Infinite mass boundary conditions for Dirac operators

TL;DR

This paper investigates the mathematical properties of a Dirac operator modeling graphene quantum dots, showing it as a limit of operators with large mass outside the domain, which helps understand boundary effects in quantum systems.

Contribution

It provides a rigorous analysis of the self-adjoint realization of the Dirac operator with infinite mass boundary conditions, connecting it to operators with large mass terms outside the domain.

Findings

The operator is the limit of Dirac operators with large outside mass as M approaches infinity.

Establishes a rigorous mathematical framework for boundary conditions in graphene quantum dots.

Provides insights into the spectral properties of Dirac operators with infinite mass boundaries.

Abstract

We study a self-adjoint realization of a massless Dirac operator on a bounded connected domain $\Omega\subset \mathbb{R}^2$ which is frequently used to model graphene quantum dots. In particular, we show that this operator is the limit, as $M\to \infty$, of a Dirac operator defined on the whole plane, with a mass term of size $M$ supported outside $\Omega$.