Excitonic physics in a Dirac quantum dot

TL;DR

This paper investigates vacuum polarization and excitonic effects in a circular Dirac quantum dot, revealing a critical Coulomb interaction strength where the ground state exhibits a crossover and degeneracy involving excitonic states.

Contribution

It introduces a simplified model for excitonic physics in Dirac quantum dots, identifying a critical interaction strength and describing the ground state as an excitonic superposition.

Findings

At a critical Coulomb strength of approximately 1.05, the lowest energy level is half-filled.

The ground state is a superposition of excitonic states forming an evolving excitonic cloud.

Degeneracy occurs between the ground state and an intervalley excitonic state at the critical point.

Abstract

We present a description of vacuum polarization in a circular Dirac quantum dot in two spatial dimensions assuming $\alpha$ - the relative strength of the Coulomb interaction small enough to render an approximation with a single electron (hole) lowest energy level relevant. Applying this approximation, we find that for $ \alpha_c \approx 1.05$ the lowest level is half-filled irrespective of the number of flavors that are present. The ground state can be represented as a superposition of particular (even number) excitonic states which constitute an excitonic cloud that evolves in a crossover manner. The ground state is degenerate with an intervalley excitonic state at $ \alpha_c \approx 1.05$, a critical strength, that in our approximation marks a point with single electron and exciton resonances.