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Title: Generalized Bloch Theorem for Complex Periodic Potentials - A Powerful Application to Quantum Transport Calculations

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 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:
 [1];  [2];  [1]
  1. ORNL
  2. 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:  
DE-AC05-00OR22725
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 = {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 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}
}