In this work, we present numerical results for the second and third order conductivities of the plain graphene and gapped graphene monolayers associated with the second and third harmonic generation, the optical rectification and the optical Kerr effect. The frequencies considered here range from the microwave to the ultraviolet portion of the spectrum, the latter end of which had not yet been studied. These calculations are performed in the velocity gauge and directly address the components of the conductivity tensor. In the velocity gauge, the radiation field is represented by a power series in the vector potential, and we discuss a very efficient way of calculating its coefficients in the context of tight-binding models.
We study a gapped graphene monolayer in a combination of uniform magnetic field and strain-induced uniform pseudomagnetic field. The presence of two fields completely removes the valley degeneracy. The resulting density of states shows a complicated behaviour that can be tuned by adjusting the strength of the fields. We analyze how these features can be observed in the sublattice, valley and full density of states. The analytical expression for the valley DOS is derived.
In the current work we have investigated the influence of the Rashba spin-orbit coupling on spin-current of a single layer gapped graphene. It was shown that the Rashba coupling has a considerable role in generation of the spin-current of vertical spins in mono-layer graphene. The behavior of the spin-current is determined by density of impurities. It was also shown that the spin-current of the system could increase by increasing the Rashba coupling strength and band-gap of the graphene and the sign of the spin-current could be controlled by the direction of the current-driving electric field.
Two-dimensional gapped semi-Dirac (GSD) materials are systems with a finite band gap that their charge carriers behave relativistically in one direction and Schrödinger-like in the other. In the present work, we show that besides the two well-known energy bands features (curvature and chirality), the band-gap parameter also play a crucial role in the index- and magnetic field-dependence of the Landau levels (LLs) in a GSD system. We take the monolayer phosphorene as a GSD representative example to explicitly provide physical insights into the role of this parameter in determining the index- an…
Generation of quasi-particle--hole pairs in gapped graphene monolayers in the combined field of two counterpropagating light waves is studied. The process represents an analogue of electron-positron pair production from the QED vacuum by the Breit-Wheeler effect. We show, however, that the two-dimensional structure of graphene causes some striking differences between both scenarios. In particular, contrary to the QED case, it allows for non-zero pair production rates at the energy threshold when the Breit-Wheeler reaction proceeds nonlinearly with absorption of three photons.
Gate tunable two-dimensional (2D) superconductors offer significant advantages when studying superconducting phase transitions. Here, we address superconductivity in exfoliated 1T'-MoTe2 monolayers with an intrinsic band gap of ~7.3 meV using electrostatic doping. Despite large differences in the dispersion of the conduction and the valence bands, superconductivity can be achieved easily for both electrons and holes. The onset of superconductivity occurs near 7-8K for both charge carrier types. This temperature is much higher than in bulk samples. Also the in-plane upper critical field is stro…
The wavefunction of massless Dirac fermions is a two-component spinor. In graphene, a one-atom-thick film showing two-dimensional Dirac-like electronic excitations, the two-component representation reflects the amplitude of the electron wavefunction on the A and B sublattices. This unique property provides unprecedented opportunities to image the two components of massless Dirac fermions spatially. Here we report atomic resolution imaging of the two-component Dirac-Landau levels in a gapped graphene monolayer by scanning tunnelling microscopy and spectroscopy. A gap of about 20 meV, driven by …
We investigate the unusual features of the quantum transport in gapped monolayer graphene, which is in a pseudospin symmetry-broken state with a net perpendicular pseudomagnetization. Using these pseudoferromagnets (PFs), we propose a perfect pseudospin valve effect that can be used for realizing pseudospintronics in monolayer graphene. The peculiarity of the associated effects of pseudo spin injection and pseudo spin accumulation are also studied. We further demonstrate the determining effect of the sublattice pseudospin degree of freedom on Andreev reflection and the associated proximity eff…
In a vicinity of the Fermi surface, graphene layers with bandgaps allow for closely simulating the vacuum of quantum electrodynamics and, thus, its yet unverified strong-field phenomenology with accessible field strengths. This striking feature is exploited to investigate a plausible materialization of dynamically assisted pair production through the analog production of light but massive pairs of Dirac quasiparticles. The process is considered in a field configuration combining a weak high-frequency electric mode and a strong low-frequency electric field oscillating in time. Its theoretical s…
