The $π$-electronic structure of graphene in the presence of a modulated electric potential is investigated by the tight-binding model. The low-energy electronic properties are strongly affected by the period and field strength. Such a field could modify the energy dispersions, destroy state degeneracy, and induce band-edge states. It should be noted that a modulated electric potential could make semiconducting graphene semimetallic, and that the onset period of such a transition relies on the field strength. There exist infinite Fermi-momentum states in sharply contrast with two crossing points (Dirac points) for graphene without external fields. The finite density of states (DOS) at the Fermi level means that there are free carriers, and, at the same time, the low DOS spectrum exhibits many prominent peaks, mainly owing to the band-edge states.
High-quality BN-Graphene-BN nanoribbon capacitors with double side-gates of graphene are experimentally realized. Graphene electronic properties can be significantly modulated by the double side-gates. The modulation effects are very obvious and followed the metallic electrode behavior of numerical simulations, while the theoretically predicted negative quantum capacitance was not observed, possibility due to the over-estimated or weakened interactions between the graphene nanoribbon and side-gate electrodes.
We study the electronic transport properties of a monolayer graphene with a one-dimensional modulated height profile caused, for instance, by substrate ondulations. We show that the combined effect of the resulting strain fields induce modulated scalar and vector potentials that give rise to Weiss oscillations in the magnetoconductivity. We also find that similar effects can be obtained by applying a parallel magnetic field to the graphene-substrate interface. The parameters of an experimental set-up for a physical realization of these findings in graphene systems are discussed.
We present a theoretical study of the electronic structure of magnetically modulated graphene. We consider monolayer graphene in the presence of a perpendicular magnetic field and a unidirectional weak magnetic modulation. The density of states and the bandwidth of the Dirac electrons in this system are determined. We have found magnetic Weiss oscillations in the bandwidth and the density of states. These oscillations are out of phase and larger in amplitude than the ones in the electrically modulated graphene. In addition, these oscillations are in phase and smaller in amplitude to those of m…
We study the adiabatic quantum pumping characteristics in the graphene modulated by two oscillating gate potentials out of phase. The angular and energy dependence of the pumped current is presented. The direction of the pumped current can be reversed when a high barrier demonstrates stronger transparency than a low one, which results from the Klein paradox. The underlying physics of the pumping process is illuminated.
We present a theoretical study of the electronic structure of modulated graphene in the presence of a perpendicular magnetic field. The density of states and the bandwidth for the Dirac electrons in this system are determined. The appearance of unusual Weiss oscillations in the bandwidth and density of states is the main focus of this work.
Quantum pumping processes are accompanied by considerable quantum noise. We investigated the pumped shot noise (PSN) properties in adiabatically modulated graphene-based double-barrier structures. General expressions for adiabatically PSN in phase-coherent mesoscopic conductors are derived based on the scattering approach. It is found that comparing with the Poisson processes, the PSN is dramatically enhanced where the dc pumped current changes flow direction, which demonstrates the effect of the Klein paradox.
We have investigated the electrical transport properties of Dirac electrons in a monolayer graphene sheet in the presence of a perpendicular magnetic field that is modulated weakly and periodically along one direction.We find that the Landau levels broaden into bands and their width oscillates as a function of the band index and the magnetic field.We determine the $σ_{yy}$ component of the magnetoconductivity tensor for this system which is shown to exhibit Weiss oscillations.We also determine analytically the asymptotic expressions for $σ_{yy}$.We compare these results with recently obtained …
Theoretical investigation of thermodynamic properties of electrically modulated monolayer graphene in the presence of a perpendicular magnetic field B is presented.This work is aimed at determining the modulation induced effects on the thermodynamic properties of electrically modulated graphene.The results obtained are compared with those of the conventional 2DEG. The one-dimensional periodic potential due to electric modulation lifts the degeneracy of the Landau Levels and converts them into bands whose width oscillates as a function of B. We find Weiss type oscillations for small values of B…
We propose a new method to use gapped graphene as barrier to confine electrons in gapless graphene and form a good quantum dot, which can be realized on an oxygen-terminated $SiO_{2}$ substrate partly H-passivated. In particular, we use ferromagnetic insulators deposited on top of barrier which give rise to a spin related energy spectrum and transport properties. Compared to the complexity of etched quantum dots in graphene, the setup suggested here is a promising candidate for practical applications.
