# 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:

- 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:
- 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}

}