Topology vs. Anderson localization: non-perturbative solutions in one dimension

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Altland, Alexander; Bagrets, Dmitry; Kamenev, Alex;
  • Related identifiers: doi: 10.1103/PhysRevB.91.085429
  • Subject: Condensed Matter - Mesoscale and Nanoscale Physics | Condensed Matter - Disordered Systems and Neural Networks

We present an analytic theory of quantum criticality in quasi one-dimensional topological Anderson insulators. We describe these systems in terms of two parameters $(g,\chi)$ representing localization and topological properties, respectively. Certain critical values of ... View more
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    55 references, page 1 of 6

    3. Our goal is to calculate transfer matrix element between two neighboring grains e S(Q( );Q~( )), where ; = denote two parts of the manifold, and and in the o -diagonal terms we kept a term / ~2. We rst evaluate ~ integral in the Gaussian approximation near ~ = 0:

    1 1 2g cosh2 y

    2 sinh2 y 4.

    4 sin y1 sinh y0 sin 2 (ei 3.

    1 We here consider a topological superconductor as a thermal insulator, i.e. our usage of the term `insulator' encompasses both conventional insulators, and superconductors.

    2 M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).

    3 B. A. Bernevig and T. L. Hughes, Topological Insulators and Topological Superconductors (Princeton Press, 2013).

    4 As a matter of principle, the momentum space description can be maintained at the expense of extending the unit cell from atomistic scales, a, to the system size, L (a disordered system is periodic in its own size.) However, the price to be payed is that the topological information is now encoded in the con guration dependent structure of O((L=a)d) bands. While the multi-band framework may still be accessible by numerical means, it is less suited for analytical theory building.

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