2D Dirac Materials Research Articles

Robust massless Dirac fermions in hydro-/halogenated trigonal borophene

The striking electronic characteristics of graphene trigger immense interests and continual explora-tions for new two-dimensional (2D) Dirac materials. By first-principles electronic structure calculations, we here identify a new set of 2D semimetals in hydro-/halogen embedding trigonalδ6borophene, namelyδ6-B3X (X = H, F, Cl), that possess the graphene-like massless Dirac fermions. Owing to the central hollow B atoms strongly hybridized to the hydro-/halogen adatoms, adequate charge transfer is induced from the hollow B to the basal honeycomb B sublattice, which electronically stabilizes the 2D sheet and decisively endows a robust (intrinsic and stable-against-strains) graphene-like Dirac cone state. The predicted high energetic, dynamic and thermal stabilities, combined with pretty geometrical match to the commonly utilized Ag/Au(111) substrates, support their experimental viabilities. Our prediction provides a new branch for exploring the intriguing 2D Dirac fermionic states in versatile boron element and its derivatives.

Nanophotonic route to control electron behaviors in 2D materials

Abstract Two-dimensional (2D) Dirac materials, e.g., graphene and transition metal dichalcogenides (TMDs), are one-atom-thick monolayers whose electronic behaviors are described by the Dirac equation. These materials serve not only as test beds for novel quantum physics but also as promising constituents for nanophotonic devices. This review provides a brief overview of the recent effort to control Dirac electron behaviors using nanophotonics. We introduce a principle of light-2D Dirac matter interaction to offer a design guide for 2D Dirac material–based nanophotonic devices. We also discuss opportunities for coupling nanophotonics with externally perturbed 2D materials.

Two-dimensional graphene+ as an anode material for calcium-ion batteries with ultra-high capacity: a first-principles study.

Multivalent-ion batteries have garnered significant attention due to their high energy density, low cost, and superior safety. Calcium-ion batteries (CIBs) are regarded as the next-generation energy storage systems for their abundant natural resources and bivalent characteristics. However, the absence of high-performance anode materials poses a significant obstacle to the progress of battery technology. Two-dimensional (2D) Dirac materials have excellent conductivity and abundant active sites, rendering them promising candidates as anode materials. A novel 2D Dirac material known as "graphene+" has been theoretically reported, exhibiting prominent properties including good stability, exceptional ductility, and remarkable electronic conductivity. By using first-principles calculations, we systematically investigate the performance of graphene+ as an anode material for CIBs. Graphene+ exhibits an ultra-high theoretical capacity (1487.7 mA h g-1), a small diffusion barrier (0.21 eV), and a low average open-circuit voltage (0.51 V). Furthermore, we investigate the impact of the electrolyte solvation on the performance of Ca-ion adsorption and migration. Upon contact with electrolyte solvents, graphene+ exhibits strong adsorption strength and rapid migration of Ca-ions on its surface. These results demonstrate the promising potential of graphene+ as a high-performance anode material for CIBs.

First-principles prediction of superconducting properties of monolayer 1T'-WS2 under biaxial tensile strain.

High-purity 1T'-WS2 film has been experimentally synthesized [Nature Materials, 20, 1113-1120 (2021)] and theoretically predicted to be a two-dimensional (2D) superconducting material with Dirac cones [arXiv:2301.11425]. In the present work, we further study the superconducting properties of monolayer 1T'-WS2 by applying biaxial tensile strain. It is shown that the superconducting critical temperature Tc firstly increases and then decreases with respect to tensile strains, with the highest superconducting critical temperature Tc of 7.25 K under the biaxial tensile strain of 3%. In particular, we find that Dirac cones also exist in several tensile strained cases. Our studies show that monolayer 1T'-WS2 may provide a good platform for understanding the superconductivity of 2D Dirac materials.

Quantum Hall coherent perfect absorption in graphene

100%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$100\\%$$\\end{document} absorption in a two-dimensional electron gas (2DEG) with Dirac spectrum is demonstrated to be obtained by controlling the interference of multiple incident radiations, referred to as coherent perfect absorption (CPA). However, when a 2DEG such as graphene is exposed to a magnetostatic bias, it resonantly could absorb electromagnetic radiation by transitions of its Dirac electrons between non-equidistant and nonlinear Landau levels. Here, the magneto-optical terahertz (THz) CPA in graphene under the quantum Hall effect (QHE) regime at both strong and subtesla magnetostatic bias fields is addressed. Our findings show that an effective magneto-optical surface conductivity corresponding to right- and left-handed circular (RHC- and LHC) polarizations could model a magneto-tunable CPA in graphene in THz range. Significantly, graphene under QHE regime reveals different tunable CPA properties for each circularly polarized beams by the intensity of the applied magnetic bias. Moreover, it is observed that different phase modulations at CPA frequencies are achieved for RHC and LHC polarizations. Considering the maximum efficiency for a 2D absorber, our results demonstrate the magnetostatic tuning of CPA in 2D Dirac materials for long-wavelength sensing applications and signal processing.

