Anisotropic Fermi Velocity Research Articles

Evolution from Topological Nodal Points to Nodal Line: Realized in Fused Carbon Allotrope

Herein, via first‐principle calculations and theoretical analysis, a new Dirac semimetal carbon system called C32, which is composed of pentagonal, hexagonal, heptagonal, and octagonal carbon rings is systematically investigated. The stability of C32 is verified by calculating the phonon dispersion, elastic constants, etc., and an appropriate pathway for experimental synthesis is proposed. Besides, it is discovered that the system holds the quadruple rotation and inversion symmetry, resulting in the emergence of eight twisted Dirac cones (D1 and D2) with a highly anisotropic Fermi velocity from 3.83 × 105 to 8.96 × 105 m s−1 along different k directions. To substantiate the semimetallic nature of C32, its nontrivial topological properties are confirmed through the presence of topologically protected edge states, and the nonzero ℤ2 topological invariant. More importantly, by introducing biaxial strain, it is uncovered that Dirac cones can gradually evolve into a nodal line, and the perfect nodal line can be obtained when the biaxial strain is 13.3%. Furthermore, by constructing the tight‐binding model, the appearance of the Dirac cone is perfectly repeated and its evolution into the nodal line under biaxial strain is explained.

Ultralow electron-surface scattering in nanoscale metals leveraging Fermi-surface anisotropy

Increasing resistivity of metal wires with reducing nanoscale dimensions is a major performance bottleneck of semiconductor computing technologies. We show that metals with suitably anisotropic Fermi velocity distributions can strongly suppress electron scattering by surfaces and outperform isotropic conductors such as copper in nanoscale wires. We derive a corresponding descriptor for the resistivity scaling of anisotropic conductors, screen thousands of metals using first-principles calculations of this descriptor and identify the most promising materials for nanoscale interconnects. Previously-proposed layered conductors such as MAX phases and delafossites show promise in thin films, but not in narrow wires due to increased scattering from side walls. We find that certain intermetallics (notably CoSn) and borides (such as YCo$_3$B$_2$) with one-dimensionally anisotropic Fermi velocities are most promising for narrow wires. Combined with first-principles electron-phonon scattering predictions, we show that the proposed materials exhibit 2-3x lower resistivity than copper at 5 nm wire dimensions.

Two-dimensional anisotropic Dirac materials PtN4C2 and Pt2N8C6 with quantum spin and valley Hall effects

We propose two different two-dimensional topological Dirac materials, planar ${\mathrm{PtN}}_{4}{\mathrm{C}}_{2}$ and ${\mathrm{Pt}}_{2}{\mathrm{N}}_{8}{\mathrm{C}}_{6}$, which exhibit graphenelike electronic structures with linearly dispersive Dirac-cone states exactly at the Fermi level. Moreover, the Dirac cone is anisotropic, resulting in anisotropic Fermi velocities and making it possible to realize orientation-dependent quantum devices. Using first-principles electronic structure calculations, we have systemically studied the structural, electronic, and topological properties. We find that spin-orbit coupling opens a sizable topological band gap so that the materials can be classified as quantum spin Hall insulators as well as quantum valley Hall insulators. Helical edge states that reside in the insulating band gap connecting the bulk conduction and valence bands are observed. Our work not only expands the Dirac-cone material family, but also provides another avenue to search for more two-dimensional topological quantum spin and valley Hall insulators.