This paper proposes the concept, analysis and design of a sinusoidally-modulated graphene leaky-wave antenna with beam scanning capabilities at a fixed frequency. The antenna operates at terahertz frequencies and is composed of a graphene sheet transferred onto a back-metallized substrate and a set of polysilicon DC gating pads located beneath it. In order to create a leaky-mode, the graphene surface reactance is sinusoidally-modulated via graphene's field effect by applying adequate DC bias voltages to the different gating pads. The pointing angle and leakage rate can be dynamically controlle…
We propose and analyze the detector of modulated terahertz (THz) radiation based on the graphene field-effect transistor with mechanically floating gate made of graphene as well. The THz component of incoming radiation induces resonant excitation of plasma oscillations in graphene layers (GLs). The rectified component of the ponderomotive force between GLs invokes resonant mechanical swinging of top GL, resulting in the drain current oscillations. To estimate the device responsivity, we solve the hydrodynamic equations for the electrons and holes in graphene governing the plasma-wave response,…
The electronic properties of graphene under any arbitrary uniaxial strain field are obtained by an exact mapping of the corresponding tight-binding Hamiltonian into an effective one-dimensional modulated chain. For a periodic modulation, the system displays a rich behavior, including quasicrystals and modulated crystals with a complex spectrum, gaps at the Fermi energy and interesting localization properties. These features are explained by the incommensurate or commensurate nature of the potential, which leads to a dense filling of the reciprocal space in the former case. Thus, the usual pert…
We present a theoretical study of Weiss oscillations in magnetoconductivity of bilayer graphene. Bilayer graphene in the presence of a perpendicular magnetic field and a unidirectional weak electric modulation is considered.We determine the $σ_{yy}$ component of the magnetoconductivity tensor for this system which is shown to exhibit Weiss oscillations. We show that Weiss oscillations in the magnetoconductivity of bilayer graphene are enhanced and more robust with temperature compared to those in conventional two-dimensional electron gas systems whereas they are less robust with temperature co…
Exploration of optical non-linear response of graphene predominantly relies on ultra-short time domain measurements. Here we propose an alternate technique that uses frequency modulated continuous wavefront optical fields, thereby probing graphene's steady state non-linear response. We predict frequency sideband generation in the reflected field that originates from coherent electron dynamics of the photo-excited carriers. The corresponding threshold in input intensity for optimal sideband generation provides a direct measure of the third order optical non-linearity in graphene. Our formulatio…
Transverse-electric (TE) surface plasmon polaritons are unique eigenmodes of a homogeneous graphene layer that are tunable with the chemical potential and temperature. However, as their dispersion curve spectrally lies just below the light line, they cannot be resonantly excited by an externally incident wave. Here, we propose a way of exciting the TE modes and tuning their peaks in the transmission by introducing a one-dimensional graphene grating. Using the scattering-matrix formalism, we show that periodic modulations of graphene make the transmission more pronounced, potentially allowing f…
The canalization of terahertz surface plasmon polaritons using a modulated graphene monolayer is investigated for subwavelength imaging. An anisotropic surface conductivity formed by a set of parallel nanoribbons with alternating positive and negative imaginary conductivities is used to realize the canalization regime required for hyperlensing. The ribbons are narrow compared to the wavelength, and are created electronically by gating a graphene layer over a corrugated ground plane. Good quality canalization of surface plasmon polaritons is shown in the terahertz even in the presence of realis…
The effect of magnetic modulation on thermodynamic properties of a graphene monolayer in presence of a constant perpendicular magnetic field is reported here. One-dimensional spatial electric or magnetic modulation lifts the degeneracy of the Landau levels and converts into bands and their band width oscillates with magnetic field leading to Weiss-type oscillation in the thermodynamic properties. The effect of magnetic modulation on thermodynamic properties of a graphene sheet is studied and then compared with electrically modulated graphene and magnetically modulated conventional two-dimensio…
In this work, we determine the effects of temperature on the magnetoplasmon spectrum of an electrically modulated graphene monolayer as well as the two-dimensional electron gas (2DEG). The intra-Landau-band magnetoplasmon spectrum within the Self Consistent Field (SCF) approach is investigated for both the aforementioned systems. Results obtained not only exhibit Shubnikov-de Hass (SdH) oscillations but also commensurability oscillations (Weiss oscillations). These oscillations are periodic as a function of inverse magnetic field. We find that both the magnetic oscillations, SdH and Weiss, hav…
The emergence of the magnetic minibads in the quasienergy spectrum of graphene superlattice subjected to the quantizing magnetic field and electromagnetic radiation was investigated. The graphene superlattice was assumed to be formed by space-periodical modulation of the gap in the vicinity of the Dirac point of the graphene band structure. The explicit form of the Floquet spectrum of electron was derived in the case of weak spatial modulation. Minibads widths were shown to change with ac electric field amplitude. The possibility of electron-electron bound states was shown. The binding energie…
We describe light scattering from a graphene sheet having a modulated optical conductivity. We show that such modulation enables the excitation of surface plasmon-polaritons by an electromagnetic wave impinging at normal incidence. The resulting surface plasmon-polaritons are responsible for a substantial increase of electromagnetic radiation absorption by the graphene sheet. The origin of the modulation can be due either to a periodic strain field or to adatoms (or absorbed molecules) with a modulated adsorption profile.
