Generalized Bloch theorem for complex periodic potentials: A powerful application to quantum transport calculations
- 11 July 2007
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 76 (3), 035108
- https://doi.org/10.1103/physrevb.76.035108
Abstract
Band-theoretic methods with periodically repeated supercells have been a powerful approach for ground-state electronic structure calculations but have not so far been adapted for quantum transport problems with open boundary conditions. Here, we introduce a generalized Bloch theorem for complex periodic potentials and use a transfer-matrix formulation to cast the transmission probability in a scattering problem with open boundary conditions in terms of the complex wave vectors of a periodic system with absorbing layers, allowing a band technique for quantum transport calculations. The accuracy and utility of the method are demonstrated by the model problems of the transmission of an electron over a square barrier and the scattering of a phonon in an inhomogeneous nanowire. Application to the resistance of a twin boundary in nanocrystalline copper yields excellent agreement with recent experimental data.Keywords
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