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 (40)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Van der Waals Density Functional for General Geometries
• Maximally-localized generalized Wannier functions for composite energy bands
• Topological Insulators with Inversion Symmetry
• Two and one-dimensional honeycomb structures of silicon and germanium
• Quantum Spin Hall Effect in Silicene
• Maximally-localized Wannier functions for entangled energy bands
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Dirac semimetal in three dimensions
• The interlayer cohesive energy of graphite from thermal desorption of polyaromatic hydrocarbons
• Intrinsic and Rashba Spin-orbit Interactions in Graphene Sheets
• Spin-orbit gap of graphene: First-principles calculations
• Observation of tunable bandgap and anisotropic Dirac semimetal state in black phosphorus
• Classification of stable three-dimensional Dirac semimetals with nontrivial topology
• Dirac Cone Protected by Non-Symmorphic Symmetry and 3D Dirac Line Node in ZrSiS
• Dirac Semimetals in Two Dimensions
• Macroscopic graphene membranes and their extraordinary stiffness
• Semimetallic Two-Dimensional Boron Allotrope with Massless Dirac Fermions
• Topological nodal-line fermions in ZrSiSe and ZrSiTe
• Dirac fermions in borophene
• The Rare Two-Dimensional Materials with Dirac Cones
• Observation of Topological Nodal Fermion Semimetal Phase in ZrSiS
• Large nonsaturating magnetoresistance and signature of non-degenerate Dirac nodes in ZrSiS
• 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
• Two-Dimensional Oxide Topological Insulator With Iron-Pnictide Superconductor LiFeAs Structure
• Dirac Line-nodes and Effect of Spin-orbit Coupling in Non-symmorphic Critical Semimetal MSiS (M=Hf, Zr)
• Bulk Dirac points in distorted spinels
• Tunability of the topological nodal-line semimetal phase in ZrSiX-type materials
• Blue Phosphorene Oxide: Strain-tunable Quantum Phase Transitions and Novel 2D Emergent Fermions
• Spin-Orbit Semimetals in the Layer Groups
• Correlation-driven topological phase transition from in-plane magnetized quantum anomalous Hall to Mott insulating phase in monolayer transition metal trichlorides
• Non-symmorphic band degeneracy at the Fermi level in ZrSiTe
• Electronic, Dielectric, and Plasmonic Properties of Two-Dimensional Electride Materials X${}_2$N (X=Ca, Sr): A First-Principles Study
• Multiple Unpinned Dirac Points in Group-Va Single-layers with Phosphorene Structure

Cited by in corpus (37)

• Chemical Principles of Topological Semimetals
• Nonsymmorphic-symmetry-protected hourglass Dirac loop, nodal line, and Dirac point in bulk and monolayer $X_3$SiTe${}_6$ ($X=$ Ta, Nb)
• Topological Semimetals in Square-Net Materials
• Predictable gate-field control of spin in altermagnets with spin-layer coupling
• Valley-Layer Coupling: A New Design Principle for Valleytronics
• Hybrid Nodal Loop Metal: Unconventional Magnetoresponse and Material Realization
• Two-dimensional nodal-loop half metal in monolayer MnN
• Surface floating 2D bands in layered nonsymmorphic semimetals: ZrSiS and related compounds
• Type-I and type-II Nodal Lines Coexistence in the Antiferromagnetic monolayer CrAs${}_2$
• A systematic study of stacked square nets: from Dirac fermions to material realizations
• Two-dimensional topological semimetals
• Hourglass Weyl loops in two dimensions: Theory and material realization in monolayer GaTeI family
• Monolayer Mg${}_2$C: Negative Poisson's ratio and unconventional 2D emergent fermions
• Two-dimensional Dirac Semimetals without Inversion Symmetry
• Nonsymmorphic cubic Dirac point and crossed nodal rings across the ferroelectric phase transition in LiOsO${}_3$
• Two-dimensional antiferromagnetic Dirac fermions in monolayer TaCoTe${}_2$
• Almost ideal nodal-loop semimetal in monoclinic CuTeO${}_3$ material
• Electronic and Magnetic Properties of Topological Semimetal Candidate NdSbTe
• Cat's cradle-like Dirac semimetals in layer groups with multiple screw axes: Application to 2D Borophene and Borophane
• Hopf-chain networks evolved from triple points
• Topological nodal lines and hybrid Weyl nodes in YCoC${}_2$
• Symmetry-protected metallic and topological phases in penta-materials
• Monolayer RhB4: half-auxeticity and almost ideal spin-orbit Dirac point semimetal
• Nonsymmorphic nodal-line metals in the two-dimensional rare earth monochalcogenides MX (M = Sc, Y; X = S, Se, Te)
• Robust Dirac lines against Ge vacancy and possible spin-orbit Dirac points in nonsymmorphic HfGe0.92Te
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• First-principles study on the bulk and two-dimensional structures of AMnBi(A =K, Rb, Cs)-family materials
• Filling-enforced Dirac loops and their evolutions under various perturbations
• Two-dimensional Dirac semiconductor and its material realization
• Valley and spin splittings in a valley-layer-locked monolayer via atomic adsorption
• Fully linear band crossings at high symmetry points in layers: classification and role of spin-orbit coupling and time reversal
• Enhanced in-plane ferroelectricity, antiferroelectricity, and unconventional 2D emergent fermions in QL-XSbO${}_2$ (X= Li, Na)
• Photon Absorption of Two-dimensional Nonsymmorphic Dirac Semimetals
• Tunable two-dimensional Dirac-Weyl semimetal phase induced by altermagnetism
• Two-dimensional Dirac semimetals with tunable edge states
• Chalcogen Doping Effect on the Insulator-to-Metal Transition in GdPS
• Two-dimensional hourglass Weyl nodal loop in monolayer Pb(ClO${}_2$)${}_2$ and Sr(ClO${}_2$)${}_2$