3,287 research outputs found
Manifestly gauge independent formulations of the Z2 invariants
We use a "monodromy" argument to derive new expressions for the
invariants of topological insulators with time-reversal symmetry in 2 and 3
dimensions. The derivations and the final expressions do not require any gauge
choice and the calculation of the invariants is based entirely on the
projectors onto the occupied states. Explicit numerical tests for tight-binding
models with strongly broken inversion symmetry are presented in 2 and
3-dimensions
Generalized Wannier Functions
We consider single particle Schrodinger operators with a gap in the en ergy
spectrum. We construct a complete, orthonormal basis function set for the inv
ariant space corresponding to the spectrum below the spectral gap, which are
exponentially localized a round a set of closed surfaces of monotonically
increasing sizes. Estimates on the exponential dec ay rate and a discussion of
the geometry of these surfaces is included
Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant
We study the effect of strong disorder in a 3-dimensional topological
insulators with time-reversal symmetry and broken inversion symmetry. Firstly,
using level statistics analysis, we demonstrate the persistence of delocalized
bulk states even at large disorder. The delocalized spectrum is seen to display
the levitation and pair annihilation effect, indicating that the delocalized
states continue to carry the Z2 invariant after the onset of disorder.
Secondly, the Z2 invariant is computed via twisted boundary conditions using an
efficient numerical algorithm. We demonstrate that the Z2 invariant remains
quantized and non-fluctuating even after the spectral gap becomes filled with
dense localized states. In fact, our results indicate that the Z2 invariant
remains quantized until the mobility gap closes or until the Fermi level
touches the mobility edges. Based on such data, we compute the phase diagram of
the Bi2Se3 topological material as function of disorder strength and position
of the Fermi level.Comment: references added; final versio
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