We have performed a detailed investigation of the electrical properties of a graphene monolayer which is modulated by a weak one dimensional periodic potential in the presence of a perpendicular magnetic field. The periodic modulation broadens the Landau Levels into bands which oscillate with B. The electronic conduction in this system can take place through either diffusive scattering or collisional scattering off impurities. Both these contributions to electronic transport are taken into account in this work. In addition to the appearance of commensurability oscillations in both the collisio…
Graphene-based superlattice (SL) formed by a periodic gap modulation is studied theoretically using a Dirac-type Hamiltonian. Analyzing the dispersion relation we have found that new Dirac points arise in the electronic spectrum under certain conditions. As a result, the gap between conduction and valence minibands disappears. The expressions for the position of these Dirac points in ${\bf k}$-space and threshold value of the potential for their emergence were obtained. At some parameters of the system, we have revealed interface states which form the top of the valence miniband.
Graphene properties can be manipulated by a periodic potential. Based on the tight-binding model, we study graphene under a one-dimensional (1D) modulated magnetic field which contains both a uniform and a staggered component. New chiral current-carrying edge states are generated at the interfaces where the staggered component changes direction. These edge states lead to an unusual integer quantum Hall effect (QHE) in graphene, which can be observed experimentally by a standard four-terminal Hall measurement. When Zeeman spin splitting is considered, a novel state is predicted where the electr…
Using the energy spectrum of graphene with spatially modulated potential, we study the Goos-Hänshen shifts near extra Dirac points located at finite energy $\varepsilon=mπ$, with $m$ integer. On both sides of such points, we show that the Goos-Hänshen shifts can be negative as well as positive under various conditions. It is found that the shifts are strongly depending on the effects of the incident energy, potential height, incident angle and width of central region of unit cell. Such effects tell us that such width can be used to tune the shifts at the extra Dirac points.
Strain engineering is a promising approach for suppressing the OFF-state conductance in graphene-based devices that arises from Klein tunnelling. In this work, we derive a comprehensive tight-binding Hamiltonian for strained graphene that incorporates strain-induced effects that have been neglected hitherto, such as the distortion of the unit cell under strain, the effect of strain on the next-nearest neighbor coupling, and the second-order contributions of the strain tensor. We derive the corresponding low-energy effective Hamiltonian about the Dirac points and reformulate the boundary condit…
We theoretically study the Josephson effect in a superconductor/normal metal/superconductor junction based on Kekulé patterned graphene. For the Kekulé-O patterned junctions, a Fermi momentum-splitting Andreev reflection at the interface can be induced by the off-resonant circularly polarized light applied in the normal region, which results in the possible $π$-state. In contrast, for the Kekulé-Y patterned junctions, the Fermi momentum-splitting Andreev reflection is strongly suppressed due to the valley-momentum locking and the junction always exhibits the 0-state. The dependence of the crit…
We draw motivation from recent experimental studies and present a comprehensive study of magnetothermoelectric transport in a graphene monolayer within the linear response regime. We employ the modified Kubo formalism developed for thermal transport in a magnetic field. Thermopower as well as thermal conductivity as a function of the gate voltage of a graphene monolayer in the presence of a magnetic field perpendicular to the graphene plane is determined for low magnetic fields (~1 Tesla) as well as high fields (~8 Tesla). We include the effects of screened charged impurities on thermal transp…
The electronic properties and optical excitations are investigated in the geometry- and field-modulated bilayer graphene systems, respectively, by using the tight-binding model and Kubo formula. The stacking symmetry of bilayer graphene can be manipulated by varying the width and position of domain wall (DW) within two normally stacked graphene. All the layer-dependent atomic interactions are taken into consideration under external fields. The modulation of stacking configuration gives rise to significant effects of zone folding on energy subbands, subenvelope wave functions, density of states…
