Semimetallic two-dimensional (2D) Dirac materials beyond graphene, especially 2D materials with robust Dirac points against the spin-orbit coupling (SOC), are still highly sought. Herein, we theoretically demonstrate the InBi monolayer as a long-sought 2D Dirac material whose exotic Dirac Fermionic states cannot be gapped out by SOC. The InBi monolayer with the litharge crystal structure possesses not only 4-fold band degeneracy, linear energy dispersion, and ultrahigh Fermi velocity in the order of 105 m/s, but also spontaneous ferroelasticity that can lead to the orthorhombic lattice deformation and semimetallic electronic structure. Specifically, the symmetry protected spin-orbit Dirac points in 2D InBi are located at the Brillouin Zone (BZ) boundary and near the Fermi level in energy. More importantly, with coexisting spin-orbit Dirac points and spontaneous ferroelasticity, the InBi monolayer exhibits an additional advantage for engineering Dirac Fermionic states by ferroelastic (FE) strain. Energy levels of Dirac points are strongly coupled to FE strain, and the semimetallic electronic structure of the InBi monolayer is also susceptible to the FE strain induced carrier self-doping effect. Depending on the strain orientation within the InBi monolayer, electron and hole Fermi pockets will develop along the two planar directions, leading to the characteristic transport coefficients (as evidenced by our transport simulations based on Boltzmann formalism) for future experimental detection. FE strain tunable Dirac Fermionic states together with the carrier self-doping effect will benefit future development of ultrathin electronic devices with both high carrier mobility and controllable charge conductivities.

InBi: A Ferroelastic Monolayer with Strain Tunable Spin-Orbit Dirac Points and Carrier Self-Doping Effect.

A two-dimensional (2D) Weyl semimetal featuring a spin-polarized linear band dispersion and a nodal Fermi surface is a new topological phase of matter. It is a solid-state realization of Weyl fermions in an intrinsic 2D system. The nontrivial topology of 2D Weyl cones guarantees the existence of a new form of topologically protected boundary states, Fermi string edge states. In this work, we report the realization of a 2D Weyl semimetal in monolayer-thick epitaxial bismuthene grown on SnS(Se) substrate. The intrinsic band gap of bismuthene is eliminated by the space-inversion-symmetry-breaking substrate perturbations, resulting in a gapless spin-polarized Weyl band dispersion. The linear dispersion and spin polarization of the Weyl fermion states are observed in our spin and angle-resolved photoemission measurements. In addition, the scanning tunneling microscopy/spectroscopy reveals a pronounced local density of states at the edge, suggesting the existence of Fermi string edge states. These results open the door for the experimental exploration of the exotic properties of Weyl fermion states in reduced dimensions.

Observation of 2D Weyl Fermion States in Epitaxial Bismuthene

In the Dirac semimetal BaNiS2, the Dirac nodes are located along the Γ-M symmetry line of the Brillouin zone, instead of being pinned at fixed high-symmetry points. We take advantage of this peculiar feature to demonstrate the possibility of moving the Dirac bands along the Γ-M symmetry line in reciprocal space by varying the concentration of K atoms adsorbed onto the surface of cleaved BaNiS2 single crystals. By means of first-principles calculations, we give a full account of this observation by considering the effect of the electrons donated by the K atom on the charge transfer gap, which establishes a promising tool for engineering Dirac states at surfaces, interfaces, and heterostructures.

Manipulating Dirac States in BaNiS2 by Surface Charge Doping.

After the exfoliation of graphene, it is appealing to seek more 2D Dirac materials with unique structures, rich physics, and intriguing properties. Herein, by means of density functional theory (DFT) computations, two planar 2D Dirac transition‐metal nitrides are reported, namely, MN4 (M = Zn, Cd) monolayers. The basal planes of these monolayers can be regarded as tiled by hexagons and pentagons, with tetracoordinated metal and tricoordinated nitrogen as vertices. Besides the demonstrated mechanical, dynamic, and thermal stabilities, the two MN4 monolayers both exhibit an anisotropic Dirac cone at the Fermi level, thus featuring anisotropic Dirac fermions. Particularly, these Dirac fermions present ultrahigh Fermi velocities, which are in the same order of magnitude as that of graphene (106 m s−1). Moreover, the Dirac cone is robust against external strains and electric fields due to the protection of σv(x) and C2z symmetry. Above all, the remarkable electronic properties suggest that MN4 (M = Zn, Cd) monolayers have potential applications as nanoelectronic devices.

Planar MN4 (M = Zn, Cd) Monolayers: 2D Anisotropic Dirac Semimetals of Ultrahigh Fermi Velocities

Materials containing Dirac fermions (DFs) have been actively researched because they often alter electrical and magnetic properties in an unprecedented manner. Although many studies have suggested the transformation between standard fermions (SFs) and DFs, the non-availability of appropriate samples has prevented the observation of the transformation process. We observed the interconversion process of DFs and SFs using organic charge-transfer (CT) salts. The samples are unique in that the constituents (the donor D and acceptor A species) are particularly close to each other in energy, leading to the temperature- and D-A-combination-sensitive CT interactions in the solid states. The three-dimensional weak D–A CT interactions in low-symmetry crystals induced the continuous reshaping of flat-bottomed bands into Dirac cones with decreasing temperature; this is a characteristic shape of bands that converts the behavior of SFs into that of DFs. Based on the first-principles band structures supported by the observed electronic properties, round-apex-Dirac-cone-like features appear and disappear with temperature variation. These band-structure snapshots are expected to add further detailed understanding to the related research fields. 

Band Structure Evolution during Reversible Interconversion between Dirac and Standard Fermions in Organic Charge-Transfer Salts

Two-dimensional (2D) Dirac states with linear dispersion have been observed in graphene and on the surface of topological insulators. 2D Dirac states discovered so far are exclusively pinned at high-symmetry points of the Brillouin zone, for example, surface Dirac states at [Formula: see text] in topological insulators Bi2Se(Te)3 and Dirac cones at K and [Formula: see text] points in graphene. The low-energy dispersion of those Dirac states are isotropic due to the constraints of crystal symmetries. In this work, we report the observation of novel 2D Dirac states in antimony atomic layers with phosphorene structure. The Dirac states in the antimony films are located at generic momentum points. This unpinned nature enables versatile ways such as lattice strains to control the locations of the Dirac points in momentum space. In addition, dispersions around the unpinned Dirac points are highly anisotropic due to the reduced symmetry of generic momentum points. The exotic properties of unpinned Dirac states make antimony atomic layers a new type of 2D Dirac semimetals that are distinct from graphene. 

/pdf/realization-of-unpinned-two-dimensional-dirac-states-in-2pi31nb1.pdf

Realization of unpinned two-dimensional dirac states in antimony atomic layers

/pdf/realization-of-unpinned-two-dimensional-dirac-states-in-16r5kgcq.pdf

Xiaoqian Zhang

Papers

Realization of unpinned two-dimensional dirac states in antimony atomic layers

Realization of unpinned two-dimensional dirac states in antimony atomic layers

Distance and adjacency spectra and eigenspaces for three (di)graph lifts: a unified approach