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Abstract:
Recently the quantum spin Hall effect was theoretically predicted and
experimentally realized in quantum wells based on the binary
semiconductor HgTe (refs 1-3). The quantum spin Hall state and
topological insulators are new states of quantum matter interesting for
both fundamental condensed-matter physics and material science(1-11).
Many Heusler compounds with C1(b) structure are ternary semiconductors
that are structurally and electronically related to the binary
semiconductors. The diversity of Heusler materials opens wide
possibilities for tuning the bandgap and setting the desired band
inversion by choosing compounds with appropriate hybridization strength
(by the lattice parameter) and magnitude of spin-orbit coupling (by the
atomic charge). Based on first-principle calculations we demonstrate
that around 50 Heusler compounds show band inversion similar to that of
HgTe. The topological state in these zero-gap semiconductors can be
created by applying strain or by designing an appropriate quantum-well
structure, similar to the case of HgTe. Many of these ternary zero-gap
semiconductors (LnAuPb, LnPdBi, LnPtSb and LnPtBi) contain the
rare-earth element Ln, which can realize additional properties ranging
from superconductivity (for example LaPtBi; ref. 12) to magnetism (for
example GdPtBi; ref. 13) and heavy fermion behaviour (for example
YbPtBi; ref. 14). These properties can open new research directions in
realizing the quantized anomalous Hall effect and topological
superconductors.
