Determining Transport Properties of Complex Multiterminal Systems: S‐Matrix of General Tight‐Binding Periodic Leads

Calculation of the scattering matrix (S‐matrix) of a system allows direct determination of its transport properties. Within the scattering theory, S‐matrices relate amplitudes of incoming and outgoing waves in semi‐infinite leads attached to a scattering region. Recently, an assembly method to calculate S‐matrices of arbitrary tight‐binding systems connected to atomic chains has been proposed, were the S‐matrices of subsystems are used to obtain S‐matrix of the total system. In this paper, a new efficient method to obtain S‐matrices of general periodic leads is established, which can be used in the mentioned assembly method, allowing to address coherent quantum transport of arbitrary multiterminal systems with complex geometries trough Landauer‐Büttiker formalism. In addition, a new method to determine extended‐state band structures of general infinite periodic wires is presented, which exploits properties of the S‐matrix. Finally, these methods are used to obtain band structure of graphene arm‐chair and zig‐zag nanoribbons and transmission functions in three terminal Z‐shaped graphene nanoribbon structures.