2D Dirac Materials Research Articles

Broadband saturable absorption in germanene for mode-locked Yb, Er, and Tm fiber lasers

Abstract Passively mode-locked lasers have been widely investigated as one of the effective methods to obtain ultrashort pulses. As an important part of passively mode-locked fiber lasers, the exploration of 2D material-based saturable absorber has become one of the hotspots in ultrafast photonics in recent years. Germanene, a novel 2D Dirac material, with ultrafast optical response and broadband optical absorption, is a promising alternative material for saturable absorber in mode-locked fiber lasers. In this paper, germanium nanosheets are prepared via liquid-phase exfoliated method, with the saturable absorption property systematically characterized in three major wavebands of the near-infrared region. The generation of ultrashort pulses based on germanene saturable absorber in fiber lasers is further realized, in a broad waveband (1000 nm) centered at 1061.1, 1559.3 and 1883.5 nm, respectively. In addition, noise-like pulses operation with central wavelength of 1558.6 nm is also obtained, and the formation of rogue waves is further demonstrated via statistical analysis. To the best of our knowledge, this is the first experimental verification of the broadband saturable absorption property of germanene-based devices, covering three major fiber laser wavelengths from 1.0 to 2.0 μm.

Dispersive interactions between standard and Dirac materials and the role of dimensionality

The van der Waals (vdW) interaction plays a prominent role between neutral objects at separations where short ranged chemical forces are negligible. This type of dispersive coupling is determined by the interplay between geometry and response properties of the materials making up the objects. Here, we investigate the vdW interaction between 1D, 2D, and 3D standard and Dirac materials within the Random Phase Approximation, which takes into account collective excitations originating from the electronic Coulomb potential. A comprehensive understanding of characteristic functionalities and scaling laws are obtained for systems with parabolic energy dispersion (standard materials) and crossing linear bands (Dirac materials). By comparing the quantum mechanical and thermal limits the onset of thermal fluctuations in the vdW interaction is discussed showing that thermal effects are significantly pronounced at smaller scales in reduced dimensions.

Quasi-exact solutions for guided modes in two-dimensional materials with tilted Dirac cones

We show that if the solutions to the (2+1)-dimensional massless Dirac equation for a given one-dimensional (1D) potential are known, then they can be used to obtain the eigenvalues and eigenfunctions for the same potential, orientated at an arbitrary angle, in a 2D Dirac material possessing tilted, anisotropic Dirac cones. This simple set of transformations enables all the exact and quasi-exact solutions associated with 1D quantum wells in graphene to be applied to the confinement problem in tilted Dirac materials such as 8-Pmmn borophene. We also show that smooth electron waveguides in tilted Dirac materials can be used to manipulate the degree of valley polarization of quasiparticles travelling along a particular direction of the channel. We examine the particular case of the hyperbolic secant potential to model realistic top-gated structures for valleytronic applications.

Valley transport driven by dynamic lattice distortion

Angular momentum conversion between mechanical rotation and the valley degree of freedom in 2D Dirac materials is investigated theoretically. Coupling between the valley and vorticity of dynamic lattice distortions is derived by applying the k.p method to 2D Dirac materials with an inertial effect. Lattice strain effects are also incorporated. Valley transfer and valley-dependent carrier localization are predicted using the dynamic lattice distortions. The transport properties are found to be controllable, allowing the system to be insulating and to generate pulsed charge current. Our formalism offers a route toward mechanical manipulation of valley dynamics in 2D Dirac materials.

First-principles prediction of strain-induced Dirac semimetal state and negative Poisson's ratio in TiZrB4 monolayer

In this work, we designed a novel 2D Dirac material, TiZrB4 monolayer, by transforming the hexagonal unit cells of the previously reported TiB2 and ZrB2 semimetals into an orthorhombic lattice. Using first-principles density functional theory (DFT) calculation, our designed 2D structure of TiZrB4 was verified to be dynamically and thermodynamically stable by phonon dispersion calculation and ab-initio molecular dynamics (AIMD). From the results, the TiZrB4 monolayer was found to be metallic with a maximum Fermi velocity (vF) of 0.409 × 106 m/s. By applying a uniaxial strain of 3.3% along the a-axis (the zigzag direction of the boron honeycomb), the TiZrB4 monolayer becomes a Dirac semimetal with an enhanced vF of 0.436 × 106 m/s. The electronic properties and vF were found to be tunable by external strain. In addition, the negative Poisson's ratio was found in the wide range of uniaxial strains due to strong transition metal d and boron p hybridization. We expect that our findings and 2D material design strategy will be suggestive and informative for the development of a new Dirac semimetal with superior properties useful in future nanotechnology.

