Dirac Electrons Research Articles

Enhanced Photodetection Performance in Graphene-Assisted Tunneling Photodetector

The vertical van der Waals heterostructures based on 2-D materials have attracted tremendous attention in optoelectronic devices as they can offer perfect interface without dangling bonds, atomic layer thicknesses, and conveniently tunable energy band alignment. However, the carrier transport mechanism in vertically stacked van der Waals heterostructure photodetectors is usually neglected in regards of photoresponse enhancement strategy, leading to low photoresponsivity and quantum efficiency. Here, we report a vertically stacked tunneling photodetector based on WSe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /graphene/WS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> van der Waals heterostructure. By introducing graphene film into the WSe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /WS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> interface, the interface composition was ameliorated and the Fowler–Nordheim tunneling (FNT) was enhanced with the reduced tunneling barrier height and thickness, caused by the elevated energy level of electrons since strong electron–electron interaction, ultrafast thermalization (~50 fs), and massless Dirac electrons of graphene. Therefore, the device exhibits a high photocurrent/dark current ratio (>10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ), fast response time ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 300~ \mu \text{s}$ </tex-math></inline-formula> ), high detectivity ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 1.58\times 10^{12}$ </tex-math></inline-formula> Jones), and high responsivity (429 mA W <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−1</sup> ) across a broad spectral range till <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1~ \mu \text{m}$ </tex-math></inline-formula> at room temperature. The optimized detectivity and responsivity are about 150 times and 50 times higher than WSe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /WS <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> device without graphene, respectively. These results contribute to offer a novel and versatile strategy for overcoming the performance limitation in van der Waals photodetector.

The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

Magnetism and Charge Order in the Honeycomb Lattice.

Despite being relevant to better understand the properties of honeycomblike systems, as graphene-based compounds, the electron-phonon interaction is commonly disregarded in theoretical approaches. That is, the effects of phonon fields on interacting Dirac electrons is an open issue, in particular when investigating long-range ordering. Thus, here we perform unbiased quantum MonteCarlo simulations to examine the Hubbard-Holstein model (HHM) in the half-filled honeycomb lattice. By performing careful finite-size scaling analysis, we identify semimetal-to-insulator quantum critical points, and determine the behavior of the antiferromagnetic and charge-density wave phase transitions. We have, therefore, established the ground state phase diagram of the HHM for intermediate interaction strength, determining its behavior for different phonon frequencies. Our findings provide quantitative and qualitative descriptions of the model at intermediate coupling strengths, and may shed light on the emergence of many-body properties in honeycomblike systems.

Giant orbital diamagnetism of three-dimensional Dirac electrons in Sr3PbO antiperovskite

In Dirac semimetals, inter-band mixing has been known theoretically to give rise to a giant orbital diamagnetism when the Fermi level is close to the Dirac point. In Bi$ _{1-x}$Sb$ _x$ and other Dirac semimetals, an enhanced diamagnetism in the magnetic susceptibility $\chi$ has been observed and interpreted as a manifestation of such giant orbital diamagnetism. Experimentally proving their orbital origin, however, has remained challenging. Cubic antiperovskite Sr$ _3$PbO is a three-dimensional Dirac electron system and shows the giant diamagnetism in $\chi$ as in the other Dirac semimetals. $ ^{207}$Pb NMR measurements are conducted in this study to explore the microscopic origin of diamagnetism. From the analysis of the Knight shift $K$ as a function of $\chi$ and the relaxation rate $T_1^{-1}$ for samples with different hole densities, the spin and the orbital components in $K$ are successfully separated. The results establish that the enhanced diamagnetism in Sr$ _3$PbO originates from the orbital contribution of Dirac electrons, which is fully consistent with the theory of giant orbital diamagnetism.

Graphene-based Saturable Absorber for Pulsed Fiber Laser Generation

Recently, graphene has been considered as great candidate to be applied as the saturable absorber (SA) with its brilliant optical characteristics such as ultrafast recovery time and ultra-wideband absorption due to its zero bandgap energy and linear dispersion of Dirac electrons. This paper focuses on reviewing the generation of short pulses from passive mode-locked fiber lasers that employ graphene-based saturable absorber (GBSA). Various parameters that make it excellent for generation ultra-short pulsed including modulation depth, nonlinearity, saturation intensity, self-amplitude modulation, its crystal lattice structure, band gap energy distribution are discuss in details. Furthermore, comparison between single layers and multilayer GBSA is made to explain the effect of layers number on the behaviour of SA in ring cavity fiber lasers.

