Abstract
Two-dimensional (2D) Stiefel-Whitney insulator (SWI), which is characterized by the second Stiefel-Whitney class, is a class of topological phases with zero Berry curvature. As an intriguing topological state, it has been well studied in theory but seldom realized in realistic materials. Here we propose that a large class of liganded Xenes, i.e., hydrogenated and halogenated 2D group-IV honeycomb lattices, are 2D SWIs. The nontrivial topology of liganded Xenes is identified by the bulk topological invariant and the existence of protected corner states. Moreover, the large and tunable bandgap (up to 3.5 eV) of liganded Xenes will facilitate the experimental characterization of the 2D SWI phase. Our findings not only provide abundant realistic material candidates that are experimentally feasible but also draw more fundamental research interest towards the topological physics associated with Stiefel-Whitney class in the absence of Berry curvature.
Highlights
With the rapid progress of topological states, the concept of Berry curvature and associated topological invariants, such as Chern numbers[1,2], mirror or spin Chern numbers[3,4,5,6,7], and Fu-Kane invariants[8,9], have been widely applied to condensed matter physics
Different from topological states associated with Chern class which possess topological boundary states due to the bulk-boundary correspondence, a 2D SW insulator (SWI) features topologically protected corner states in the presence of additional chiral symmetry, indicating it is a special class of 2D second-order topological insulators (SOTIs)[17,18,19,20,21]
We extend the theoretical prediction and experimental applicability of the topological physics associated with SW class by recognizing that the liganded Xene family XL (X=C, Si, Ge, Sn, L=H, F, Cl, Br, I), a large, well studied, and readily synthesizable class of materials[48,49,50,51], are 2D SWIs
Summary
With the rapid progress of topological states, the concept of Berry curvature and associated topological invariants, such as Chern numbers[1,2], mirror or spin Chern numbers[3,4,5,6,7], and Fu-Kane invariants[8,9], have been widely applied to condensed matter physics. A class of topological state with zero Berry curvature, which is characterized by the Stiefel-Whitney (SW) class, was proposed in spinless systems with space-time inversion symmetry IST = PT or C2zT, where P, T, and C2z are spatial inversion, time-reversal, and two-fold rotation symmetry, respectively[10,11,12,13,14,15]. This is the so-called SW insulator (SWI), which is topologically distinguished by a different topological invariant, i.e., the second SW number w216. In the field of 2D materials, a monoelemental class of 2D honeycomb crystals termed Xenes (X refers to C, Si, Ge, Sn, and so on)[33,34,35] have attracted tremendous attention as they provide an ideal platform to explore various topological physics
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