Generalized Bloch Theorem for Complex Periodic Potentials  A Powerful Application to Quantum Transport Calculations
Abstract
Bandtheoretic methods with periodically repeated supercells have been a powerful approach for groundstate 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 transfermatrix 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 is 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.
 Authors:
 ORNL
 Vanderbilt University
 Publication Date:
 Research Org.:
 Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 931721
 DOE Contract Number:
 DEAC0500OR22725
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review B; Journal Volume: 76; Journal Issue: 3
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97; 36 MATERIALS SCIENCE; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BOUNDARY CONDITIONS; PERIODICITY; POTENTIALS; BLOCH THEORY; COPPER; NANOSTRUCTURES; ELECTRON TRANSFER; SCATTERING; PHONONS
Citation Formats
Zhang, Xiaoguang, Varga, Kalman, and Pantelides, Sokrates T. Generalized Bloch Theorem for Complex Periodic Potentials  A Powerful Application to Quantum Transport Calculations. United States: N. p., 2007.
Web. doi:10.1103/PhysRevB.76.035108.
Zhang, Xiaoguang, Varga, Kalman, & Pantelides, Sokrates T. Generalized Bloch Theorem for Complex Periodic Potentials  A Powerful Application to Quantum Transport Calculations. United States. doi:10.1103/PhysRevB.76.035108.
Zhang, Xiaoguang, Varga, Kalman, and Pantelides, Sokrates T. Mon .
"Generalized Bloch Theorem for Complex Periodic Potentials  A Powerful Application to Quantum Transport Calculations". United States.
doi:10.1103/PhysRevB.76.035108.
@article{osti_931721,
title = {Generalized Bloch Theorem for Complex Periodic Potentials  A Powerful Application to Quantum Transport Calculations},
author = {Zhang, Xiaoguang and Varga, Kalman and Pantelides, Sokrates T},
abstractNote = {Bandtheoretic methods with periodically repeated supercells have been a powerful approach for groundstate 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 transfermatrix 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 is 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.},
doi = {10.1103/PhysRevB.76.035108},
journal = {Physical Review B},
number = 3,
volume = 76,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}

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