Optical absorption in two-dimensional materials with tilted Dirac cones

The interband optical absorption of linearly polarized light by two-dimensional (2D) semimetals hosting tilted and anisotropic Dirac cones in the band structure is analysed theoretically. Supercritically tilted (type-II) Dirac cones are characterized by an absorption that is highly dependent on the incident photon polarization and frequency and is tunable by changing the Fermi level with a back-gate voltage. Type-II Dirac cones exhibit open Fermi surfaces and large regions of the Brillouin zone where the valence and conduction bands sit either above or below the Fermi level. As a consequence, unlike their subcritically tilted (type-I) counterparts, type-II Dirac cones have many states that are Pauli blocked even when the Fermi level is tuned to the level crossing point. We analyze the interplay of the tilt parameter with the Fermi velocity anisotropy, demonstrating that the optical response of a Dirac cone cannot be described by its tilt alone. As a special case of our general theory, we discuss the proposed 2D type-I semimetal 8-$Pmmn$ borophene. Guided by our in-depth analytics, we develop an optical recipe to fully characterize the tilt and Fermi velocity anisotropy of any 2D tilted Dirac cone solely from its absorption spectrum. We expect our paper to encourage Dirac cone engineering as a major route to create gate-tunable thin-film polarizers.

Two-Dimensional Dirac Nodal Line Carbon Nitride to Anchor Single-Atom Catalyst for Oxygen Reduction Reaction.

Two-dimensional carbon nitride (2DCN) materials have emerged as an important class of 2D materials beyond graphene. However, 2DCN materials with nodal-line semimetal characteristic are rarely reported. In this work, a new nodal-line semimetal 2DCN with the stoichiometry C4 N4 is designed by using density functional theory (DFT) calculations and its application to anchor single-atom catalysts (SACs) for the oxygen reduction reaction (ORR) is investigated. C4 N4 is a planar covalent network (sp2 hybridization) with regular holes formed by the four N atoms, which is dynamically, thermodynamically, and mechanically stable. The nodal line is contributed by the pz orbitals of C and px/y orbitals of N atoms. C4 N4 shows an anisotropic Fermi velocity and high electron mobility. Because of its porous structure, C4 N4 can anchor heteroatoms as SACs for electrocatalysis. C4 N4 anchored with Fe or Co is shown to be highly active for the ORR with a rather high half-wave potential of around 0.90 V, which is higher than those of SACs on other carbon nitrides. These findings may provide a new strategy to design novel substrates for SACs.

Worm-graphene: A two-dimensional orthorhombic carbon semimetal with massless Dirac fermion

Low energy Dirac material of carbon other than graphene has always enthralled researchers for their unique properties. Based on first-principles calculation we propose a carbon polymorph identified by the predominance of a Dirac cone in the contiguity of the Fermi level in the Two-dimensional domain. Moreover, the stable pristine structure known as Worm-graphene involves six non-equivalent carbon atoms to effectuate an atomic density 0.372 atoms/Å2 which is close to graphene. The Dirac cone exhibits anisotropic Fermi velocity with 6.85×105 m/s being its highest value. Besides, simple tight-binding Hamiltonian can be formulated to express the origin of the Dirac cone. Interestingly, strain resilient semimetallic behavior with robust Dirac cone of the system can be validated within 10% compressive to 10% tensile strain. Further, the material also possesses anisotropic In-plane Young’s modulus unlike graphene. Appreciable degree of spin-polarization due to monovacancy defect can be established from induced magnetic moment. Additionally, nanotubes rolled-up from this sheet can be both semimetallic or semiconducting depending on the rolling direction. Free standing Worm-graphene sheet shows strikingly different optical response compared to graphene. Two collective oscillations of the system within visible range happen to be the distinguishing trait.

Prediction of nodal-line semimetals in 2D ScX (X = P, As) with high stability and considerable fermi velocities

• New nodal–line ternary semimetals of ScX (X = P, As) are proposed. • Fully optimized structures still keep good structural integrity at high temperature of 1000 K. • The SOC effect and physical biaxial strain are negligible for the nodal-line of ScX. • The considerable Fermi velocities which are the same order of magnitude as graphene. • The elastic constants and transport properties of ScX (X = P, As) show nice anisotropy. The nodal–line structure provides higher carrier mobility, massless and special features in which the conduction band and the valence band cross at the Fermi level. The anisotropic nodal–line structure has the advantage of anisotropic Fermi velocity for novel 2D quantum device. Here we report two binary monolayers with anisotropic nodal–line based on first-principles calculation. Fully optimized ScX (X = P, As) structure can still keep good structural integrity at high temperature of 1000 K in ab initio molecular dynamics simulation. Besides, we analyze structural symmetry and wave function to illustrate the existence of nodal–line, the Young’s modulus and Poisson’s ratio of ScX show nice anisotropy. The Fermi velocities of ScX are larger than 10 5 m/s, which are the same order of magnitude as graphene. This work provides novel candidates of nodal–line semimetals for massless and stable quantum devices.

