Relativistic embedding method: the transfer matrix, complex band structures, transport, and surface calculations

We develop the relativistic embedding method for electronic-structure studies. An expression for the transfer matrix is derived in terms of the Green’s function of the Dirac equation, and we outline its evaluation within the relativistic embedding framework. The transfer matrix is used to find the complex band structure and an embedding potential that can replace a semi-infinite substrate in ab initio electronic-structure calculations. We show that this embedding potential may be used to define an operator that gives the current flowing across a surface; the eigenstates of which define channel functions for conductance studies, and which enable the derivation of a relativistic generalization of the known expression for the conductance across a nanodevice connected to leads. Finally, the application of the embedding potential in relativistic electronic-structure studies is illustrated using an electronlike basis to solve the surface-embedded Dirac equation for Au(111). A calculation with a single layer of atoms within the embedded volume correctly predicts the magnitude of the Rashba-type splitting of the zone center surface state.