphere and compares these with planar geometries, revealing geometry-dependent quantum effects.

Findings

Correlation functions are enhanced at antipodal points on the sphere.

Quantum coherence effects diminish when sphere radius exceeds temperature coherence length.

Explicit formulas for RKKY, Cooper loop, and density-density correlations are derived.

Abstract

We consider the correlation functions in a gas of electrons moving within a thin layer on the surface of nanosize sphere. A closed form of expressions for the RKKY indirect exchange, superconducting Cooper loop and `density-density' correlation function is obtained. The systematic comparison with planar results is made, the effects of spherical geometry are outlined. The quantum coherence of electrons leads to the enhancement of all correlations for the points--antipodes on the sphere. This effect is lost when the radius of the sphere exceeds the temperature coherence length.