Dirac Fermions In Monolayer Graphene Research Articles

Selective excitation of four-wave mixing by helicity in gated graphene.

Gapless Dirac fermions in monolayer graphene give rise to an abundance of peculiar physical properties, including exceptional broadband nonlinear optical responses. By tuning the chemical potential, stacking order, and photonic structures, the effective modulation of nonlinear optical phenomena in graphene has been demonstrated in recent years. Here, we demonstrate that optical helicity can be used as an extra tuning knob for four-wave mixing in gated graphene. Our results reveal the helicity selection rule for four-wave mixing in monolayer graphene, revealing nearly perfect circular polarization. Corresponding theoretical interpretations of the helicity selection rule that are also applicable to other nonlinear optical processes and materials are presented.

Floquet–Dirac fermions in monolayer graphene by Wannier functions

Wannier functions have been widely applied in the study of topological properties and Floquet–Bloch bands of materials. Usually, the real-space Wannier functions are linked to the k-space Hamiltonian by two types of Fourier transform (FT), namely lattice-gauge FT (LGFT) and atomic-gauge FT (AGFT), but the differences between these two FTs on Floquet–Bloch bands have rarely been addressed. Taking monolayer graphene as an example, we demonstrate that LGFT gives different topological descriptions on the Floquet–Bloch bands for the structurally equivalent directions which are obviously unphysical, while AGFT is immune to this dilemma. We introduce the atomic-laser periodic effect to explain the different Floquet–Bloch bands between the LGFT and AGFT. Using AGFT, we showed that linearly polarized laser could effectively manipulate the properties of the Dirac fermions in graphene, such as the location, generation and annihilation of Dirac points. This proposal offers not only deeper understanding on the role of Wannier functions in solving the Floquet systems, but also a promising platform to study the interaction between the time-periodic laser field and materials.

Interaction-disorder-driven characteristic momentum in graphene, approach of multi-body distribution functions

Multi-point probability measures along with the dielectric function of Dirac Fermions in mono-layer graphene containing particle-particle and white-noise (out-plane) disorder interactions on an equal footing in the Thomas-Fermi-Dirac approximation is investigated. By calculating the one-body carrier density probability measure of the graphene sheet, we show that the density fluctuation (ζ−1) is related to the disorder strength (ni), the interaction parameter (rs) and the average density (bar{{boldsymbol{n}}}) via the relation {{boldsymbol{zeta }}}^{-{bf{1}}}{boldsymbol{propto }}{{boldsymbol{r}}}_{{boldsymbol{s}}}{{boldsymbol{n}}}_{{boldsymbol{i}}}^{{bf{2}}}{bar{{boldsymbol{n}}}}^{-{bf{1}}} for which bar{{boldsymbol{n}}}to {bf{0}} leads to strong density inhomogeneities, i.e. electron-hole puddles (EHPs), in agreement with the previous works. The general equation governing the two-body distribution probability is obtained and analyzed. We present the analytical solution for some limits which is used for calculating density-density response function. We show that the resulting function shows power-law behaviors in terms of ζ with fractional exponents which are reported. The disorder-averaged polarization operator is shown to be a decreasing function of momentum like ordinary 2D parabolic band systems. It is seen that a disorder-driven momentum qch emerges in the system which controls the behaviors of the screened potential. We show that in small densities an instability occurs in which imaginary part of the dielectric function becomes negative and the screened potential changes sign. Corresponding to this instability, some oscillations in charge density along with a screening-anti-screening transition are observed. These effects become dominant in very low densities, strong disorders and strong interactions, the state in which EHPs appear. The total charge probability measure is another quantity which has been investigated in this paper. The resulting equation is analytically solved for large carrier densities, which admits the calculation of arbitrary-point correlation function.

Evidence of electronic cloaking from chiral electron transport in bilayer graphene nanostructures

The coupling of charge carrier motion and pseudospin via chirality for massless Dirac fermions in monolayer graphene has generated dramatic consequences, such as the unusual quantum Hall effect and Klein tunneling. In bilayer graphene, charge carriers are massive Dirac fermions with a finite density of states at zero energy. Because of their non-relativistic nature, massive Dirac fermions can provide an even better test bed with which to clarify the importance of chirality in transport measurement than massless Dirac fermions in monolayer graphene. Here, we report an electronic cloaking effect as a manifestation of chirality by probing phase coherent transport in chemical-vapor-deposited bilayer graphene. Conductance oscillations with different periodicities were observed on extremely narrow bilayer graphene heterojunctions through electrostatic gating. Using a Fourier analysis technique, we identified the origin of each individual interference pattern. Importantly, the electron waves on the two sides of the potential barrier can be coupled through the evanescent waves inside the barrier, making the confined states underneath the barrier invisible to electrons. These findings provide direct evidence for the electronic cloaking effect and hold promise for the realization of pseudospintronics based on bilayer graphene.