Thermal Properties of 2D Dirac Materials MN4 (M = Be and Mg): A First-Principles Study.

Recently, a novel two-dimensional (2D) Dirac material BeN4 monolayer has been fabricated experimentally through high-pressure synthesis. In this work, we investigate the thermal properties of a new class of 2D materials with a chemical formula of MN4 (M = Be and Mg) using first-principles calculations. First, the cohesive energy and phonon dispersion curve confirm the dynamical stability of BeN4 and MgN4 monolayers. Besides, BeN4 and MgN4 monolayers have the anisotropic lattice thermal conductivities of 842.75 (615.97) W m–1 K–1 and 52.66 (21.76) W m–1 K–1 along the armchair (zigzag) direction, respectively. The main contribution of the lattice thermal conductivities of BeN4 and MgN4 monolayers are from the low frequency phonon branches. Moreover, the average phonon heat capacity, phonon group velocity, and phonon lifetime of BeN4 monolayer are 3.54 × 105 J K–1 m–3, 3.61 km s–1, and 13.64 ps, which are larger than those of MgN4 monolayer (3.42 × 105 J K–1 m–3, 3.27 km s–1, and 1.70 ps), indicating the larger lattice thermal conductivities of BeN4 monolayer. Furthermore, the mode weighted accumulative Grüneisen parameters (MWGPs) of BeN4 and MgN4 monolayers are 2.84 and 5.62, which proves that MgN4 monolayer has stronger phonon scattering. This investigation will enhance an understanding of thermal properties of MN4 monolayers and drive the applications of MN4 monolayers in nanoelectronic devices.

Quantized Nonlinear Conductance in Ballistic Metals.

We introduce a nonlinear frequency-dependent D+1 terminal conductance that characterizes a D-dimensional Fermi gas, generalizing the Landauer conductance in D=1. For a 2D ballistic conductor, we show that this conductance is quantized and probes the Euler characteristic of the Fermi sea. We critically address the roles of electrical contacts and Fermi liquid interactions, and we propose experiments on 2D Dirac materials, such as graphene, using a triple point contact geometry.

Photon absorption of two-dimensional nonsymmorphic Dirac semimetals

Two-dimensional Dirac semimetals have attracted much attention because of their linear energy dispersion and non-trivial Berry phase. Graphene-like 2D Dirac materials are gapless only within certain approximations, e.g., if spin-orbit coupling (SOC) is neglected. It has recently been reported that materials with nonsymmorphic crystal lattice possess symmetry-enforced Dirac-like band dispersion around certain high-symmetry momenta even in the presence of SOC. Here we calculate the optical absorption coefficient of nonsymmorphic semimetals, such as $\alpha$-bismuthene, which hosts two anisotropic Dirac cones with different Fermi velocities along $x$ and $y$ directions.We find that the optical absorption coefficient depends strongly on the anisotropy factor and the photon polarization. When a magnetic field is applied perpendicular to the plane of the material, the absorption coefficient also depends on an internal parameter we termed the mixing angle of the band structure. We further find that an in-plane magnetic field, while leaving the system gapless, can induce a Van-Hove singularity in the joint density of states: this causes a significant enhancement of the optical absorption at the frequency of the singularity for one direction of polarization but not for the orthogonal one, making the optical properties even more strongly dependent on polarization. Due to the anisotropy present in our model, the Dirac cones at two high-symmetry momenta in the Brillouin zone contribute very differently to the optical absorbance. Consequently, it might be possible to preferentially populate one valley or the other by varying photon polarization and frequency. These results suggest that nonsymmorphic 2D Dirac semimetals are excellent candidate materials for tunable magneto-optic devices.

