We study three-dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where a single Z2 topological invariant governs the effect, in three dimensions there are 4 invariants distinguishing 16 phases with two general classes: weak (WTI) and strong (STI) topological insulators. The WTI are like layered 2D QSH states, but are destroyed by disorder. The STI are robust and lead to novel "topological metal" surface states. We introduce a tight binding model which realizes the WTI and STI phases, and we discuss its relevance to real materials, including bismuth.
The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge st...
We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluri...
Recent experimental advances in controlling dissipation have brought about\nunprecedented flexibility in engineering non-Hermitian Hamiltonians in open\nclassical and quantum sy...
We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two dimensional insulators. It is shown that whenever there is a to...
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped b...
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