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 HfGeTe-family 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 ${\mathbb{Z}}_2$ topological metal, which possesses nontrivial ${\mathbb{Z}}_2$ 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.

9 pages, 6 figures

References in corpus (14)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Topological Insulators with Inversion Symmetry
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Spin-orbit gap of graphene: First-principles calculations
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Macroscopic graphene membranes and their extraordinary stiffness
• Dirac fermions in borophene
• The Rare Two-Dimensional Materials with Dirac Cones
• Co-existence of size-dependent and size-independent thermal conductivities in single layer black phosphorus
• Unexpected Dirac-Node Arc in the Topological Line-Node Semimetal HfSiS
• Dirac Line-nodes and Effect of Spin-orbit Coupling in Non-symmorphic Critical Semimetal MSiS (M=Hf, Zr)
• Blue Phosphorene Oxide: Strain-tunable Quantum Phase Transitions and Novel 2D Emergent Fermions
• Non-symmorphic band degeneracy at the Fermi level in ZrSiTe

Cited by in corpus (2)

• Nonsymmorphic-symmetry-protected hourglass Dirac loop, nodal line, and Dirac point in bulk and monolayer $X_3$SiTe${}_6$ ($X=$ Ta, Nb)
• Surface floating 2D bands in layered nonsymmorphic semimetals: ZrSiS and related compounds