论文标题
描述石墨烯量子点的四组分运算符的块对基形式
A Block-diagonal form for four-component operators describing Graphene Quantum Dots
论文作者
论文摘要
我们考虑了飞机域中的四组分狄拉克运算符。在适当的边界条件下，这些操作员描述了石墨烯量子点。最通用的边界条件由矩阵定义，具体取决于四个实际参数。对于具有恒定边界参数的运算符，我们表明哈密顿量与两个组件操作员的两个副本相等。这允许将这种类型的运算符的已知结果扩展到四组分情况。作为应用程序，我们从石墨烯的紧密结合模型中识别边界条件，从而在连续限制中引起块对基管操作员。
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.
