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

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