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We study transport via edge modes in a disordered 2D topological insulator allowing for the presence of non-protected diffusive channels in addition to the topologically protected edge channels. This scenario can be realized at the interface between two quantum Hall system (class A), in a Weyl semimetal in a magnetic field (Class A) or at the edge of a quantum spin Hall system (class AII). The edge transport is described by a one-dimensional field theory in the form of a supersymmetric non-linear sigma model with a topological term. The transfer-matrix formalism is employed to map the problem to the problem of finding the eigenfunctions of the Laplace operator on a symmetric superspace with an additional vector potential. The latter problem is solved exactly, enabling us to obtain the full counting statistics and mesoscopic conductance fluctuations in the system. Our main finding is that disorder is much more effective in localizing the diffusive (non-protected) channels in the presence of topologically protected ones. This manifests itself as a suppression of the shot noise at scales much shorter than the localization length and the appearance of a gap in the distribution function of transmission eigenvalues close to unit transmission.

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Eslam Khalaf, MPI Stuttgart
Seminarraum Theoretische Physik
Contact: Dmitry Bagrets