Novel Two-Dimensional ABX3 Dirac Materials: Achieving a High-Speed Strain Sensor via a Self-Doping Effect

The pristine semimetal property of two-dimensional (2D) Dirac materials has limited their practical applications in today's electronic devices. Here we report a new type of 2D Dirac material, termed ABX3 (A = F, Cl, Br, or I; B = P or As; X = C or Si) monolayers. We demonstrate that 14 ABX3 monolayers possess good stability and high Fermi velocities. The FPC3, ClPC3, BrPC3, and FAsC3 monolayers exhibit a pristine n-type self-doping Dirac cone due to the interactions of electrons between the A-B units and C6 rings, which is beneficial for realizing high-speed carriers. Interestingly, the ClPSi3 monolayer exhibits remarkable responses to strain because a self-doping Dirac cone can be induced by relatively small in-plane biaxial strains (-5%), and the current-voltage (I-V) curves verified that the response strength is 11.57 times that of the graphene-based strain sensor at a bias of 1.10 V, indicating that the ClPSi3 monolayer could be used as a potential excellent strain sensor.

Chiral symmetry breaking through spontaneous dimerization in kagomé metals

Due to an uprise in the variety of candidate compounds, kagome metals have recently gained significant attention. Among other features, kagome metals host Dirac cones as a key band structure feature away from half filling, and potentially yield an exceptionally large fine structure, beyond values found in other 2D Dirac materials such as graphene. We investigate the possibility of chiral symmetry breaking in kagome metals. Based on a heuristic lattice model, we determine the critical coupling strength and the ordering pattern by means of a Schwinger-Dyson mean-field analysis. As the leading instability we identify a dimerization pattern which spontaneously opens an excitation gap at the Dirac point and breaks the chiral symmetry.

Higher-order topological insulators in two-dimensional Dirac materials

As a novel topological state, a higher-order topological insulator has attracted enormous interest, which in d spatial dimensions has gapless boundary states at (d−n) dimensions (integer n is larger than 1). Until now, merely few two-dimensional (2D) materials have been identified as higher-order topological insulators and their experimental confirmations are still absent. Here we propose a universal strategy of antidot engineering to realize second-order topological insulators (SOTIs) in 2D Dirac materials. Based on symmetry analysis, tight-binding model, and first-principles calculations, we demonstrate SOTIs in antidot-decorated Xene (X=C, Si,and Ge) by displaying its finite bulk quadrupole moment, weak topological edge states, and in-gap topological corner states. An inherent connection is established for the existing various mechanisms of the SOTIs, including quadrupole polarization, filling anomaly, and generalized Su-Schrieffer-Heeger model on a Kekulé lattice. The robustness of topological corner states of the SOTIs against edge perturbations and bulk disorders is explicitly demonstrated, rendering our strategy appealing to experimental realization of topological corner states.Received 5 September 2021Accepted 30 November 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.L042044Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEdge statesFirst-principles calculationsTopological materialsPhysical SystemsGermaneneGrapheneHoneycomb latticeTechniquesDensity functional theorySymmetriesTight-binding modelWannier function methodsCondensed Matter, Materials & Applied Physics

Anisotropic charge transport in 1D and 2D BeN4 and MgN4 nanomaterials: A first-principles study

Low-dimensional Dirac materials have a great potential for practical applications due to their exceptional electronic properties and large surface to volume ratio. Here, we use density functional theory calculations in combination with nonequilibrium Green’s functional formalism to study the ballistic transport properties of recently synthesized single layer BeN4 [Bykov et al., Phys. Rev. Lett. 126 (2021) 175501] and dynamically stable MgN4 [Mortazavi et al., Materials Today Nano 15 (2021) 100125]. We found that these new types of 2D Dirac material show strongly anisotropic electronic transport with current along the armchair direction being significantly larger than in the zig-zag direction. Such in-plane anisotropic electronic transport properties of the materials originate from lattice direction-dependent electron localizations and electrostatic potential variations. Anisotropic charge transport is also obtained for BeN4 nanotube structures. MgN4 sample shows larger current as compared to BeN4 which indicates the possibility of increasing the conductance of BeN4 by replacing Be atoms on the polymeric nitrogen chains with other metal atoms. These findings can be of practical interest in exploring the potential of this novel type of 2D materials for the development of anisotropic multifunctional electronic devices.