Pressure-induced reconstructive phase transition in Cd3As2

Cadmium arsenide Cd$_3$As$_2$ hosts massless Dirac electrons in its ambient-conditions tetragonal phase. We report X-ray diffraction and electrical resistivity measurements of Cd$_3$As$_2$ upon cycling pressure beyond the critical pressure of the tetragonal phase and back to ambient conditions. We find that at room temperature the transition between the low- and high-pressure phases results in large microstrain and reduced crystallite size both on rising and falling pressure. This leads to non-reversible electronic properties including self-doping associated with defects and a reduction of the electron mobility by an order of magnitude due to increased scattering. Our study indicates that the structural transformation is sluggish and shows a sizable hysteresis of over 1~GPa. Therefore, we conclude that the transition is first-order reconstructive, with chemical bonds being broken and rearranged in the high-pressure phase. Using the diffraction measurements we demonstrate that annealing at ~200$^\circ$C greatly improves the crystallinity of the high-pressure phase. We show that its Bragg peaks can be indexed as a primitive orthorhombic lattice with a_HP~8.68 A b_HP~17.15 A and c_HP~18.58 A. The diffraction study indicates that during the structural transformation a new phase with another primitive orthorhombic structure may be also stabilized by deviatoric stress, providing an additional venue for tuning the unconventional electronic states in Cd3As2.

Scalar electrodynamics and the decays of the neutral pion

We propose an effective model of scalar electrodynamics (SED) in which a (nonscalar) Dirac electron field is included in the general Lagrangian density. This approach is intended to predict possible electrodynamics processes with a discussion of the role of pions that might be significant in QED.

Doping Graphene with Substitutional Mn.

We report the incorporation of substitutional Mn atoms in high-quality, epitaxial graphene on Cu(111), using ultralow-energy ion implantation. We characterize in detail the atomic structure of substitutional Mn in a single carbon vacancy and quantify its concentration. In particular, we are able to determine the position of substitutional Mn atoms with respect to the Moiré superstructure (i.e., local graphene-Cu stacking symmetry) and to the carbon sublattice; in the out-of-plane direction, substitutional Mn atoms are found to be slightly displaced toward the Cu surface, that is, effectively underneath the graphene layer. Regarding electronic properties, we show that graphene doped with substitutional Mn to a concentration of the order of 0.04%, with negligible structural disorder (other than the Mn substitution), retains the Dirac-like band structure of pristine graphene on Cu(111), making it an ideal system in which to study the interplay between local magnetic moments and Dirac electrons. Our work also establishes that ultralow-energy ion implantation is suited for substitutional magnetic doping of graphene. Given the flexibility, reproducibility, and scalability inherent to ion implantation, our work creates numerous opportunities for research on magnetic functionalization of graphene and other two-dimensional materials.

Theory of the Strain Engineering of Graphene Nanoconstrictions

Strain engineering is one of the key technologies for using graphene as an electronic device: the strain-induced pseudo-gauge field reflects Dirac electrons, thus opening the so-called conduction gap. Since strain accumulates in constrictions, graphene nanoconstrictions can be a good platform for this technology. On the other hand, in the graphene nanoconstrictions, Fabry-Perot type quantum interference dominates the electrical conduction at low bias voltages. We argue that these two effects have different strain dependence; the pseudo-gauge field contribution is symmetric with respect to positive (tensile) and negative (compressive) strain, whereas the quantum interference is antisymmetric. As a result, a peculiar strain dependence of the conductance appears even at room temperatures.

Persistent Friedel oscillations in graphene due to a weak magnetic field

Two opposite chiralities of Dirac electrons in a two-dimensional (2D) graphene sheet modify the Friedel oscillations strongly: electrostatic potential around an impurity in graphene decays much faster than in 2D electron gas. At distances $r$ much larger than the de Broglie wavelength, it decays as $1/{r}^{3}$. Here we show that a weak uniform magnetic field affects the Friedel oscillations in an anomalous way. It creates a field-dependent contribution which is dominant in a parametrically large spatial interval ${p}_{0}^{\ensuremath{-}1}\ensuremath{\lesssim}r\ensuremath{\lesssim}{k}_{F}{l}^{2}$, where $l$ is the magnetic length, ${k}_{F}$ is Fermi momentum, and ${p}_{0}^{\ensuremath{-}1}={({k}_{F}l)}^{4/3}/{k}_{F}$. Moreover, in this interval, the field-dependent oscillations do not decay with distance. The effect originates from a spin-dependent magnetic phase accumulated by the electron propagator. The obtained phase may give rise to novel interaction effects in transport and thermodynamic characteristics of graphene and graphene-based heterostructures.

