Quantum spin Hall effect protected by spin U(1) quasi-symmetry
arxiv(2024)
Abstract
Quantum spin Hall (QSH) effect, where electrons with opposite spin channels
are deflected to opposite sides of a two-dimensional system with a quantized
conductance, was believed to be characterized by a nontrivial topological index
Z_2. However, spin mixing effects in realistic materials often lead to
deviation of the spin Hall conductance from exact quantization. In this Letter,
we present a universal symmetry indicator for diagnosing QSH effect in
realistic materials, termed spin U(1) quasi-symmetry. Such a symmetry
eliminates the first-order spin-mixing perturbation and thus protects the
near-quantization of SHC, applicable to time-reversal-preserved cases with
either Z_2=1 or Z_2=0, as well as time-reversal-broken scenarios. We
propose that spin U(1) quasi-symmetry is hidden in the subspace spanned by
the doublets with unquenched orbital momentum and emerges when SOC is present,
which can be realized in 19 crystallographic point groups. Particularly, we
identify a previous overlooked even spin Chern phase with a trivial Z_2
index as an ideal platform for achieving a near-double-quantized SHC, as
exemplified by twisted bilayer transition metal dichalcogenides and monolayer
RuBr_3. Our work offers a new perspective for understanding QSH effect and
significantly expands the material pool for the screening of exemplary material
candidates.
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