A g-SiC[formula omitted] monolayer and its analogs: A new class of tunable Dirac cone materials and novel quantum spin Hall insulators

Two-dimensional (2D) Dirac cone materials have received wide attention for their advanced properties, such as nearly-zero effective masses and ultrahigh carrier mobility. However, the robust zero bandgap limited their applications in high-performance electronic devices. In this work, we proposed a series of new 2D Dirac cone materials, termed as g-AB6 monolayers (A = C, Si, and Ge; B = C, Si, Ge, and Sn). We found that the coexistence of sp2 and sp3 hybridization would heavily decrease the structural stability, hence the stable g-AB6 monolayers were only composed of sp2 or sp3 hybridized atoms. The electronic calculations revealed that all g-AB6 monolayers considered are 2D Dirac materials with linear energy dispersions near Fermi level, and they possess high Fermi velocities. Among them, the Fermi velocity of the g-SiC6 monolayer is up to 7.11 × 105m/s, which is the highest value among the known group IVA binary Dirac materials. Additionally, the Dirac cone of g-SiC6 monolayer could be modulated by applying moderate in-plane uniaxial or shear strains (<5%), which are much easier than that of graphene and silicene. Moreover, the g-SiC6, g-GeSi6, g-SiGe6, and g-GeSn6 monolayer have been identified with nontrivial Z2 topological invariant (Z2 = 1), and the g-GeSn6 monolayer was demonstrated as a room temperature topological insulator due to that spin–orbit coupling opens a large bandgap of 319 meV. Considering that the g-AB6 monolayers possess excellent dynamical, thermal, and mechanical stability, the g-AB6 monolayers are a promising candidate for realizing high-speed tunable electronic devices.

Design and modulation of two-dimensional Dirac materials in beryllium/boron-based binary monolayers

In the periodic table, beryllium (Be) and boron (B) as typical light element are near neighbors of carbon (C). Survey the electron-deficiency in Be and B as compared with C, if introducing external electrons in principle can offset the electron-deficiency, it seems that a Dirac cone have a possibility to exist in Be/B-based structures, like as C-structure (e.g., graphene). Motivated by this inference, here we selected elements P/Se as electron-rich donors to make up special Be/B-based binary compositions (BeP2/B2Se) being isoelectronic with graphene. Using a global structure search method combined with first-principles calculation, we identified three stable two-dimensional (2D) monolayers, namely o-BeP2, α-B2Se and β-B2Se. As expected, these three monolayers are verified to possess intrinsic or strain-inducing Dirac cone. When applied with a 6% compressive strain, the o-BeP2 even can be converted to Dirac cone material. The two low-lying B2Se monolayers (α-B2Se and β-B2Se) possess a hexagonal honeycomb lattice, showing a natural Dirac cone and their Fermi velocities are in the same order of that of graphene. These configurations can be further expanded to the isoelectronic BeAs2 and B2S stoichiometries and a Dirac cone can be found. This isoelectronic strategy offers a possible route to design the 2D Dirac material in Be/B-based binary compounds.

Multiple Dirac cones and Lifshitz transition in a two-dimensional Cairo lattice as a Hawking evaporation analogue

The linear energy–momentum dispersion of Dirac cones offers a unique platform for mimicking the fantastical phenomena in high energy physics, such as Dirac fermions and black hole (BH) horizons. Three types of Dirac cones (I, III, and II) with different tilts have been proposed individually in specific materials but lack of integral lattice model. Here, we demonstrated the three types of Dirac cones inherited in a π-conjugated Cairo lattice of double-degenerate d π and p z orbitals by means of tight-binding (TB) approach, which paves a way for the design of two-dimensional (2D) Dirac materials. From first-principles calculations, we predicted a candidate material, penta-NiSb2 monolayer, to achieve these multiple Dirac cones and the Lifshitz transition between different Dirac cones driven by external biaxial strain. The coexistence of the three types of Dirac cones renders penta-NiSb2 monolayer a promising 2D fermionic analogue to simulate the event-horizon evaporation with a high Hawking temperature.

Wavepacket Self‐Rotation and Helical Zitterbewegung in Symmetry‐Broken Honeycomb Lattices

AbstractThe toolbox quantities used for manipulating the flow of light include typically amplitude, phase, and polarization. Pseudospins, such as those arising from valley degrees of freedom in photonic structures, have recently emerged as an excellent candidate for this toolbox, in parallel with rapid development of spintronics and valleytronics in condensed‐matter physics. Here, by employing symmetry‐broken honeycomb photonic lattices, valley‐dependent wavepacket self‐rotation manifested in spiraling intensity patterns is demonstrated, which occurs without any initial orbital angular momentum. Theoretically, it is shown that such wavepacket self‐rotation is induced by the Berry phase and results in Zitterbewegung oscillations. The frequency of Zitterbewegung is proportional to the gap size, while the helicity of self‐rotation is valley‐dependent, i.e., correlated with the Berry curvature. These results lead to new understanding of the venerable Zitterbewegung phenomenon from the perspective of topology and are readily applicable on other platforms such as 2D Dirac materials and ultracold atoms.