One-dimensional spin–orbit coupled Dirac system with extended s-wave superconductivity: Majorana modes and Josephson effects

Motivated by the spin–momentum locking of electrons at the boundaries of certain topological insulators, we study a one-dimensional system of spin–orbit coupled massless Dirac electrons with s-wave superconducting pairing. As a result of the spin–orbit coupling, our model has only two kinds of linearly dispersing modes, and we take these to be right-moving spin-up and left-moving spin-down. Both lattice and continuum models are studied. In the lattice model, we find that a single Majorana zero energy mode appears at each end of a finite system provided that the s-wave pairing has an extended form, with the nearest-neighbor pairing being larger than the on-site pairing. We confirm this both numerically and analytically by calculating the winding number. We find that the continuum model also has zero energy end modes. Next we study a lattice version of a model with both Schrödinger and Dirac-like terms and find that the model hosts a topological transition between topologically trivial and non-trivial phases depending on the relative strength of the Schrödinger and Dirac terms. We then study a continuum system consisting of two s-wave superconductors with different phases of the pairing, with a δ-function potential barrier lying at the junction of the two superconductors. Remarkably, we find that the system has a single Andreev bound state (ABS) which is localized at the junction. When the pairing phase difference crosses a multiple of 2π, an ABS touches the top of the superconducting gap and disappears, and a different state appears from the bottom of the gap. We also study the AC Josephson effect in such a junction with a voltage bias that has both a constant V 0 and a term which oscillates with a frequency ω. We find that, in contrast to standard Josephson junctions, Shapiro plateaus appear when the Josephson frequency ω J = 2eV 0/ℏ is a rational fraction of ω. We discuss experiments which can realize such junctions.

Spintronic properties of topological surface Dirac electrons with hexagonal warping

We study spin-torque and electrical transport properties of Dirac electrons on the surface of magnetic topological insulators. Usually, surface Dirac electrons are described by a linear-dispersion model, which exhibits various peculiar features originating from the spin-velocity equivalence or spin-momentum locking. In this paper, a focus is placed on the effects of hexagonal warping (parametrized by $\ensuremath{\lambda}$) of the otherwise linear dispersion, which removes such peculiar features. Focusing on perpendicular magnetization, we calculate Gilbert damping, spin-orbit torque (SOT), and electrical conductivity, which are ``degenerate'' in the absence of hexagonal warping, $\ensuremath{\lambda}=0$, but this degeneracy is lifted in its presence, $\ensuremath{\lambda}\ensuremath{\ne}0$. The electrical conductivity was found to be greatly enhanced by $\ensuremath{\lambda}$ at large doping, whereas the other two remain moderate. Their reactive counterparts (spin renormalization, reactive SOT, and Hall conductivity), which are nonzero even in the undoped (insulating) state and also mutually degenerate at $\ensuremath{\lambda}=0$, become differentiated by $\ensuremath{\lambda}$, with the Hall conductivity remaining unchanged at the universal value. We next study current-induced torques with magnetization gradient. We first classify all possible forms allowed by symmetry, and find there are three ways of representation (SOT, spin-transfer torque, and gradient torque), which we call ``viewpoints,'' each of which forms a complete set of torques. Explicit calculation is then performed in the SOT viewpoint. While such torques are exhausted by two SOT-type ones at $\ensuremath{\lambda}=0$, examination of magnon Doppler shift and effects on domain-wall motion indicates that the spin-transfer torques (in a narrow sense) do exist even at $\ensuremath{\lambda}=0$. Finally, the current-induced Dzyaloshinskii-Moriya interaction is shown to arise starting linearly with $\ensuremath{\lambda}$, in contrast to the other effects mentioned above that start quadratically $(\ensuremath{\sim}{\ensuremath{\lambda}}^{2})$.

Zitterbewegung of Electrons and High-Frequency Conductivity of Single-Layer Graphene at Low Temperatures

Zitterbewegung (jittery motion) of Dirac electrons in single-layer graphene is considered as a nonrelativistic analog of the phenomenon predicted by Erwin Schrodinger for relativistic electrons in free space. It is shown that Dirac electrons in single-layer graphene experience fast fluctuations of their positions around the mean value with fairly a high frequency, which, however, is much lower than for relativistic electrons in free space. The interplay of Zitterbewegung of the wavepackage of conduction electrons formed by the Fermi–Dirac distribution and the low-temperature high-frequency complex conductivity of single-layer graphene has been examined. It is shown that, at low temperatures, the electromagnetic resonance properties of single-layer graphene above the threshold can be simulated using a set of equivalent electric oscillating circuits (oscillators) so that there is always the one that resonates and generates active conductivity. This can be used to visualize electromagnetic processes, which is especially important for including graphene into micro- and nanoelectronic systems. The results obtained can be used, in particular, in the development of a graphene nanoantenna.

