# Density matrix approach to photon-assisted tunneling in the transfer Hamiltonian formalism

## Abstract

The transfer Hamiltonian tunneling current is derived in a time-dependent density matrix formulation and is used to examine photon-assisted tunneling. Bardeen's tunneling expression arises as the result of first-order perturbation theory in a mean-field expansion of the density matrix. Photon-assisted tunneling from confined electromagnetic fields in the forbidden tunnel barrier region occurs due to time-varying polarization and wave-function overlap in the gap which leads to a nonzero tunneling current in asymmetric device structures, even in an unbiased state. The photon energy is seen to act as an effective temperature-dependent bias in a uniform barrier asymmetric tunneling example problem. Higher-order terms in the density matrix expansion give rise to multiphoton enhanced tunneling currents that can be considered an extension of nonlinear optics where the nonlinear conductance plays a similar role as the nonlinear susceptibilities in the continuity equations.

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1465798

- Alternate Identifier(s):
- OSTI ID: 1420017

- Report Number(s):
- SAND-2017-11873J

Journal ID: ISSN 2469-9950; PRBMDO; 663116

- Grant/Contract Number:
- AC04-94AL85000; NA0003525

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 7; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Davids, Paul S., and Shank, Joshua.
```*Density matrix approach to photon-assisted tunneling in the transfer Hamiltonian formalism*. United States: N. p., 2018.
Web. doi:10.1103/PhysRevB.97.075411.

```
Davids, Paul S., & Shank, Joshua.
```*Density matrix approach to photon-assisted tunneling in the transfer Hamiltonian formalism*. United States. doi:10.1103/PhysRevB.97.075411.

```
Davids, Paul S., and Shank, Joshua. Fri .
"Density matrix approach to photon-assisted tunneling in the transfer Hamiltonian formalism". United States.
doi:10.1103/PhysRevB.97.075411.
```

```
@article{osti_1465798,
```

title = {Density matrix approach to photon-assisted tunneling in the transfer Hamiltonian formalism},

author = {Davids, Paul S. and Shank, Joshua},

abstractNote = {The transfer Hamiltonian tunneling current is derived in a time-dependent density matrix formulation and is used to examine photon-assisted tunneling. Bardeen's tunneling expression arises as the result of first-order perturbation theory in a mean-field expansion of the density matrix. Photon-assisted tunneling from confined electromagnetic fields in the forbidden tunnel barrier region occurs due to time-varying polarization and wave-function overlap in the gap which leads to a nonzero tunneling current in asymmetric device structures, even in an unbiased state. The photon energy is seen to act as an effective temperature-dependent bias in a uniform barrier asymmetric tunneling example problem. Higher-order terms in the density matrix expansion give rise to multiphoton enhanced tunneling currents that can be considered an extension of nonlinear optics where the nonlinear conductance plays a similar role as the nonlinear susceptibilities in the continuity equations.},

doi = {10.1103/PhysRevB.97.075411},

journal = {Physical Review B},

number = 7,

volume = 97,

place = {United States},

year = {Fri Feb 09 00:00:00 EST 2018},

month = {Fri Feb 09 00:00:00 EST 2018}

}

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