There is growing experimental interest in coupling cavity photons to the cyclotron resonance excitations of electron liquids in high-mobility semiconductor quantum wells or graphene sheets. These media offer unique platforms to carry out fundamental studies of exciton-polariton condensation and cavity quantum electrodynamics in a regime in which electron-electron interactions are expected to play a pivotal role. Focusing on graphene, we present a theoretical study of the impact of electron-electron interactions on a quantum Hall polariton fluid, that is a fluid of magneto-excitons resonantly c…
The stacking and bending of graphene are trivial but extremely powerful agents of control over graphene's manifold physics. By changing the twist angle, one can drive the system over a plethora of exotic states via strong electron correlation, thanks to the moiré superlattice potentials, while the periodic or triaxial strains induce discretization of the band structure into Landau levels without the need for an external magnetic field. We fabricated a hybrid system comprising both the stacking and bending tuning knobs. We have grown the graphene monolayers by chemical vapor deposition, using $…
We investigate the spin-resolved transport in a two-terminal zigzag graphene nanoribbon device with two independent gate induced Rashba spin-orbit coupling regions and in the presence of strain. By employing a recursive Green's function technique to the tight-binding model for the graphene nanoribbon, we calculate the spin-resolved conductance of the system. We show that by switching the sign of one of the gates it is possible to select which spin component will be transmitted. Moreover, our results show that an uniaxial strain applied to the nanoribbon plays a significant role in the transpor…
It has been shown that Bernal stacked bilayer graphene (BLG) in a uniform magnetic field demonstrates integer quantum Hall effect with a zero Landau-level anomaly \cite{Geimbilayer}. In this article we consider such system in a two dimensional periodic magnetic modulation with square lattice symmetry. It is shown algebraically that the resulting Hofstadter spectrum can be expressed in terms of the corresponding spectrum of monolayer graphene in a similar magnetic modulation. In the weak-field limit, using the tight-binding model, we also derive the Harper-Hofstadter equation for such BLG syste…
The elecrooptical response of graphene due to heating and drift of carriers is studied theoretically. Real and imaginary parts of the dynamic conductivity tensor are calculated for the case of effective momentum relaxation, when anisotropic contributions are small. We use the quasiequilibrium distribution of electrons and holes, characterized by the effective temperature of carriers and by concentrations, which are controlled by gate voltage and in-plane electric field. The geometry of normal propagation of probe radiation is considered, spectral and field dependences of the reflection coeffic…
The effect of a modulated magnetic field on the electronic structure of neutral graphene is examined in this paper. It is found that application of a small staggered modulated magnetic field does not destroy the Dirac-cone structure of graphene and so preserves its 4-fold zero-energy degeneracy. The original Dirac points (DPs) are just shifted to other positions in k space. By varying the staggered field gradually, new DPs with exactly the same electron-hole crossing energy as that of the original DPs, are generated, and both the new and original DPs are moving continuously. Once two DPs are s…
We study transport properties of graphene nanostructures consisted of alternating slabs of gapless and gapped graphene in the presence of piecewise constant external potential equal to zero in the gapless regions. The transmission through single-, double-barrier structures and superlattices has been studied. It was revealed that any n-barrier structure is perfectly transparent at certain conditions defining the positions of new Dirac points created in the superlattice. The conductance and the shot noise were as well computed and investigated for the considered graphene systems. In a general ca…
We present fabrication and optical characterization of micro-cavities made of multilayer graphene (MLG) cantilevers clamped by metallic electrodes and suspended over Si/Si02 substrate. Graphene cantilevers act as a semi-transparent mirrors closing an air-wedge optical cavity. This simple geometry implements a standing-wave optical resonator along with a mechanical one. Equal thickness interference fringes are observed in both Raman and Rayleigh backscattered signals with interfringe given by their specific wavelength.Chromatic dispersion within the cavity makes possible spatial modulation of g…
In certain configurations, the aromatic properties of benzene ring structured molecules allow for unpaired, reactive valence electrons (known as radicals). Clar's goblets are such molecules. With an even number of unpaired radicals, these nanographenes are topologically frustrated hydrocarbons in which pi-bonding network and topology of edges give rise to the magnetism. Clar's goblets are therefore valued as prospective qubits provided they can be modulated between magnetic states. Using first principles DFT, we demonstrate the effects of adsorption on both molecule and substrate in a graphene…
