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T. Fabian, F. Libisch:
"Inelastic Scattering in Tight-Binding";
Poster: "Novel Materials and Superconductors" Workshop, Obertraun, Obertraun; 11.02.2018 - 17.02.2018.

We present an approximate but highly efficient method
for quantum transport calculations. Our approach is based on
the eigenstates of the infinite waveguide, the so-called modes. By
projecting the scattering problem onto the propagating and selected
evanescent modes, we reduce the system size and improve the speed
drastically. We find and implement a numerically stable procedure
even for non-separable Hamiltonians , which has not been done
before.
We test our algorithm on graphene scattering structures. For
simple geometries and weak magnetic fields, the approximation is
in very good agreement with the exact calculations. The mode-basis
approach is not valid whenever the assumption of propagation in one
direction and quantized modes in the other direction fails.
We exploit the speed of the mode basis to couple the equations for
a discrete set of energies spaced E = ~ω apart. This serves as a model
for inelastic electron-phonon scattering on optical phonons with
frequency ω. We find that resulting transmission curves typically get
smeared out, as peaks in the transmission curve now appear multiple
times. Conversely, dips in the transmission remain unaffected.
This work is a step towards understanding the effects of realistic
experimental conditions on ideally fully coherent quantum mechanical
systems.