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Quantum transport with strong scattering: Beyond the nonlinear sigma model

Transport properties of a two-band system with spectral nodes are studied in the presence of random scattering. Starting from a Grassmann functional integral, we derive a bosonic representation that is based on random phase fluctuations. Averaging leads to a graphical representation of the correlation function with entangled random walks and 4-vertices. In the strong scattering limit we derive a complex transition amplitude. For the example of two-dimensional Dirac fermions we obtain a localization length proportional to the inverse scattering rate.

preprint2014arXivOpen access
K. Ziegler
cond-mat.dis-nn
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K. Ziegler

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