Prediction of tunable spin-orbit gapped materials for dark matter detection

New ideas for low-mass dark matter direct detection suggest that narrow band gap materials, such as Dirac semiconductors, are sensitive to the absorption of meV dark matter or the scattering of keV dark matter. Here we propose spin-orbit semiconductors - materials whose band gap arises due to spin-orbit coupling - as low-mass dark matter targets owing to their ~10 meV band gaps. We present three material families that are predicted to be spin-orbit semiconductors using Density Functional Theory (DFT), assess their electronic and topological features, and evaluate their use as low-mass dark matter targets. In particular, we find that that the tin pnictide compounds are especially suitable having a tunable range of meV-scale band gaps with anisotropic Fermi velocities allowing directional detection. Finally, we address the pitfalls in the DFT methods that must be considered in the ab initio prediction of narrow-gapped materials, including those close to the topological critical point.

Schrödinger-type 2D coherent states of magnetized uniaxially strained graphene

We revisit the uniaxially strained graphene immersed in a uniform homogeneous magnetic field orthogonal to the layer in order to describe the time evolution of coherent states built from a semi-classical model. We consider the symmetric gauge vector potential to render the magnetic field, and we encode the tensile and compression deformations on an anisotropy parameter ζ. After solving the Dirac-like equation with an anisotropic Fermi velocity, we define a set of matrix ladder operators and construct electron coherent states as eigenstates of a matrix annihilation operator with complex eigenvalues. Through the corresponding probability density, we are able to study the anisotropy effects on these states on the xy plane and their time evolution. Our results clearly show that the quasi period of electron coherent states is affected by the uniaxial strain.

PAI-graphene: A new topological semimetallic two-dimensional carbon allotrope with highly tunable anisotropic Dirac cones

Using evolutionary algorithm for crystal structure prediction, we present a new stable two-dimensional (2D) carbon allotrope composed of polymerized as-indacenes (PAI) in a zigzag pattern, namely PAI-graphene whose energy is lower than most of the reported 2D allotropes of graphene. Crucially, the crystal structure realizes a nonsymmorphic layer group that enforces a nontrivial global topology of the band structure with two Dirac cones lying perfectly at the Fermi level. The absence of electron/hole pockets makes PAI-graphene a pristine crystalline topological semimetal having anisotropic Fermi velocities with a high value of 7.0×105 m/s. We show that while the semimetallic property of the allotrope is robust against the application of strain, the positions of the Dirac cone and the Fermi velocities can be modified significantly with strain. Moreover, by combining strain along both the x- and y-directions, two band inversions take place at Γ leading to the annihilation of the Dirac nodes demonstrating the possibility of strain-controlled conversion of a topological semimetal into a semiconductor. Finally we formulate the bulk-boundary correspondence of the topological nodal phase in the form of a generalized Zak-phase argument finding a perfect agreement with the topological edge states computed for different edge-terminations.

Critical behavior for point monopole and dipole electric impurities in uniformly and uniaxially strained graphene

We revisit the problem of bound states in graphene under the influence of point electric monopole and dipole impurity potentials extended to the case in which the membrane of this material is uniformly and uniaxially strained, which leads to a redefinition of the charge and dipole moment, respectively. By considering an anisotropic Fermi velocity, we analytically solve the resulting Dirac equation for each potential. We observe that the effect of the anisotropy is to promote or inhibit the critical behavior known to occur for each kind of impurity, depending on the direction along which strain is applied: both the atomic collapse, for the monopole impurity, and the emergence of cascades of infinitely many bound states with a universal Efimov-like scaling, for the dipole impurity, are phenomena that occur under less or more restrictive conditions due to strain.

