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Time-dependent quantum transport: an efficient method based on Liouville-von-Neumann equation for single-electron
Hang Xie1, Feng Jiang, Heng Tian
1Department of Chemistry, The University of Hong Kong, Pofkulam Road, Hong Kong, China.
The Journal of Chemical Physics
|August 3, 2012
Summary
We developed an efficient numerical method to simulate electron transport in atomic chains. This quantum transport approach accurately models transient currents, enabling simulations of larger systems than previously possible.
Area of Science:
- Quantum transport phenomena
- Computational condensed matter physics
Background:
- Accurate simulation of time-dependent quantum transport is crucial for understanding nanoscale electronic devices.
- Existing methods, like master equations, face computational limitations for larger systems.
Purpose of the Study:
- To develop an efficient and accurate numerical algorithm for solving the Liouville-von-Neumann equation for quantum transport.
- To simulate the real-time evolution of the reduced single-electron density matrix in atomic systems.
Main Methods:
- Utilized hierarchical equations of motion for time-dependent quantum transport.
- Employed a Lorentzian-Padè decomposition scheme for the self-energy matrix and Fermi distribution function.
- Simulated transient currents in a linear atomic chain model at the tight-binding level.
Main Results:
- The developed algorithm accurately captures lead spectral functions and dynamic responses.
- Achieved significant computational efficiency, with time scaling cubically with system size and linearly with simulation time.
- Successfully simulated transient currents in systems up to one hundred atoms.
Conclusions:
- The Lorentzian-Padè decomposition scheme provides an efficient and accurate method for quantum transport simulations.
- The approach is generalizable for first-principles simulations of realistic systems using density functional theory.
- Enables the study of quantum transport in larger and more complex nanoscale systems.
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