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

Davids, Paul S.; Shank, Joshua

doi:10.1103/PhysRevB.97.075411

Title: 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:

Davids, Paul S. ^[1]; Shank, Joshua ^[1]

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

Publication Date:: 2018-02-09

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; TRN: US1902559

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

Resource Type:: 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.

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

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                    Davids, Paul S., and Shank, Joshua. Fri .  
"Density matrix approach to photon-assisted tunneling in the transfer Hamiltonian formalism".  United States.  https://doi.org/10.1103/PhysRevB.97.075411.  https://www.osti.gov/servlets/purl/1465798.

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@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         = {2018},

  month        = {2}

}

Copy to clipboard

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https://doi.org/10.1103/PhysRevB.97.075411

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Cited by: 7 works

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Figures / Tables:

FIG. 1.: Illustration transfer interaction for a simple 1D potential barrier. (a) The schematic shows the right and left wave functions, $\phi$_$k$ and $\psi$_$q$, respectively. These become evanescent in the potential barrier region. The overlap in this region leads to the tunneling current. (b) Energy level diagram showing the onemore »

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Works referencing / citing this record:

Electrical power generation from moderate-temperature radiative thermal sources
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Figures / Tables found in this record:

FIG. 1. (p. 5)

FIG. 2. (p. 6)

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Similar Records

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

Abstract

Citation Formats

Figures / Tables:

Zero-Bias Anomalies and Boson-Assisted Tunneling Through Quantum Dots journal, March 1996

Calculation of transmission tunneling current across arbitrary potential barriers journal, February 1987

Multiphoton Process Observed in the Interaction of Microwave Fields with the Tunneling between Superconductor Films journal, January 1963

Infrared rectification in a nanoantenna-coupled metal-oxide-semiconductor tunnel diode journal, September 2015

Superconductive Tunneling journal, April 1962

Theory of Tunneling journal, January 1961

Powerful and efficient energy harvester with resonant-tunneling quantum dots journal, February 2013

Tunneling from a Many-Particle Point of View journal, August 1963

Electron Tunneling Between Two Superconductors journal, November 1960

Kondo-assisted and resonant tunneling via a single charge trap: A realization of the Anderson model out of equilibrium journal, May 1994

Tunneling Into Superconductors journal, August 1962

Quantum detection at millimeter wavelengths journal, October 1985

Energy Gap in Superconductors Measured by Electron Tunneling journal, August 1960

Direct calculation of the tunneling current journal, June 1971

Gate tunneling currents in ultrathin oxide metal–oxide–silicon transistors journal, February 2001

Long journey into tunneling journal, April 1974

Theory of Many-Body Effects in Tunneling journal, October 1969

Photon-Phonon-Enhanced Infrared Rectification in a Two-Dimensional Nanoantenna-Coupled Tunnel Diode journal, December 2016

Resonant tunneling through ultrasmall quantum dots: Zero-bias anomalies, magnetic-field dependence, and boson-assisted transport journal, December 1996

The MOM tunneling diode: Theoretical estimate of its performance at microwave and infrared frequencies journal, October 1978

Tunneling matrix elements in three-dimensional space: The derivative rule and the sum rule journal, November 1990

Theory of tunneling into interface states journal, November 1970

Quantum Interaction of Microwave Radiation with Tunneling Between Superconductors journal, March 1962

Thermoelectric energy harvesting with quantum dots journal, December 2014

Thermionic Emission, Field Emission, and the Transition Region journal, June 1956

The Wentzel-Brillouin-Kramers Method of Solving the Wave Equation journal, September 1932

Photon-assisted transport in semiconductor nanostructures journal, May 2004

Tunneling from an Independent-Particle Point of View journal, July 1961

Physics of Semiconductor Devices book, January 2007

Physics of Semiconductor Devices journal, October 1990

Long journey into tunneling journal, January 1974

Quantum tunneling theory of Cooper pairs as bosonic particles journal, April 2021

Long Journey into Tunneling journal, March 1974

Zero-bias anomalies and boson-assisted tunneling through quantum dots text, January 1996

Physics of Semiconductor Devices journal, June 1970

Physics of Semiconductor Devices book, January 2015

Photon-assisted transport in semiconductor nanostructures text, January 2003

Electrical power generation from moderate-temperature radiative thermal sources journal, February 2020

Power generation from a radiative thermal source using a large-area infrared rectenna text, January 2018

Zero-Bias Anomalies and Boson-Assisted Tunneling Through Quantum Dots
journal, March 1996

Calculation of transmission tunneling current across arbitrary potential barriers
journal, February 1987

Multiphoton Process Observed in the Interaction of Microwave Fields with the Tunneling between Superconductor Films
journal, January 1963

Infrared rectification in a nanoantenna-coupled metal-oxide-semiconductor tunnel diode
journal, September 2015

Superconductive Tunneling
journal, April 1962

Theory of Tunneling
journal, January 1961

Powerful and efficient energy harvester with resonant-tunneling quantum dots
journal, February 2013

Tunneling from a Many-Particle Point of View
journal, August 1963

Electron Tunneling Between Two Superconductors
journal, November 1960

Kondo-assisted and resonant tunneling via a single charge trap: A realization of the Anderson model out of equilibrium
journal, May 1994

Tunneling Into Superconductors
journal, August 1962

Quantum detection at millimeter wavelengths
journal, October 1985

Energy Gap in Superconductors Measured by Electron Tunneling
journal, August 1960

Direct calculation of the tunneling current
journal, June 1971

Gate tunneling currents in ultrathin oxide metal–oxide–silicon transistors
journal, February 2001

Long journey into tunneling
journal, April 1974

Theory of Many-Body Effects in Tunneling
journal, October 1969

Photon-Phonon-Enhanced Infrared Rectification in a Two-Dimensional Nanoantenna-Coupled Tunnel Diode
journal, December 2016

Resonant tunneling through ultrasmall quantum dots: Zero-bias anomalies, magnetic-field dependence, and boson-assisted transport
journal, December 1996

The MOM tunneling diode: Theoretical estimate of its performance at microwave and infrared frequencies
journal, October 1978

Tunneling matrix elements in three-dimensional space: The derivative rule and the sum rule
journal, November 1990

Theory of tunneling into interface states
journal, November 1970

Quantum Interaction of Microwave Radiation with Tunneling Between Superconductors
journal, March 1962

Thermoelectric energy harvesting with quantum dots
journal, December 2014

Thermionic Emission, Field Emission, and the Transition Region
journal, June 1956

The Wentzel-Brillouin-Kramers Method of Solving the Wave Equation
journal, September 1932

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journal, May 2004

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journal, July 1961

Physics of Semiconductor Devices
book, January 2007

Physics of Semiconductor Devices
journal, October 1990

Long journey into tunneling
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Quantum tunneling theory of Cooper pairs as bosonic particles
journal, April 2021

Long Journey into Tunneling
journal, March 1974

Zero-bias anomalies and boson-assisted tunneling through quantum dots
text, January 1996

Physics of Semiconductor Devices
journal, June 1970

Physics of Semiconductor Devices
book, January 2015

Photon-assisted transport in semiconductor nanostructures
text, January 2003

Electrical power generation from moderate-temperature radiative thermal sources
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Power generation from a radiative thermal source using a large-area infrared rectenna
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