Realization of Symmetry-Enforced Two-Dimensional Dirac Fermions in Nonsymmorphic α-Bismuthene

Abstract

Two-dimensional (2D) Dirac-like electron gases have attracted tremendous research interest ever since the discovery of free-standing graphene [1-3]. The linear energy dispersion and non-trivial Berry phase play the pivotal role in the remarkable electronic, optical, mechanical and chemical properties of 2D Dirac materials [4]. The known 2D Dirac materials are gapless only within certain approximations, for example, in the absence of SOC. Here we report a route to establishing robust Dirac cones in 2D materials with nonsymmorphic crystal lattice. The nonsymmorphic symmetry enforces Dirac-like band dispersions around certain high-symmetry momenta in the presence of SOC [5, 6]. Through µ-ARPES measurements we observe Dirac-like band dispersions in α-bismuthene. The nonsymmorphic lattice symmetry is confirmed by µ-LEED and STM. Our firstprinciples simulations and theoretical topological analysis demonstrate the correspondence between nonsymmorphic symmetry and Dirac states. This mechanism can be straightforwardly generalized to other nonsymmorphic materials. The results open the door for the search of symmetry enforced Dirac fermions in the vast uncharted world of nonsymmorphic 2D materials.

Nucleation and growth of ultrathin Bi films

“…In contrast, the surface buckling was found to be one order of magnitude smaller for Bi(110) islands on the HOPG substrate. Kowalczyk et al: reported the buckling was smaller than 0.004 � 0.0005 nm [36]. The BP-like Bi(110) islands with a thickness of 2 ML (= 1 BL) on the HOPG substrate were observed to display gapless states at the edge, as expected for a 2D topological insulator [30].…”

“…In this respect, the results do not contradict the findings of Lu and co-workers. In a recent experiment, the Bi(110) film on the graphite substrate was reported to have an extremely small buckling less than 0.004 � 0.0005 nm [36]. [51], and icosahedral Al-Pd-Mn quasicrystals [52].…”

Dirac Semimetal Protected by Nonsymmorphic Mirror Symmetries in TPH‐Graphene

“…Although a large number of 2D Dirac semimetals have been proposed, the Dirac cones in these materials are protected by point symmetry operations. So far, the 2D nonsymmorphic Dirac semimetals are rarely reported in the literature, including the HfGeTe family, [47] X 3 SiTe 6 (X ¼ Ta, Nb), [48] α-bismuthene, [49] and MX (M ¼ Sc, Y; X ¼ S, Se, Te). [50] Unfortunately, only α-bismuthene has been experimentally confirmed to be a Dirac semimetal.…”

Fully linear band crossings at high symmetry points in layers: classification and role of spin-orbit coupling and time reversal

“…Square LG 64 supports Dirac cones at X and S only in the presence of SO interaction; this is confirmed by DFT band structure of MX compounds (M = Sc, Y; X = S, Se, Te)[39] as well as in X point (S point was not discussed since the corresponding energies are too far from the Fermi level) in ARPES experiments and DFT calculations in synthesised layered 3D ZrSiS[40] and numerically in monolayer HfGeTe[41]. Experimentally synthesised α-Bismuthene belongs to LG 42 and hosts spinfull Dirac cones at X and Y points, as confirmed by micro-ARPES technique and DFT calculations[42].Among already reported structures with PF or FT dispersions are monolayer GaXY(X = Se, Te; Y = Cl, Br, I), with non-centrosymmetric symmetry LG 32 providing SO caused Dirac cones at X point and PF at Y point. Indeed, fourfold degeneracy at Y point (called Dirac point in…”