Anisotropic basic electronic properties of strained black phosphorene

The gap modulation is an intriguing feature of the single-layer black phosphorene (BP) in optoelectronics. In this paper, the uniaxial and biaxial strain effects are systematically investigated to tailor the band gap, Fermi velocity, and effective mass along both armchair (AC) and zigzag (ZZ) directions in BP. The tight-binding model and the Harrison rule propose the electronic phase transitions. In the presence of uniaxial strains, in-plane strains keep the semiconducting phase, while the semiconductor-to-insulator and semiconductor-to-semimetal phase transitions emerge for biaxial strains. Although the anisotropic Fermi velocity introduces critical strains for which the concavity inversion occurs, Fermi velocity increases (decreases) with in-plane (out-of-plane) strain along the AC direction, while it remains constant along the ZZ direction. Further, we found that the heavy (light)-effective mass is related to the ZZ (AC) direction. Moreover, both in-plane and out-of-plane strains lead to effective mass sign-changing due to the concavity inversion of bands. Additionally, the heaviest effective masses are dedicated to critical strains corresponding to the phase transitions after which the concavity inversion of bands emerges. Our results propose interesting information for the strain tuning of electronic properties in BP.

Broadband strong optical dichroism in topological Dirac semimetals with Fermi velocity anisotropy**Project supported by Singapore Ministry of Education (MOE) Tier 2 Grant No. (2018-T2-1-007) and USA ONRG Grant No. (N62909-19-1-2047). JL is supported by MOE PhD RSS. KJAO acknowledges the funding support of Xiamen University Malaysia Research Fund, Grant Nos. XMUMRF/2019-C3/IECE/0003 and XMUMRF/2020-C5/IENG/0025, and the Ministry of Higher Education Malaysia

Prototypical three-dimensional (3D) topological Dirac semimetals (DSMs), such as Cd3As2 and Na3Bi, contain electrons that obey a linear momentum–energy dispersion with different Fermi velocities along the three orthogonal momentum dimensions. Despite being extensively studied in recent years, the inherent Fermi velocity anisotropy has often been neglected in the theoretical and numerical studies of 3D DSMs. Although this omission does not qualitatively alter the physics of light-driven massless quasiparticles in 3D DSMs, it does quantitatively change the optical coefficients which can lead to nontrivial implications in terms of nanophotonics and plasmonics applications. Here we study the linear optical response of 3D DSMs for general Fermi velocity values along each direction. Although the signature conductivity-frequency scaling, σ(ω) ∝ ω, of 3D Dirac fermion is well-protected from the Fermi velocity anisotropy, the linear optical response exhibits strong linear dichroism as captured by the universal extinction ratio scaling law, Λij = (vi/vj)2 (where i ≠ j denotes the three spatial coordinates x,y,z, and vi is the i-direction Fermi velocity), which is independent of frequency, temperature, doping, and carrier scattering lifetime. For Cd3As2 and Na3Bi3, an exceptionally strong extinction ratio larger than 15 and covering a broad terahertz window is revealed. Our findings shed new light on the role of Fermi velocity anisotropy in the optical response of Dirac semimetals and open up novel polarization-sensitive functionalities, such as photodetection and light modulation.

Coherent states in magnetized anisotropic 2D Dirac materials

In this work, we construct coherent states for electrons in anisotropic 2D Dirac materials immersed in a uniform magnetic field orthogonal to the sample. In order to describe the bidimensional effects on electron dynamics in a semiclassical approach, we adopt the symmetric gauge vector potential to describe the magnetic field. By solving a Dirac-like equation with an anisotropic Fermi velocity, we define two sets of generalized ladder operators that are generators of either the Heisenberg–Weyl or su(1,1) algebra and construct coherent states as eigenstates of the generalized annihilation operators with complex eigenvalues. In order to illustrate the anisotropy effects on these states, we obtain their probability density and mean energy value. Depending upon the anisotropy, expressed by the ratio between the Fermi velocities along the x- and y -axes, the shape of the probability density is modified on the xy-plane with respect to the isotropic case and according to the classical dynamics.