Piezoelectric surface acoustical phonon amplification in graphene on a GaAs substrate

We study the interaction of Dirac Fermions in monolayer graphene on a GaAs substrate in an applied electric field by the combined action of the extrinsic potential of piezoelectric surface acoustical phonons of GaAs (piezoelectric acoustical (PA)) and of the intrinsic deformation potential of acoustical phonons in graphene (deformation acoustical (DA)). We find that provided the dc field exceeds a threshold value, emission of piezoelectric (PA) and deformation (DA) acoustical phonons can be obtained in a wide frequency range up to terahertz at low and high temperatures. We found that the phonon amplification rate RPA,DA scales with TBGS−1 (S=PA,DA), TBGS being the Block−Gru¨neisen temperature. In the high-T Block−Gru¨neisen regime, extrinsic PA phonon scattering is suppressed by intrinsic DA phonon scattering, where the ratio RPA/RDA scales with ≈1/n, n being the carrier concentration. We found that only for carrier concentration n≤1010cm−2, RPA/RDA>1. In the low-T Block−Gru¨neisen regime, and for n=1010cm−2, the ratio RPA/RDA scales with TBGDA/TBGPA≈7.5 and RPA/RDA>1. In this regime, PA phonon dominates the electron scattering and RPA/RDA<1 otherwise. This study is relevant to the exploration of the acoustic properties of graphene and to the application of graphene as an acoustical phonon amplifier and a frequency-tunable acoustical phonon device.

Gap structure of the Hofstadter system of interacting Dirac fermions in graphene.

The effects of mutual Coulomb interactions between Dirac fermions in monolayer graphene on the Hofstadter energy spectrum are investigated. For two flux quanta per unit cell of the periodic potential, interactions open a gap in each Landau level with the smallest gap in the n=1 Landau level. For more flux quanta through the unit cell, where the noninteracting energy spectra have many gaps in each Landau level, interactions enhance the low-energy gaps and strongly suppress the high-energy gaps and almost close a high-energy gap for n=1. The signature of the interaction effects in the Hofstadter system can be probed through magnetization, which is governed by the mixing of the Landau levels and is enhanced by the Coulomb interaction.

Feasibility of a drift-induced instability in modulated graphene

We examine the feasibility of a drift-induced instability of Dirac fermions in monolayer graphene in a weak periodic potential, taking into account of a steady current. In this work, we treat magnetic field induced Landau quantization including the effects of drift induced current (an in-plane dc electric field), and analyze both the inter-and the intra-Landau band aspects of the magnetoplasmon spectrum. We employ the framework of self-consistent-field approximation to determine the plasmon spectrum. The existence of the drift induced instability regions in the intra-Landau band magnetoplasmon spectrum as a function of inverse magnetic field is shown and discussed. The unstable intra-Landau band plasmon excitation could be a potential source of THz radiation with electronic device applications.

Piezoelectric surface acoustical phonon limited mobility of electrons in graphene on a GaAs substrate

We study the mobility of Dirac fermions in monolayer graphene on a GaAs substrate, limited by the combined action of the extrinsic potential of piezoelectric surface acoustical phonons of GaAs (PA) and of the intrinsic deformation potential of acoustical phonons in graphene (DA). In the high-temperature ($T$) regime, the momentum relaxation rate exhibits the same linear dependence on $T$ but different dependencies on the carrier density $n$, corresponding to the mobility $\ensuremath{\mu}\ensuremath{\propto}1/\sqrt{n}$ and $1/n$, respectively for the PA and DA scattering mechanisms. In the low-$T$ Bloch-Gr\"uneisen regime, the mobility shows the same square-root density dependence $\ensuremath{\mu}\ensuremath{\propto}\sqrt{n}$, but different temperature dependencies $\ensuremath{\mu}\ensuremath{\propto}{T}^{\ensuremath{-}3}$ and ${T}^{\ensuremath{-}4}$, respectively for PA and DA phonon scattering.

Reversal of Klein reflection by magnetic barriers in bilayer graphene

Massless Dirac fermions in monolayer graphene exhibit total transmission when normally incident on a scalar potential barrier, a consequence of the Klein paradox originally predicted by O Klein for relativistic electrons obeying the 3 + 1 dimensional Dirac equation. For bilayer graphene, charge carriers are massive Dirac fermions and, due to different chiralities, electron and hole states are not coupled to each other. Therefore, the wavefunction of an incident particle decays inside a barrier as for the non-relativistic Schrödinger equation. This leads to exponentially small transmission upon normal incidence. We show that, in the presence of magnetic barriers, such massive Dirac fermions can have transmission even at normal incidence. The general consequences of this behavior for multilayer graphene consisting of massless and massive modes are mentioned. We also briefly discuss the effect of a bias voltage on such magnetotransport.

Designer Dirac fermions and topological phases in molecular graphene

The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system-molecular graphene-assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p-n and p-n-p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields, wherein Dirac electrons react to 'pseudo' electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the relativistic magnetic quantum limit, which has so far been inaccessible in natural graphene. Molecular graphene provides a versatile means of synthesizing exotic topological electronic phases in condensed matter using tailored nanostructures.