Quantum and Many-Body Effects on the Capacitance of a Quantum Dot

TL;DR

This paper provides an exact quantum mechanical analysis of the self-capacitance of a spherical quantum dot under extreme confinement, revealing oscillations and scaling behaviors that support semiclassical models at nanoscale.

Contribution

It introduces an exact finite size calculation of quantum and many-body effects on quantum dot capacitance, demonstrating the validity of semiclassical Coulomb models at very small scales.

Findings

Self-capacitance oscillates with electron number near classical values

Electrostatic energy approaches zero at N=1

Energy scales as e^2 N(N-1)

Abstract

We calculate exactly, using finite size techniques, the quantum mechanical and many-body effects to the self-capacitance of a spherical quantum dot in the regime of extreme confinement, where the radius of the sphere is much smaller than the effective Bohr radius. We find that the self-capacitance oscillates as a function of the number of electrons close to its classical value. We also find that the electrostatic energy extrapolates to zero when $N=1$, suggesting that the energy scales like $e^{2}N(N-1)$. This establishes, at least for this configuration, that the semiclassical description of Coulomb charging effects in terms of capacitances holds to a good approximation even at very small scales.