We propose two schemes of field-effect transistor based on gapped armchair graphene nanoribbons connected to metal leads, by introducing sidearms or on-site gate voltages. We make use of the band gap to reach excellent switch-off character. By introducing one sidearm or on-site gate to the graphene nanoribbon, conduction peaks appear inside the gap regime. By further applying two sidearms or on-site gates, these peaks are broadened to conduction plateaus with a wide energy window, thanks to the resonance from the dual structure. The position of the conduction windows inside the gap can be full…
A dilute distribution of magnetic impurities is assumed to be present in doped graphene. We calculate the interaction energy between two magnetic impurities which are coupled via the indirect-exchange or Ruderman-Kittel-Kasuva-Yosida (RKKY) interaction by the doped conduction electrons. The current model is a half-filled $AB$-lattice structure. Our calculations are based on the retarded lattice Green's function formalism in momentum-energy space which is employed in linear response theory to determine the magnetic susceptibility in coordinate space. Analytic results are obtained for gapped gra…
Cyclotron resonance has been measured in far-infrared transmission of GaAs/Al$_x$Ga$_{1-x}$As heterostructures with an etched hexagonal lateral superlattice. Non-linear dependence of the resonance position on magnetic field was observed as well as its splitting into several modes. Our explanation, based on a perturbative calculation, describes the observed phenomena as a weak effect of the lateral potential on the two-dimensional electron gas. Using this approach, we found a correlation between parameters of the lateral patterning and the created effective potential and obtain thus insights on…
The Zitterbewegung (ZB) effect is investigated in graphene with spacially modulated potential near the original Dirac point (ODP) and extra Dirac points (EDPs). Our calculations show that to get the large ZB oscillations, the wave packet center must be at the angle $θ_0=0$ for EDPs located at zero-energy, or $θ_0=π/2$ for both ODP and EDPs at finite energy $\varepsilon=mπ$ ($m$ integer). By varying the parameters ($q_2, \mathbb{V}$) of the periodic potential and the initial momentum ($κ_0, θ_0$) of Gaussian wave packet, it is found that the frequency of the ZB oscillations is in the range $[10…
The electronic structure of a graphene superlattice composed by two periodic regions with different Fermi velocity, energy gap and electrostatic potential is investigated by using an effective Dirac-like Hamiltonian. It must be expected that the change of the Fermi velocity in one region of the graphene superlattice is equivalent to changing the width of this region keeping the Fermi velocity unchanged, provided that the time taken to charge carriers cross the region is the same. However, it is shown here that these two systems are not equivalent. We found extra Dirac points induced by the per…
We have investigated the electrical transport properties of Dirac electrons in a monolayer graphene sheet in the presence of both electric and magnetic modulations. The effects of the modulations on quantum transport when they are in phase and out of phase are considered. We present the energy spectrum and the bandwidth of the Dirac electrons in the presence of both the modulations. We determine the $σ_{yy}$ component of the magnetoconductivity tensor for this system which is shown to exhibit Weiss oscillations.Asymptotic expressions for $σ_{yy}$ are also calculated to better illustrate the ef…
Superlattice potentials are theoretically predicted to modify the single-particle electronic structures. The resulting Coulomb-interaction-dominated low-energy physics would generate highly novel many-body phenomena. Here, by in situ tunneling spectroscopy, we show the signatures of superstructure-modulated correlated electron states in epitaxial bilayer graphene (BLG) on 6H-SiC(0001). As the carrier density is locally quasi-'tuned' by the superlattice potentials of a 6x6 interface reconstruction phase, the spectral-weight transfer occurs between the two broad peaks flanking the charge-neutral…
We demonstrate a vertical field-effect transistor based on a graphene/MoSe2 van der Waals (vdW) heterostructure. The vdW interface between the graphene and MoSe2 exhibits a Schottky barrier with an ideality factor of around 1.3, suggesting a high-quality interface. Owing to the low density of states in graphene, the position of the Fermi level in the graphene can be strongly modulated by an external electric field. Therefore, the Schottky barrier height at the graphene/MoSe2 vdW interface is also modulated. We demonstrate a large current ON-OFF ratio of 10^5. These results point to the potenti…
