3,184 research outputs found
Non-Commutative Tools for Topological Insulators
This paper reviews several analytic tools for the field of topological
insulators, developed with the aid of non-commutative calculus and geometry.
The set of tools includes bulk topological invariants defined directly in the
thermodynamic limit and in the presence of disorder, whose robustness is shown
to have non-trivial physical consequences for the bulk states. The set of tools
also includes a general relation between the current of an observable and its
edge index, relation that can be used to investigate the robustness of the edge
states against disorder. The paper focuses on the motivations behind creating
such tools and on how to use them.Comment: Final version (some arguments were corrected
Three-dimensional phase diagram of disordered HgTe/CdTe Quantum spin-Hall wells
We compute the phase diagram of the HgTe/CdTe quantum wells in the 3
dimensional (3D) parameter space of Dirac mass, Fermi level and disorder
strength. The phase diagram reveals the Quantum spin-Hall, the metallic and the
normal insulating phases. The phase boundary of the Quantum spin-Hall state is
shown to be strongly deformed by the disorder. Taking specific cuts into this
3D phase diagram, we recover the so called topological Anderson insulator (TAI)
phase, but now we can demonstrate explicitly that TAI is not a distinct phase
and instead it is part of the Quantum spin-Hall phase. The calculations are
performed with -conserving and -nonconserving Hamiltonians.Comment: Final for
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