A potential candidate material for quantum anomalous Hall effect: Heterostructures of ferromagnetic insulator and graphene

Discovery of novel topological materials have motivated tremendous research owing to their peculiar energy bands and potential fundamental and practical prospects. In contrast to conventional nonmagnetic topological insulators (TIs), new type of magnetic TIs, such as Cr2Ge2Te6, revealed a quantum Hall effect (QHE) at zero magnetic field. The phenomenon is called anomalous QHE. In the magnetic TIs showing QAHE, the interaction of spontaneous magnetism with conducting surface states opens an insulating band gap at the Dirac points by breaking the time-reversal symmetry. In contrast to inducing the phenomenon of QHE through spontaneous magnetism by chemical doping, the alternative suitable option is the heterostructure engineering of 2D Dirac materials with semiconductor magnetic insulators. In this study, we first time investigate the phenomenon of QAHE in semiconducting magnetic insulator Cr2Ge2Te6 by proposing its bulk and monolayer heterostructure with graphene by the first-principles calculations. We employed density functional theory to compute electronic properties of Cr2Ge2Te6 and its heterostructure with graphene. The exchange-correlation in view of meta-generalized gradient approximations with tight binding method reveal the results for bulk Cr2Ge2Te6 are close to the experimental values. The maximum achieved energy gap in the heterostructure is up to 5 meV.

Polysilyne chains bridged with beryllium lead to flat 2D Dirac materials

Polysilyne with repeating disilyne units, a silicon analogue of polyacetylene, has a high potential for application to various novel silicon-based electronic devices because of the unique properties of Si=Si units with a smaller HOMO–LUMO energy gap than that of C=C units. However, one-dimensional (1D) polysilyne has not been synthesized yet. Here we propose a planar and air-stable two-dimensional (2D) silicon-based material with one-atom thickness consisting of beryllium-bridged 1D all-trans polysilyne, based on the first-principles calculations. The flat structure of 1D polysilyne, which is essential for the air stability of silicon π-electron conjugated systems, is realized by embedding polysilyne in a planar sheet. It was found that the 2D crystal optimized at the rhombus unit cell with the D2h group symmetry is a silicon-based Dirac semimetal with linear dispersion at the Fermi energy and hosts anisotropic Dirac fermions.

First-principles calculations of Li-decorated Dirac semimetal NP monolayer as a potential reversible hydrogen storage medium

To explore the potential applications of the recently proposed two-dimensional (2D) Dirac material, the NP monolayer, the hydrogen storage properties of a Li-decorated NP monolayer were calculated using first-principles methods. DFT calculation results revealed that a Li atom can stably bind to the surface of the NP monolayer and, in turn, is able adsorb two H2 molecules that exhibit a suitable adsorption energy (-0.20 eV/H2). As such, a hydrogen storage gravimetric density of 5.5 wt% may be achieved in the fully Li-decorated NP system (18H2-Li12N12P12). Further, MD simulations demonstrated that the H2 adsorbed on the Li12N12P12 surface were released at 300 K, and the reusability of this material was promoted by its excellent structural stability. These findings give a theoretical basis for the potential hydrogen storage application of the Li-decorated NP monolayer.

Topological semimetal phases in a family of monolayer X3YZ6 (X=Nb,Ta, Y=Si,Ge,Sn, Z=S,Se,Te) with abundant nodal lines and nodes

The electronic and topological properties of single-layer X3YZ6 (X=Nb,Ta, Y=Si,Ge,Sn, Z=S,Se,Te) materials have been studied with the aid of first principles calculations. This kind of materials belong to topological semimetals (TMs) with abundant nodal lines and nodes. Considering their similar properties, we focus on the analysis of Ta3SnTe6 and Ta3SiSe6. The presence of spin–orbit coupling (SOC) leads to the transition from type-I nodal lines to Dirac points as well as the disappear of type-II Dirac points. The three-dimensional (3D) plot of the band structure reproduces vividly the characteristics of nodes and nodal lines. The appearance of the flat bands in (110) edge states further confirm their nontrivial topological properties. We also explore the relationship among different nodal lines (nodes), crystal symmetry and SOC. The type-I nodal lines are protected by Mz and Mỹ symmetry in the absence of SOC. Symmetry breaking leads to band splitting even in the presence of SOC. The single-layer X3YZ6 can be used as candidates for two-dimensional (2D) Dirac materials and provide a platform for further study of interesting physical phenomena.

