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Journal of Spectral Theory

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Volume 9, Issue 2, 2019, pp. 569–600
DOI: 10.4171/JST/256

Published online: 2018-10-24

Infinite mass boundary conditions for Dirac operators

Edgardo Stockmeyer[1] and Semjon Vugalter[2]

(1) Pontificia Universidad Católica de Chile, Santiago, Chile
(2) Karlsruhe Institute of Technology, Germany

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. 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 $\Omega$.

Keywords: Dirac operator, Berry Mondragon, graphene, infinite mass boundary conditions

Stockmeyer Edgardo, Vugalter Semjon: Infinite mass boundary conditions for Dirac operators. J. Spectr. Theory 9 (2019), 569-600. doi: 10.4171/JST/256