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Lead Green's functions from quadratic eigenvalue problems without mode velocity calculations.

Gunnar Thorgilsson1, Sigurdur I Erlingsson1

  • 1Department of Engineering, Reykjavik University, Menntavegi 1, IS-102 Reykjavik, Iceland.

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Summary

This study introduces a new, efficient method for calculating lead self-energies in quantum transport. The approach speeds up calculations by avoiding mode velocity computations, crucial for accurate Green's function analysis.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Computational physics

Background:

  • Accurate calculation of lead self-energies is crucial for quantum transport.
  • Existing methods for self-energy calculation can be computationally intensive.
  • Retarded Green's functions require proper handling of incoming and outgoing modes.

Purpose of the Study:

  • To present an alternative, computationally efficient method for calculating lead self-energies.
  • To improve upon standard approaches for solving quadratic eigenvalue problems in quantum transport.
  • To circumvent the need for calculating mode velocities.

Main Methods:

  • Perturbative analysis of the generalized Schur decomposition.
  • Determining relevant eigenvalues for transmitting modes.
  • Calculating lead Green's functions from translationally invariant Green's functions without explicit mode velocities.

Main Results:

  • The proposed method is more computationally efficient than the standard eigenvalue method when the number of propagating modes exceeds a small threshold.
  • Both eigenvalue methods (ours and the standard one) are more robust than the iterative method.
  • Computational time savings are independent of the imaginary part of the energy.

Conclusions:

  • The presented perturbative method offers a robust and computationally advantageous alternative for calculating lead self-energies.
  • This method enhances the efficiency of quantum transport modeling.
  • It provides a valuable tool for researchers in condensed matter and computational physics.