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

doi:10.1103/PhysRevB.76.035108

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

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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:

Zhang, Xiaoguang ^[1]; Varga, Kalman ^[2]; Pantelides, Sokrates T ^[1]

ORNL
Vanderbilt University

Publication Date:: Mon Jan 01 00:00:00 EST 2007

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.

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                    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.

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                    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.

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@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}

}

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DOI: 10.1103/PhysRevB.76.035108

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