Two-dimensional spin-orbit Dirac point in monolayer HfGeTe

Abstract

Dirac points in two-dimensional (2D) materials have been a fascinating subject of research, with graphene as the most prominent example. However, the Dirac points in existing 2D materials, including graphene, are vulnerable against spin-orbit coupling (SOC). Here, based on first-principles calculations and theoretical analysis, we propose a new family of stable 2D materials, the HfGeTefamily monolayers, which represent the first example to host so-called spin-orbit Dirac points (SDPs) close to the Fermi level. These Dirac points are special in that they are formed only under significant SOC, hence they are intrinsically robust against SOC. We show that the existence of a pair of SDPs are dictated by the nonsymmorphic space group symmetry of the system, which are very robust under various types of lattice strains. The energy, the dispersion, and the valley occupation around the Dirac points can be effectively tuned by strain. We construct a low-energy effective model to characterize the Dirac fermions around the SDPs. Furthermore, we find that the material is simultaneously a 2D Z2 topological metal, which possesses nontrivial Z2 invariant in the bulk and spin-helical edge states on the boundary. From the calculated exfoliation energies and mechanical properties, we show that these materials can be readily obtained in experiment from the existing bulk materials. Our result reveals HfGeTe-family monolayers as a promising platform for exploring spin-orbit Dirac fermions and novel topological phases in two-dimensions.

Surface Floating 2D Bands in Layered Nonsymmorphic Semimetals: ZrSiS and Related Compounds

“…Therefore, they lead to completely different behavior at the X point. In a monolayer all bands are still fourfold degenerate, as explicitly shown by Guan et al on a monolayer HfGeTe [52] (isostructural to ZrSiS). A slab calculation, which models the surface more appropriately, shows that the surface bands are only doubly degenerate, while the bulk bands remain fourfold degenerate at X, describing the exact behavior we observe in ZrSiS.…”

Hourglass Weyl loops in two dimensions: Theory and material realization in monolayer GaTeI family

“…As an example, the "Dirac points" in most 2D materials including graphene are in fact not stable under SOC. Young and Kane [36] pointed out that a truly stable Dirac point in 2D requires certain nonsymmorphic symmetry protection, and the first realistic 2D material system with such spin-orbit Dirac points was found by Guan et al [37] in monolayer HfGeTe-family materials. Here, it should be mentioned that an additional difficulty in finding 2D topological materials comes from the structural stability: Existing 2D materials respecting the particular symmetry requirement are quite limited, while materials artificially constructed to follow the symmetry requirement are often structurally unstable.…”

Topological node line semimetal state in two-dimensional tetragonal allotrope of Ge and Sn

“…More intriguingly, single layer Cu 2 Si [38] and CuSe [39] have been experimentally demonstrated to be 2D node line semimetals. Up to now, single layer HfGeTe [40] have been theoretically proposed to be 2D Z 2 topological metal.…”