Ambient-pressure Dirac electron system in the quasi-two-dimensional molecular conductor α−(BETS)2I3

We investigated the precise crystal structures and electronic states of a quasi-two-dimensional molecular conductor $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BETS})}_{2}{\mathrm{I}}_{3}$ at ambient pressure. The electronic resistivity of this molecular solid shows metal-to-insulator (MI) crossover behavior at ${T}_{\mathrm{MI}}=50\phantom{\rule{4pt}{0ex}}\mathrm{K}$. Our x-ray diffraction and $^{13}\mathrm{C}$ nuclear magnetic resonance experiments revealed that $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BETS})}_{2}{\mathrm{I}}_{3}$ maintains the inversion symmetry below ${T}_{\mathrm{MI}}$. First-principles calculations found a pair of anisotropic Dirac cones at a general $k$ point, with the degenerate contact points at the Fermi level. The origin of the insulating state in this system is a small energy gap of $\ensuremath{\sim}2\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ opened by the spin-orbit interaction. The ${Z}_{2}$ topological invariants indicate that this system is a weak topological insulator. Our results suggest that $\ensuremath{\alpha}\text{\ensuremath{-}}{(\mathrm{BETS})}_{2}{\mathrm{I}}_{3}$ is a promising material for studying the bulk Dirac electron system in two dimensions.

A Novel Method to Observe Topological Nature Using Nonlinear Thermoelectricity

Researchers at the Institute for Solid State Physics, University of Tokyo, recently proposed a current-induced thermoelectric phenomenon called the “nonlinear anomalous Ettingshausen effect” in organic massive Dirac electron systems. This phenomenon allowed for a novel method of observing the topological nature of Dirac electron systems by inducing the time-reversal-symmetry breaking using an electric current, which can then be detected via simple thermoelectric measurements.

Transmission Characteristics of Electrons in Graphene Incident on Cantor-like Potential

We study the tunneling of Dirac electrons in graphene passing through Cantor-like electrostatic and electromagnetic potentials. It is found that transmittance can be expressed theoretically using t...

Nonlinear Thermoelectric Transport Will Open a New and Exotic Way to Detect Topological Nature of Dirac Electrons in Solids

Recently, it was proposed that a novel nonlinear anomalous Ettingshausen effect enabled a new and exotic approach to observe topological nature of Dirac electrons in solids using thermoelectric properties.

First-principles study of the effective Hamiltonian for Dirac fermions with spin-orbit coupling in two-dimensional molecular conductor $$\alpha $$-(BETS)$$_2 \hbox {I}_3$$

We employed first-principles density-functional theory (DFT) calculations to characterize Dirac electrons in quasi-two-dimensional molecular conductor $$\alpha $$ -(BETS) $$_2 \hbox {I}_3$$ [= $$\alpha $$ -(BEDT–TSeF) $$_2 \hbox {I}_3$$ ] at a low temperature of 30 K. We provide a tight-binding model with intermolecular transfer energies evaluated from maximally localized Wannier functions, where the number of relevant transfer integrals is relatively large due to the delocalized character of Se p orbitals. The spin–orbit coupling gives rise to an exotic insulating state with an indirect band gap of about 2 meV. We analyzed the energy spectrum with a Dirac cone close to the Fermi level to develop an effective Hamiltonian with site potentials, which reproduces the spectrum obtained by the DFT band structure.

Особенности затухания и усиления терагерцовых плазмонных мод в графене с учетом пространственной дисперсии

In this paper, we consider the effect of charge carrier drift on plasmon modes (plasmons) in electron Dirac liquid in graphene with a shifted Fermi level. Dispersion relations for plasmons were obtained using an electromagnetic approach and a hydrodynamic description of an electron liquid. Damped and amplified plasmon eigenmodes are studied numerically depending on the relationship of the magnitudes and directions of the direct electric current and the phase velocity of the plasmon.

Transparent mirror effect in twist-angle-disordered bilayer graphene

When light is incident on a medium with spatially disordered index of refraction, interference effects lead to near-perfect reflection when the number of dielectric interfaces is large, so that the medium becomes a "transparent mirror." We investigate the analog of this effect for electrons in twisted bilayer graphene (TBG), for which local fluctuations of the twist angle give rise to a spatially random Fermi velocity. In a description that includes only spatial variation of Fermi velocity, we derive the incident-angle-dependent localization length for the case of quasi-one-dimensional disorder by mapping this problem onto one dimensional Anderson localization. The localization length diverges at normal incidence as a consequence of Klein tunneling, leading to a power-law decay of the transmission when averaged over incidence angle. In a minimal model of TBG, the modulation of twist angle also shifts the location of the Dirac cones in momentum space in a way that can be described by a random gauge field, and thus Klein tunneling is inexact. However, when the Dirac electron's incident momentum is large compared to these shifts, the primary effect of twist disorder is only to shift the incident angle associated with perfect transmission away from zero. These results suggest a mechanism for disorder-induced collimation, valley filtration, and energy filtration of Dirac electron beams, so that TBG offers a promising new platform for Dirac fermion optics.