Two-dimensional germanium islands with Dirac signature on Ag2Ge surface alloy

Two-dimensional (2D) Dirac materials have attracted intense research efforts due to their promise for applications ranging from field-effect transistors and low-power electronics to fault-tolerant quantum computation. One key challenge is to fabricate 2D Dirac materials hosting Dirac electrons. Here, monolayer germanene is successfully fabricated on a Ag2Ge surface alloy. Scanning tunneling spectroscopy measurements revealed a linear energy dispersion relation. The latter was supported by density functional theory calculations. These results demonstrate that monolayer germanene can be realistically fabricated on a Ag2Ge surface alloy. The finding opens the door to exploration and study of 2D Dirac material physics and device applications.

Edge photogalvanic effect caused by optical alignment of carrier momenta in two-dimensional Dirac materials

We show that the inter-band absorption of radiation in a 2D Dirac material leads to a direct electric current flowing at sample edges. The photocurrent originates from the momentum alignment of electrons and holes and is controlled by the radiation polarization. We develop a microscopic theory of such an edge photogalvanic effect and calculate the photocurrent for gapped and gapless 2D Dirac materials, also in the presence of a static magnetic field which introduces additional imbalance between the electron and hole currents. Further, we show that the photocurrent can be considerably multiplied in a ratchet-like structure with an array of narrow strips.

Prediction of massless Dirac fermions in a carbon nitride covalent network

Two-dimensional (2D) Dirac materials have received tremendous attention due to their potential applications in spintronics and energy applications. Motivated by recent experimental synthesis of a carbon nitride network with a C22N4 stoichiometry, the N-doped graphdiyne, or pyrazinoquinoxaline-based graphdiyne (PQ-GDY), we studied the electronic and topological properties of the PQ-GDY monolayer using first-principles calculations. Surprisingly, we found that the PQ-GDY monolayer indeed is a 2D Dirac semimetal also known as 2D topologically nontrivial semimetal. The linear band dispersions around the Dirac point are mainly composed of the bonding and antibonding pz-orbitals of C and N atoms. In combination with parity analysis, we found that the mechanism of band inversion in PQ-GDY is similar to the strain-induced Dirac cone in GDY. The underlying physical property of strained GDY is equivalent to expanding the single center benzene into the three benzene rings observed in PQ-GDY. Finally, the formed Dirac cone located on the Y−Γ high-symmetry line is very robust, and a bandgap is opened only after including a large artificial spin–orbit coupling, which transforms it to a 2D topological insulator.

Space–charge limited current in nanodiodes: Ballistic, collisional, and dynamical effects

This Perspective reviews the fundamental physics of space–charge interactions that are important in various media: vacuum gap, air gap, liquids, and solids including quantum materials. It outlines the critical and recent developments since a previous review paper on diode physics [Zhang et al. Appl. Phys. Rev. 4, 011304 (2017)] with particular emphasis on various theoretical aspects of the space–charge limited current (SCLC) model: physics at the nano-scale, time-dependent, and transient behaviors; higher-dimensional models; and transitions between electron emission mechanisms and material properties. While many studies focus on steady-state SCLC, the increasing importance of fast-rise time electric pulses, high frequency microwave and terahertz sources, and ultrafast lasers has motivated theoretical investigations in time-dependent SCLC. We particularly focus on recent studies in discrete particle effects, temporal phenomena, time-dependent photoemission to SCLC, and AC beam loading. Due to the reduction in the physical size and complicated geometries, we report recent studies in multi-dimensional SCLC, including finite particle effects, protrusive SCLC, novel techniques for exotic geometries, and fractional models. Due to the importance of using SCLC models in determining the mobility of organic materials, this paper shows the transition of the SCLC model between classical bulk solids and recent two-dimensional (2D) Dirac materials. Next, we describe some selected applications of SCLC in nanodiodes, including nanoscale vacuum-channel transistors, microplasma transistors, thermionic energy converters, and multipactor. Finally, we conclude by highlighting future directions in theoretical modeling and applications of SCLC.