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Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions | | Lukas Kimme
; Timo Hyart
; | | Date: |
20 Oct 2015 | | Abstract: | We consider the effects of impurities on topological insulators and
superconductors. We start by identifying the general conditions under which the
eigenenergies of an arbitrary Hamiltonian H belonging to one of the
Altland-Zirnbauer symmetry classes undergo a robust zero energy crossing as a
function of an external parameter which can be, for example, the impurity
strength. We define a generalized root of det H, and use it to predict or rule
out robust zero-energy crossings in all symmetry classes. We complement this
result with an analysis based on almost degenerate perturbation theory, which
allows a derivation of the asymptotic low-energy behavior of the ensemble
averaged density of states $
ho sim E^alpha$ for all symmetry classes, and
makes it transparent that the exponent alpha does not depend on the choice of
the random matrix ensemble. Finally, we show that a lattice of impurities can
drive a topologically trivial system into a nontrivial phase, and in particular
we demonstrate that impurity bands carrying extremely large Chern numbers can
appear in different symmetry classes of two-dimensional topological insulators
and superconductors. We use the generalized root of det H(k) to reveal a
spiderweb-like momentum space structure of the energy gap closings that
separate the topologically distinct phases in p_x + i p_y superconductors in
the presence of an impurity lattice. | | Source: | arXiv, 1510.5909 | | Services: | Forum | Review | PDF | Favorites | |
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