We formulate and solve the perhaps simplest two-body bound state problem for interacting Dirac fermions in two spatial dimensions. A two-body bound state is predicted for gapped graphene monolayers in the presence of weakly repulsive electron-electron interactions and a Coulomb impurity with charge $Ze>0$, where the most interesting case corresponds to $Z=1$. We introduce a variational Chandrasekhar-Dirac spinor wave function and show the existence of at least one bound state. This state leaves clear signatures accessible by scanning tunneling microscopy. One may thereby obtain direct informat…
We demonstrate theoretically that the interaction of electrons in gapped Dirac materials (gapped graphene and transition-metal dichalchogenide monolayers) with a strong off-resonant electromagnetic field (dressing field) substantially renormalizes the band gaps and the spin-orbit splitting. Moreover, the renormalized electronic parameters drastically depend on the field polarization. Namely, a linearly polarized dressing field always decreases the band gap (and, particularly, can turn the gap into zero), whereas a circularly polarized field breaks the equivalence of valleys in different points…
We develop a theory of the excitonic phase recently proposed as the zero-field insulating state observed near charge neutrality in monolayer WTe$_2$. Using a Hartree-Fock approximation, we numerically identify two distinct gapped excitonic phases: a spin density wave state for weak non-zero interaction strength and spin spiral order at stronger interactions, separated by a narrow window of non-excitonic quantum spin Hall insulator. We introduce a simplified model capturing key features of the WTe$_2$ band structure, in which these phases appear as distinct valley ferromagnetic orders. We link …
We investigate the Goos-Hänchen shift for ballistic electrons (i) reflected from a step-like inhomogeneity of the potential energy and (or) effective mass, and (ii) transmitted through a ferromagnetic barrier region in monolayer silicene or gapped graphene. For the electrons reflected from a single interface we found that the Goos-Hänchen shift is valley-polarized for gapped graphene structure, and valley- and spin-polarized for silicene due to the spin-valley coupling. Incontrast, for example, to gapless graphene the lateral beam shift in gapped structures occurs not only in the case of total…
Photon drag current in monolayer graphene with degenerate electron gas is studied under interband excitation near the threshold of fundamental transitions. Two main mechanisms generate an emergence of electron current. Non-resonant drag effect (NDE) results from direct transfer of in-plane photon momentum ${\bf q}$ to electron and dependence of matrix elements of transitions on ${\bf q}$. Resonant drag effect (RDE) originates from ${\bf q}$-dependent selection of transitions due to a sharp form of the Fermi distribution in energy. The drag current essentially depends on the polarization of rad…
We study theoretically the strong-field absorption of an ultrafast optical pulse by a gapped graphene monolayer. At low field amplitudes, the absorbance in the pristine graphene is equal to the universal value of $2.3$ percent. Although the ultrafast optical absorption for low field amplitudes is independent of the polarization, linear or circular, of the applied optical pulse, for high field amplitudes, the absorption strongly depends on the pulse polarization. For a linearly polarized pulse, the optical absorbance is saturated at the value of $\approx 1.4$ percent for the pulse's amplitude o…
Monolayer graphene with an energy gap presents a pseudospin symmetry broken ferromagnet with a perpendicular pseudomagnetization whose direction is switched by altering the type of doping between n and p. We demonstrate an electrical current switching effect in pseudospin version of a spin valve in which two pseudoferromagnetic regions are contacted through a normal graphene region. The proposed structure exhibits a pseudomagnetoresistance, defined as the relative difference of resistances of parallel and antiparallel alignments of the pseudomagnetizations, which can be tuned to unity. This pe…
Surface effects on the plasmons in two-dimemsional heterostructures: Application to tilted semi-Dirac materials
Hunter College, City University of New York（纽约市立大学亨特学院）；The Graduate School and University Center, The City University of New York（纽约市立大学研究生院与大学中心）；The University of Tampa（坦帕大学）；Medgar Evers College of City University of New York（纽约市立大学梅加尔·伊弗斯学院）；US Air Force Research Laboratory（美国空军研究实验室）
New losses mechanism in monolayer graphene nanoresonators caused by dissipative intravalley currents stipulated by the synthetic electric fields is considered. These fields are generated by time-dependent gauge fields arising in graphene membrane due to its intrinsic out-of- plain distortions and the influence of the external periodic electromotive force. This losses mechanism accounts for essential part (about 40 percents) of losses in graphene nanoresonator and is specific just for graphene. The ways of the minimization of this kind of dissipation (increase of the quality factor of the elect…
Measurement and theory of the two-terminal conductance of monolayer and bilayer graphene in the quantum Hall regime are compared. We examine features of conductance as a function of gate voltage that allow monolayer, bilayer, and gapped samples to be distinguished, including N-shaped distortions of quantum Hall plateaus and conductance peaks and dips at the charge neutrality point. Generally good agreement is found between measurement and theory. Possible origins of discrepancies are discussed.