We report on the observation of the ratchet effect -- generation of direct electric current in response to external terahertz (THz) radiation -- in bilayer graphene, where inversion symmetry is broken by an asymmetric dual-grating gate potential. As a central result, we demonstrate that at high temperature, $T = 150~\textrm{K}$, the ratchet current decreases at high frequencies as $ \propto 1/ω^2$, while at low temperature, $T = 4.2~\textrm{K}$, the frequency dependence becomes much stronger $\propto 1/ω^6$. The developed theory shows that the frequency dependence of the ratchet current is ver…
Combining experiment and theory, we investigate how the naturally created heterojunction at a graphene and metallic contact is modulated via interaction with molecular hydrogen (H2). Due to electrostatic interaction, a Cr/Au electrode induces a pn junction in graphene, leading to an asymmetrical resistance between the charge carriers (electron and hole). This asymmetry is well modeled by considering the preferential charge scattering at the pn junction, and we show that it can be modulated in a reversible, selective and asymmetrical manner by exposing H2 to the metal-graphene interface. Our re…
Based on the transmission coefficient of tunneling electrons, we have presented tunneling current and conductivity across a square-potential barrier for both graphene and $α$-$\mathcal{T}_3$ lattices under a linearly-polarized off-resonant dressing field. The presence of such a dressing field introduces an anisotropy factor in the energy dispersion of tunneling electrons so that the cross section of a Dirac-cone appears as elliptical. Consequently, the field-polarization controlled major axis of the ellipse will be misaligned with the normal direction of a barrier layer in the tunneling system…
We compare the three most commonly used scanning probe techniques to obtain a reliable value of the work function in graphene domains of different thickness. The surface potential (SP) of graphene is directly measured in Hall bar geometry via a combination of electrical functional microscopy and spectroscopy techniques, which enables calibrated work function measurements of graphene domains with values ~4.55+/-0.02 eV and ~4.44+/-0.02eV for single- and bi-layer, respectively. We demonstrate that frequency-modulated Kelvin probe force microscopy (FM-KPFM) provides more accurate measurement of t…
A monolayer graphene exists in an environment where a uniform magnetic field interacts a spatially modulated magnetic field. The spatially modulated magnetic field could affect Landau levels due to a uniform magnetic field. The modulation effects on Landau levels are investigated through the Peierl's tight-binding model. The magneto-electronic properties are dominated by the period, the strength, and the direction of a spatially modulated magnetic field. Such a field could induce the growth in dimensionality, the change of energy dispersions, the destroy of state degeneracy, and the creation o…
The band structure and transport properties of massive Dirac Fermions in bilayer graphene with velocity modulation in space are investigated in presence of the previously created band gap. It is pointed out that the velocity engineering is considered as a factor to control the band gap of symmetry-broken bilayer graphene. The band gap is direct and independent of velocity value if velocity modulated in two layers is set up equally. Otherwise, in the case of interlayer asymmetric velocity, not only the band gap is indirect, but also the electron-hole symmetry fails. This band gap is controllabl…
The electronic and optical response of Bernal stacked bilayer graphene with geometry modulation and gate voltage are studied. The broken symmetry in sublattices, one dimensional periodicity perpendicular to the domain wall and out-of-plane axis introduces substantial changes of wavefunctions, such as gapless topological protected states, standing waves with bonding and anti-bonding characteristics, rich structures in density of states and optical spectra. The wavefunctions present well-behaved standing waves in pure system and complicated node structures in geometry-modulated system. The optic…
Gate-modulated low-temperature Raman spectra reveal that the electric field effect (EFE), pervasive in contemporary electronics, has marked impacts on long wavelength optical phonons of graphene. The EFE in this two dimensional honeycomb lattice of carbon atoms creates large density modulations of carriers with linear dispersion (known as Dirac fermions). Our EFE Raman spectra display the interactions of lattice vibrations with these unusual carriers. The changes of phonon frequency and line-width demonstrate optically the particle-hole symmetry about the charge-neutral Dirac-point. The linear…