Long-range adsorbate interactions mediated by two-dimensional Dirac fermions

We provide here an analytical formalism to describe the indirect interaction between adsorbed atom or molecule pairs mediated by two-dimensional (2D) Dirac fermions. We show that in contrast to the case of traditional 2D electron gas, in the 2D Dirac system, the long-range interaction behaves as 1/r 3 decaying Friedel oscillation. This analytical formalism is fully consistent with a tight-binding numerical calculation of honeycomb lattices. Our formalism is suitable for the realistic 2D Dirac materials, such as graphene and surface states of three-dimensional topological insulators.

Irregular Bloch-Zener oscillations in two-dimensional flat-band Dirac materials

When a static electrical field is applied to a two-dimensional (2D) Dirac material, Landau-Zener transition (LZT) and Bloch-Zener oscillations can occur. Employing $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathcal{T}}_{3}$ lattices as a paradigm for a broad class of 2D Dirac materials, we uncover two phenomena. First, due to the arbitrarily small energy gaps near a Dirac point that make it more likely for LZTs to occur than in other regions of the Brillouin zone, the distribution of differential LZT probability in the momentum space can form a complicated morphological pattern. Second, a change in the LZT morphology as induced by a mutual switching of the two distinct Dirac points can lead to irregular Bloch-Zener oscillations characterized by a nonsmooth behavior in the time evolution of the electrical current density associated with the oscillation. These phenomena are due to mixed interference of quantum states in multiple bands modulated by the geometric and dynamic phases. We demonstrate that the adiabatic-impulse model describing Landau-Zener-St\"uckelberg interferometry can be exploited to calculate the phases, due to the equivalence between the $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathcal{T}}_{3}$ lattice subject to a constant electrical field and strongly periodically driven two- or three-level systems. The degree of irregularity of Bloch-Zener oscillations can be harnessed by selecting the morphology pattern, which is potentially experimentally realizable.

Substrate effects on spin relaxation in two-dimensional Dirac materials with strong spin-orbit coupling

Understanding substrate effects on spin dynamics and relaxation is of key importance for spin-based information technologies. However, the key factors that determine such effects, in particular for materials with strong spin-orbit coupling (SOC), have not been well understood. Here we performed first-principles real-time density-matrix dynamics simulations with SOC and the electron-phonon and electron-impurity scattering for spin lifetimes (τs) of supported/free-standing germanene, a prototypical strong SOC 2D Dirac material. We show that the effects of different substrates on τs can surprisingly differ by two orders of magnitude. We find that substrate effects on τs are closely related to substrate-induced modifications of the SOC-field anisotropy, which changes the spin-flip scattering matrix elements. We propose a new electronic quantity, named spin-flip angle θ↑↓, to characterize spin relaxation through intervalley spin-flip scattering. We find that {tau }_{s}^{-1} is approximately proportional to the averaged value of {sin }^{2}left({theta }^{uparrow downarrow }/2right), which serves as a guiding parameter of controlling spin relaxation.

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

Ultrahigh Fermi Velocities It is appealing to seek 2D Dirac materials with unique structures and intriguing properties. In article number 2200326, Xiaodong Lv, Fengyu Li, and co-workers predict planar 2D Dirac ZnN4 and CdN4 monolayers. Their first-principles calculations demonstrate that the two monolayers both exhibit high stability and an anisotropic Dirac cone at the Fermi level. Particularly, these Dirac fermions present ultrahigh Fermi velocities, and the Dirac cone is robust against external strains and electric fields.

Two-dimensional AlB4/Al2B2: high-performance Dirac anode materials for sodium-ion batteries.

Sodium-ion batteries (SIBs) have attracted much attention due to their abundant earth-reserves and low cost. Two-dimensional (2D) Dirac materials show great application prospects as anodes for SIBs because of their excellent electronic conductivity. We explore the performances of AlB4 (Al2B2) monolayers and bilayers as anodes for SIBs by using first-principles calculations. The AlB4 (Al2B2) monolayer exhibits a high theoretical storage capacity of 954.15 (709.17) mA h g-1 and a low diffusion barrier of 0.36 (0.03) eV. The calculated average open-circuit voltage (0.68/0.18 V) falls within the acceptance range of 0.1-1.0 V for anode materials. The fully sodiated AlB4 (Al2B2) monolayer shows a tiny lattice expansion of 0.9% (2.4%), suggesting good reversibility. Furthermore, in comparison with the AlB4 (Al2B2) monolayer, the AlB4 (Al2B2) bilayer can provide stronger binding with Na on the outside surface. These results contribute to a better understanding of the AlB4 (Al2B2) monolayers and bilayers as potential high-performance anode materials for SIBs.