An energy gap can be opened in the electronic spectrum of graphene by lifting its sublattice symmetry. In bilayers, it is possible to open gaps as large as 0.2 eV. However, these gaps rarely lead to a highly insulating state expected for such semiconductors at low temperatures. This long-standing puzzle is usually explained by charge inhomogeneity. Here we investigate spatial distributions of proximity-induced superconducting currents in gapped graphene and, also, compare measurements in the Hall bar and Corbino geometries in the normal state. By gradually opening the gap in bilayer graphene, …
Measurement of magnetic oscillations on thermodynamic quantities (like magnetization and specific heat), is one of the experimental methods to access the density of states of electronic systems. In the present paper we therefore theoretically explore the oscillatory phenomena on the specific heat of graphenes considering gapped and gapless cases in a quantized magnetic field. Further situations is also considered, as the influence of impurities, Coulomb interaction and phonons. We could then map the magnetic oscillations on the specific heat of graphenes under these constraints and the obtaine…
Graphene, as an atomic-thick ultrasoft membrane, almost has no resistance against out-of-plane deformations and, therefore, it is always wrinkled to a certain degree. Recently, corrugated structures and their effects on the electronic properties of monolayer graphene have been studied extensively. However, similar experimental studies in bilayer graphene have yet to be reported. Here, we show that corrugations in bilayer graphene can generate incommensurate stacking solitons (domain walls) between commensurate Bernal-stacked domains. By using scanning tunneling microscopy, we microscopically s…
Bilayer graphene contains, compared to graphene monolayer, an additional graphene sheet and, therefore, extra degrees of freedom, making it a unique system for complex electronic states to emerge. Here, we show that there are two types of domain walls, i.e., coupling domain wall and potential domain wall, in gapped graphene bilayers, which make microscopic electronic properties of the bilayers varying spatially. The coupling domain wall separates two graphene bilayer regions with different interlayer coupling strengths and the potential domain wall is a boundary separating two adjacent regions…
We study the effect of a uniform pseudomagnetic field, induced by a strain in a monolayer and double layer of gapped graphene, acting on excitons. For our analysis it is crucial that the pseudomagnetic field acts on the charges of the constituent particles of the excitons, i.e., the electrons and holes, the same way in contrast to a magnetic field. Moreover, using a circularly polarized laser field, the electrons and the holes can be excited only in one valley of the honeycomb lattice of gapped graphene. This breaks the time-reversal symmetry and provides the possibility to observe the various…
We study the physics of Dirac fermions in a gapped graphene monolayer containing two Coulomb impurities. For the case of equal impurity charges, we discuss the ground-state energy using the linear combination of atomic orbitals (LCAO) approach. For opposite charges of the Coulomb centers, an electric dipole potential results at large distances. We provide a nonperturbative analysis of the corresponding low-energy scattering problem.
In this work, we present the analytical expression for the second order divergence in the third order DC response of a cold semiconductor, which can be probed by different electric field setups. Results from this expression were then compared, for the response of the gapped graphene monolayer, with numerical results from a velocity gauge calculation of the third order conductivity. The good agreement between the two validates our analytical expression.
