Far-infrared edge modes in quantum dots

TL;DR

This paper explores the behavior of edge modes in quantum dots under magnetic fields using a microscopic approach, revealing classical dispersion laws modified by quantum and size effects.

Contribution

It introduces a variational microscopic method for analyzing edge modes in axially symmetric quantum dots, incorporating sum rules and quantum effects.

Findings

Classical hydrodynamic dispersion law for edge waves is valid with quantum corrections.

Sum rules for edge modes are derived within the local Current Density Functional Theory.

Quantum and finite size effects modify the classical dispersion relation.

Abstract

We have investigated edge modes of different multipolarity sustained by quantum dots submitted to external magnetic fields. We present a microscopic description based on a variational solution of the equation of motion for any axially symmetric confining potential and multipole mode. Numerical results for dots with different number of electrons whose ground-state is described within a local Current Density Functional Theory are discussed. Two sum rules, which are exact within this theory, are derived. In the limit of a large neutral dot at B=0, we have shown that the classical hydrodynamic dispersion law for edge waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size effects are taken into account.