title: Real-space finite-difference calculation method of generalized Bloch wave functions and complex band structures with reduced computational cost.
abstract: Generalized Bloch wave functions of bulk structures, which are composed of not only propagating waves but also decaying and growing evanescent waves, are known to be essential for defining the open boundary conditions in the calculations of the electronic surface states and scattering wave functions of surface and junction structures. Electronic complex band structures being derived from the generalized Bloch wave functions are also essential for studying bound states of the surface and junction structures, which do not appear in conventional band structures. We present a novel calculation method to obtain the generalized Bloch wave functions of periodic bulk structures by solving a generalized eigenvalue problem, whose dimension is drastically reduced in comparison with the conventional generalized eigenvalue problem derived by Fujimoto and Hirose [Phys. Rev. B 67, 195315 (2003)]. The generalized eigenvalue problem derived in this work is even mathematically equivalent to the conventional one, and, thus, we reduce computational cost for solving the eigenvalue problem considerably without any approximation and losing the strictness of the formulations. To exhibit the performance of the present method, we demonstrate practical calculations of electronic complex band structures and electron transport properties of Al and Cu nanoscale systems. Moreover, employing atom-structured electrodes and jellium-approximated ones for both of the Al and Si monatomic chains, we investigate how much the electron transport properties are unphysically affected by the jellium parts.
authors.affiliation: Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany.
authors.forename: Shigeru
authors.initials: S
authors.lastname: Tsukamoto
authors.affiliation: Graduate School of Engineering, Osaka University, Suita, Osaka 565-0871, Japan.
authors.forename: Kikuji
authors.initials: K
authors.lastname: Hirose
authors.affiliation: Peter Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, D-52425 Jülich, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Blügel
mesh_terms: D000535:Aluminum / Q000737:chemistry; D003300:Copper / Q000737:chemistry; D004579:Electron Transport; D053768:Metal Nanoparticles / Q000737:chemistry; D008958:Models, Molecular; D008968:Molecular Conformation; D013997:Time Factors
chemical_list: D003300:Copper; D000535:Aluminum