A Block-diagonal form for four-component operators describing Graphene Quantum Dots

Hanne van den Bosch, Rafael D. Benguria, Edgardo Stockmeyer, Cristobal Vallejos

Publication date: 14 November 2022

Abstract: We consider four-component Dirac operators on domains in the plane. With suitable boundary conditions, these operators describe graphene quantum dots. The most general boundary conditions are defined by a matrix depending on four real parameters. For operators with constant boundary parameters we show that the Hamiltonian is unitary equivalent to two copies of the two-component operator. This allows to extend the known results for this type of operators to the four-component case. As an application, we identify the boundary conditions from the tight-binding model for graphene that give rise to a block-diagonal operator in the continuum limit.

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