Electronic and optical properties of metal decorated nitrogen-doped vacancy defects in graphene

We present a first principles study of the stability, and of the electronic and optical properties of graphene with nitrogen doped vacancies. Moreover, we use the vacancies as anchoring sites for Mg, Zn, Pd al Pt atoms and vary the concentration of defects. Decoration of the defects with metal atoms produces semi-metallic systems for any studied size of the cell, with linear bands crossing at the Fermi level. The peculiar electronic properties of massless Dirac fermions in graphene are hence kept, although with anisotropic Fermi velocities. New sharp peaks appear in the optical conductivity in the visible range, thus strongly enhancing the optical response of graphene.

An accurate and compact tight-binding model for GeS

In this work we calculate the bands structure for the GeS monolayer from a multi-orbital tight-binding model, where the effect of s-p mixing are considered in slater-Koster equations. The model parameters are adjusting and optimising compared with the band structure obtained by density-functional theory calculation based on the hybrid HSE06 functional. It reproduces the conduction and valence bands as well as the orbital compositions. The anisotropic effective masses and Fermi velocities are identified directly from the anisotropy bands structure.

Supersymmetric quantum electronic states in graphene under uniaxial strain

We study uniaxially strained graphene under the influence of non-uniform magnetic fields perpendicular to the material sample with a coordinate independent strain tensor. For that purpose, we solve the Dirac equation with anisotropic Fermi velocity and explore the conditions upon which such an equation possesses a supersymmetric structure in the quantum mechanical sense through examples. Working in a Laudau-like gauge, wave functions and energy eigenvalues are found analytically in terms of the magnetic field intensity, the anisotropy scales and other relevant parameters that shape the magnetic field profiles.

Effects of Carrier Doping on the Transport in the Dirac Electron System α-(BEDT-TTF)2I3 under High Pressure

A zero-gap state with a Dirac cone type energy dispersion was discovered in an organic conductor α-(BEDT-TTF)2I3 under high hydrostatic pressures. This is the first two-dimensional (2D) zero-gap state discovered in bulk crystals with a layered structure. Moreover, the Dirac cones are highly tilted in a k-space. This system, thus, provides a testing ground for the investigation of physical phenomena in the multilayered, massless Dirac electron system with anisotropic Fermi velocity. Recently, the carrier injection into this system has been succeeded. Thus, the investigations in this system have expanded. The recent developments are remarkable. This effect exhibits peculiar (quantum) transport phenomena characteristic of electrons on the Dirac cone type energy structure.

Lattice field theory simulations of Dirac semimetals

In this paper the observed Dirac semimetals Na3Bi and Cd3As2 are studied within lattice simulation. We formulate lattice field theory with rooted staggered fermions on anisotropic lattice. It is shown that in the limit of zero temporal lattice spacing this theory reproduces low energy effective theory of Dirac semimetals. Using this lattice theory we study the phase diagram of Dirac semimetals in the plane effective coupling constant—Fermi velocity anisotropy. Within the formulated theory the results are practically volume independent in contrast with our previous study. Our results confirm our previous finding that within the Dirac model with bare Coulomb interaction both Na3Bi and Cd3As2 lie deep in the insulator phase.

Phase diagram and Chiral Magnetic Effect in Dirac Semimetals from Lattice Simulation

Dirac Semimetals Na3Bi and Cd3As2 are recently discovered materials, which low energy electronic spectrum is described by two flavours of massless 3+1D fermions. In order to study electronic properties of these materials we formulated lattice field theory with rooted staggered fermions on anisotropic lattice. It is shown that in the limit of zero temporal lattice spacing this theory reproduces effective theory of Dirac semimetals. Using the lattice field theory we study the phase diagram of Dirac semimetals in the plane effective coupling constant - Fermi velocity anisotropy. We also measure conductivity of Dirac Semimetals within lattice field theory in external magnetic field. Our results confirm the existence of Chiral Magnetic Effect in Dirac Semimetals.