Two-dimensional Dirac materials: Tight-binding lattice models and material candidates

The discovery of graphene has led to the devotion of intensive efforts, theoretical and experimental, to produce two-dimensional (2D) materials that can be used for developing functional materials and devices. This work provides a brief review of the recent developments in the lattice models of 2D Dirac materials and their relevant real material counterparts that are crucial for understanding the origins of 2D Dirac cones in electronic band structures as well as their material design and device applications. We focus on the roles of lattice symmetry, atomic orbital hybridization, and spin–orbit coupling in the presence of a Dirac cone. A number of lattice models, such as honeycomb, kagome, ruby, star, Cairo, and line-centered honeycomb, with different symmetries are reviewed based on the tight-binding approach. Inorganic and organic 2D materials, theoretically proposed or experimentally synthesized to satisfy these 2D Dirac lattice models, are summarized.

Generating extreme quantum scattering in graphene with machine learning

Graphene quantum dots provide a platform for manipulating electron behaviors in two-dimensional (2D) Dirac materials. Most previous works were of the ``forward'' type in that the objective was to solve various confinement, transport, and scattering problems with given structures that can be generated by, e.g., applying an external electrical field. There are applications such as cloaking or superscattering where the challenging problem of inverse design needs to be solved: Finding a quantum-dot structure according to certain desired functional characteristics. A brute-force search of the system configuration based directly on the solutions of the Dirac equation is computationally infeasible. We articulate a machine-learning approach to addressing the inverse-design problem where artificial neural networks subject to physical constraints are exploited to replace the rigorous Dirac equation solver. In particular, we focus on the problem of designing a quantum-dot structure to generate both cloaking and superscattering in terms of the scattering efficiency as a function of the energy. We construct a physical loss function that enables accurate prediction of the scattering characteristics. We demonstrate that, in the regime of Klein tunneling, the scattering efficiency can be designed to vary over two orders of magnitude, allowing any scattering curve to be generated from a proper combination of the gate potentials. Our physics-based machine-learning approach can be a powerful design tool for 2D Dirac material-based electronics.

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

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.

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

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.

Topology and applications of 2D Dirac and semi-Dirac materials

Abstract Two dimensional (2D) Dirac materials, such as graphene, hold promise of being useful in energy storage, and thus have merged as candidates that are worth exploring through the last couple of decades. In this chapter, we mainly focus on three aspects of these materials, namely, the electronic properties, via computing the band structure, the topological properties through the topological invariants, and the prospects of these 2D materials for spintronic applications, via studying the spin polarized transport. All of these properties are correlated, and hence warrant a thorough discussion. Further, in order to ascertain whether a band deformation induces noticeable effects on the electronic, topological and spintronic properties, we have considered a 2D semi-Dirac system, that does not have Dirac cones, however the conduction and the valence bands touch at an intermediate to the Dirac points in the Brillouin zone. From our studies, we infer that the behaviour of these semi-Dirac systems is quite distinct from their Dirac counterpart. Finally, in order to have noticeable spin polarized transport, we use heavy adatoms (such as, Au) on the graphene matrix which enhances the spin–orbit coupling, and thereby propose a mechanism that will ramify on the spintronic applications.

Scanning tunneling spectroscopy of two-dimensional Dirac materials on substrates with a band gap

In this paper we show that conventional current-voltage spectroscopy can provide quantitative information on the dispersion relation of the low-energy electrons of monoelemental group-IV two-dimensional (2D) Dirac materials provided that (1) the 2D material is placed on a substrate with a band gap and (2) the density of states of the scanning tunneling microscopy tip is constant. We have derived an expression for the differential conductivity of a monoelemental group-IV 2D Dirac material that is placed on a substrate with a band gap. The differential conductivity scales as $|E\ensuremath{-}{E}_{D}|{e}^{b|E\ensuremath{-}{E}_{D}|},$ rather than the commonly assumed $|E\ensuremath{-}{E}_{D}|$ scaling, where $E$ and ${E}_{D}$ refer to the energy of the electrons and the Dirac point, respectively. The parameter $b$ is inversely proportional to the Fermi velocity.