Systems with strong light-matter interaction opens up new avenues for studying topological phases of matter. Examples include exciton-polaritons, mixed light-matter quasiparticles, where the topology of the polaritonic band structure arises from the collective coupling between matter wave and optical fields strongly confined in periodic dielectric structures. Distinct from light-matter interaction in a uniform environment, the spatially varying nature of the optical fields leads to a fundamental modification of the well-known optical selection rules, which were derived under the plane wave app…
The superconductor PdTe$_2$ is known to host bulk Dirac bands and topological surface states. The coexistence of superconductivity and topological surface states makes PdTe$_2$ a promising platform for exploring topological superconductivity and Majorana bound states. In this work, we report the layer-by-layer molecular beam epitaxy growth and spectroscopic characterization of high quality PdTe$_2$ films with thickness down to 3 monolayers (ML). In the 3 ML PdTe$_2$ film, we observed spin-polarized surface resonance states, which are isolated from the bulk bands due to the quantum size effects…
We present analytical expressions for the eigenstates and eigenvalues of electrons confined in a graphene monolayer in the presence of a disclination. The calculations are performed in the continuum limit approximation in the vicinity of the Dirac points, solving Dirac equation by freezing out the carrier radial motion. We include the effect of an external magnetic field and show the appearence of Aharonov-Bohm oscillation and find out the conditions of gapped and gapless states in the spectrum. We show that the gauge field due to a disclination lifts the orbital degeneracy originating from th…
Since the first realization of reversible charge doping in graphene via field-effect devices, it has become evident how the induction a gap could further enhance its potential for technological applications. Here we show that the gap opening due to a sublattice symmetry breaking has also a profound impact on the polar response of graphene. By combining ab-initio calculations and analytical modelling we show that for realistic band-gap values ($Δ\lesssim 0.5$ eV) the piezoelectric coefficient and the Born effective charge of graphene attain a giant value, independent on the gap. In particular t…
We discover an unusual phenomenon that occurs when a graphene monolayer is illuminated by a short and intense pulse at normal incidence. Due to the pulse-induced oscillations of the Dirac cones, a dynamical breaking of the layer's centrosymmetry takes place, leading to the generation of second harmonic waves. We prove that this result can only be found by using the full Dirac equation and show that the widely used semiconductor Bloch equations fail to reproduce this and some other important physics of graphene. Our results open new windows in the understanding of nonlinear light-matter interac…
The graphene family materials are two-dimensional staggered monolayers with a gapped energy band structure due to intrinsic spin-orbit coupling. The mass gaps in these materials can be manipulated on-demand via biasing with a static electric field, an off-resonance circularly polarized laser, or an exchange interaction field, allowing the monolayer to be driven through a multitude of topological phase transitions. We investigate the dynamics of spin-orbit coupled graphene family materials to unveil topological phase transition fingerprints embedded in the nonlinear regime and show how these si…
In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflect…
We analyze the valley selection rules for optical transitions from impurity states to the conduction band in two-dimensional Dirac materials, taking a monolayer of MoS2 as an example. We employ the analytical model of a shallow impurity potential which localizes electrons described by a spinor wave function, and, first, find the system eigenstates taking into account the presence of two valleys in the Brillouin zone. Then, we find the spectrum of the absorbance and calculate the photon-drag electric current due to the impurity-band transitions, drawing the general conclusions regarding the val…
1T$^\prime$-MoS$_2$ exhibits valley-spin-polarized tilted Dirac bands in the presence of external vertical electric field and undergoes a topological phase transition between the topological insulator and band insulator around the critical value of the electric field. Within the linear response theory, we theoretically investigate the anisotropic longitudinal optical conductivities of tilted Dirac bands in both undoped and doped 1T$^\prime$-MoS$_2$, including the effects of the vertical electric field. The influence of the spin-orbit coupling gap, band tilting, and vertical electric field on t…
DC photoelectrical currents can be generated purely as a non-linear effect in uniform media lacking inversion symmetry without the need for a material junction or bias voltages to drive it, in what is termed photogalvanic effect. These currents are strongly dependent on the polarization state of the radiation, as well as on topological properties of the underlying Fermi surface such as its Berry curvature. In order to study the intrinsic photogalvanic response of gapped graphene (GG), biased bilayer graphene (BBG), and hexagonal boron nitride (hBN), we compute the non-linear current using a pe…
Two-dimensional (2D) massive Dirac electrons possess a finite Berry curvature, with Chern number $\pm 1/2$, that entails both a quantized dc Hall response and a subgap full-quarter Kerr rotation. The observation of these effects in 2D massive Dirac materials such as gapped graphene, hexagonal boron nitride or transition metal dichalcogenides (TMDs) is obscured by the fact that Dirac cones come in pairs with opposite sign Berry curvatures, leading to a vanishing Chern number. Here, we show that the presence of spin-orbit interactions, combined with an exchange spin splitting induced either by d…
We show that band topology can dramatically change the photophysics of two-dimensional (2D) semiconductors. For systems in which states near the band extrema are of multiple orbitals character and the spinors describing the orbital components (pseudospins) pick up nonzero winding numbers (topological invariants) around the extremal k-point, the optical strength and nature (i.e., helicity) of the excitonic states are dictated by the optical matrix element winding number, a unique and heretofore unrecognized characteristic. We illustrate these findings in three gapped graphene systems - monolaye…
We report the interesting possibilities related to the plasmonics and the key parameters of optoelectronics, such as the absorbance and the transmittance, in Van der Waals heterostructures of graphene monolayer on 2D transition metal dichalcogenide (GrTMD) substrate here. We obtain the gapped bands with a Rashba spin-orbit coupling dependent pseudo Zeeman field due to the interplay of substrate induced interactions. This enables us to obtain an expression of the dielectric function in the finite doping case ignoring the spin-flip scattering events completely. We observe that the relative stren…
