Room temperature quantum spin Hall states in two-dimensional crystals composed of pentagonal rings and their quantum wells

Abstract

Quantum spin Hall (QSH) insulators are a peculiar phase of matter exhibiting excellent quantum transport properties with potential applications in lower-power-consuming electronic devices. Currently, among all predicted or synthesized QSH insulators, square and hexagonal atomic rings are the dominant structural motifs, and QSH insulators composed of pentagonal rings have not yet been reported. Here, based on first-principles calculations, we predict a family of large-gap QSH insulators in SnX 2 (X = S, Se, or Te) two-dimensional (2D) crystals by the direct calculation of Z 2 topological invariants and edge states. Remarkably, in contrast to all known QSH insulators, the QSH insulators predicted here are composed entirely of pentagonal rings. Moreover, these systems can produce sizeable nontrivial gaps ranging from 121 to 224 meV, which is sufficiently large for practical applications at room temperature. Additionally, we propose a quantum well by sandwiching an SnTe 2 2D crystal between two BiOBiS 2 sheets and reveal that the considered 2D crystal remains topologically nontrivial with a sizeable gap. This finding demonstrates the robustness of its band topology against the effect of the substrate and provides a viable method for further experimental studies. The resultant Dirac surface states in three-dimensional (3D) TIs as well as the helical edge states in two-dimensional (2D) TIs are spin locked because of protection by time-reversal symmetry; thus, they are robust against perturbations. Particularly in 2D TIs, also known as quantum spin Hall (QSH) insulators, 3,4 all the low-energy scatterings of the edge states caused by the nonmagnetic defects are completely forbidden because the edge electrons can only propagate along two directions with opposite spins, which makes 2D TIs more suitable for lowpower-consuming applications than 3D TIs. Unfortunately, the material realization of 2D TIs is challenging: while 3D TIs have been discovered in many materials, such as the Bi 2 Se 3 family, 5,6 the experimental realization of 2D TIs is thus far limited to the HgTe/ CdTe 7 and InAs/GaSb 8 quantum wells. Moreover, the QSH effect in these two quantum wells can occur only at ultralow temperature (o10 K) because of their extremely small bulk band gaps, and this limitation greatly obstructs their possible applications. The search for new 2D TIs with large band gaps that could support room temperature applications has thus become critically important.

From node-line semimetals to large-gap quantum spin Hall states in a family of pentagonal group-IVA chalcogenide

“…It is known that, from S atom to Te atom (also from C atom to Pb atom), the atomic radius becomes larger in the order of S < Se < Te (C < Si < Ge < Sn < Pb), thus the lattice constants and bond lengths should be increased correspondingly. As shown in the top view, one can see those 2D p-IVX 2 crystals are akin to the structure of experimentally identified pentagraphene and are composed completely of the pentagonal rings [46][47][48]. The summary of the topological states of the full 15 different p-IVX 2 based on HSE06 method is given in Fig.…”

Geometrically frustrated Cairo pentagonal lattice stripe with Ising and Heisenberg exchange interactions

“…Analogously, we can obtain the corresponding states | s3 s4 ∼ s5 s6 , by the same relation to that (11)(12)(13)(14), consequently the eigenvalues are expressed merely by substituting J → J ′ , ∆ → ∆ ′ and {s 1 , s 2 , s 3 , s 4 } → {s 6 , s 4 , s 3 , s 5 }. Thus, the energy eigenvalues become…”

“…There are even more new compounds studied with the same structure, such the 2D crystals SnX 2 (X = S, Se, or Te) [11] which have been investigated using a first-principle calculation. Another investigation was carried out by Chainani and Sheshadri [12] for the Ising model with Cairo pentagonal pattern with a nearest-neighbor antiferromagnetic coupling.…”

Robust quantum spin Hall state and quantum anomalous Hall state in graphenelike BC3 with adatoms

“…Hence hunting of feasible roomtemperature QSH insulators is of great significance for practical applications. To this end, extensive effort has been devoted and many strategies to obtain the 2D TIs with large nontrivial gaps have been followed [13][14][15][16][17][18].…”