Dirac Electrons In Graphene Research Articles

Emergence of tunable intersubband-plasmon-polaritons in graphene superlattices

On-demand modification of the electronic band structures of high-mobility two-dimensional (2D) materials is of great interest for various applications that require rapid tuning of electrical and optical responses of solid-state devices. Although electrically tunable superlattice (SL) potentials have been proposed for band structure engineering of the Dirac electrons in graphene, the ultimate goal of engineering emergent quasiparticle excitations that can hybridize with light has not been achieved. We show that an extreme modulation of one-dimensional (1D) SL potentials in monolayer graphene produces ladder-like electronic energy levels near the Fermi surface, resulting in optical conductivity dominated by intersubband transitions (ISBTs). A specific and experimentally realizable platform comprising hBN-encapsulated graphene on top of a 1D periodic metagate and a second unpatterned gate is shown to produce strongly modulated electrostatic potentials. We find that Dirac electrons with large momenta perpendicular to the modulation direction are waveguided via total internal reflections off the electrostatic potential, resulting in flat subbands with nearly equispaced energy levels. The predicted ultrastrong coupling of surface plasmons to electrically controlled ISBTs is responsible for emergent polaritonic quasiparticles that can be optically probed. Our study opens an avenue for exploring emergent polaritons in 2D materials with gate-tunable electronic band structures.

Tilt-induced many-body corrections to optical conductivity of tilted Dirac cone materials

Katsnelson has shown that, within the Fermi-liquid approach, the optical conductivity of Dirac electrons in graphene is not affected by many-body interactions [M. I. Katsnelson, Eur. Phys. Lett. 84, 37001 (2008)]. We show that, when the Dirac cone is tilted, the Fermi-liquid corrections arise in the optical conductivity in a manner that the correction depends on the angle between the electric field of the incident light and the tilt direction. Therefore the mapping of the optical conductivity for various directions of the incident light enables a determination of the many-body effect in the optical conductivity spectrum of the two-dimensional tilted Dirac cone materials.

Dirac imprints on the g -factor anisotropy in graphene

Dirac electrons in graphene are to lowest order spin 1/2 particles, owing to the orbital symmetries at the Fermi level. However, anisotropic corrections in the $g$-factor appear due to the intricate spin-valley-orbit coupling of chiral electrons. We resolve experimentally the $g$-factor along the three orthogonal directions in a large-scale graphene sample. We employ a Hall bar structure with an external magnetic field of arbitrary direction, and extract the effective $g$-tensor via resistively-detected electron spin resonance. We employ a theoretical perturbative approach to identify the intrinsic and extrinsic spin orbit coupling and obtain a fundamental parameter inherent to the atomic structure of $^{12}$C, commonly used in ab-initio models.

Fizeau drag in graphene plasmonics.

Dragging of light by moving media was predicted by Fresnel1 and verified by Fizeau's celebrated experiments2 with flowing water. This momentous discovery is among the experimental cornerstones of Einstein's special relativitytheory and is well understood3,4 in the context of relativistic kinematics. By contrast, experiments on dragging photons by an electron flow in solids are riddled with inconsistencies and have so far eluded agreement with the theory5-7. Here we report on the electron flow dragging surface plasmon polaritons8,9 (SPPs): hybrid quasiparticles of infrared photons and electrons in graphene. The drag is visualized directly through infrared nano-imaging of propagating plasmonic waves in the presence of a high-density current. The polaritons in graphene shorten their wavelength when propagating against the drifting carriers. Unlike the Fizeau effect for light, the SPP drag by electrical currents defies explanation by simple kinematics and is linked to the nonlinear electrodynamics of Dirac electrons in graphene. The observed plasmonic Fizeau drag enables breaking of time-reversal symmetry and reciprocity10 at infrared frequencies without resorting to magnetic fields11,12 or chiral optical pumping13,14. The Fizeau drag also provides a tool with which to study interactions and nonequilibrium effects in electron liquids.

Programmable Bloch polaritons in graphene.

Efficient control of photons is enabled by hybridizing light with matter. The resulting light-matter quasi-particles can be readily programmed by manipulating either their photonic or matter constituents. Here, we hybridized infrared photons with graphene Dirac electrons to form surface plasmon polaritons (SPPs) and uncovered a previously unexplored means to control SPPs in structures with periodically modulated carrier density. In these periodic structures, common SPPs with continuous dispersion are transformed into Bloch polaritons with attendant discrete bands separated by bandgaps. We explored directional Bloch polaritons and steered their propagation by dialing the proper gate voltage. Fourier analysis of the near-field images corroborates that this on-demand nano-optics functionality is rooted in the polaritonic band structure. Our programmable polaritonic platform paves the way for the much-sought benefits of on-the-chip photonic circuits.

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...

Hall effect for Dirac electrons in graphene exposed to an Abrikosov flux lattice

The proposals for realizing exotic particles through coupling of quantum Hall effect to superconductivity involve spatially non-uniform magnetic fields. As a step toward that goal, we study, both theoretically and experimentally, a system of Dirac electrons exposed to an Abrikosov flux lattice. We theoretically find that the non-uniform magnetic field causes a carrier-density–dependent reduction of the Hall conductivity. Our studies show that this reduction originates from a rather subtle effect: a levitation of the Berry curvature within Landau levels broadened by the non-uniform magnetic field. Experimentally, we measure the magneto-transport in a monolayer graphene-hexagonal boron nitride-niobium diselenide (NbSe2) heterostructure, and find a density-dependent reduction of the Hall resistivity of graphene as the temperature is lowered from above the superconducting critical temperature of NbSe2, when the magnetic field is uniform, to below, where the magnetic field bunches into an Abrikosov flux lattice.

Anomalous Thermodiffusion of Electrons in Graphene

We reveal a dramatic departure of electron thermodiffusion in solids relative to the commonly accepted picture of the ideal free-electron gas model. In particular, we show that the interaction with the lattice and impurities, combined with a strong material dependence of the electron dispersion relation, leads to counterintuitive diffusion behavior, which we identify by comparing a two-dimensional electron gas (2DEG) and single-layer graphene. When subject to a temperature gradient ∇T, thermodiffusion of massless Dirac fermions in graphene exhibits an anomalous behavior with electrons moving along ∇T and accumulating in hot regions, in contrast to normal electron diffusion in a 2DEG with parabolic dispersion, where net motion against ∇T is observed, accompanied by electron depletion in hot regions. These findings bear fundamental importance for the understanding of the spatial electron dynamics in emerging materials, establishing close relations with other branches of physics dealing with electron systems under nonuniform temperature conditions.

Interplay between effects of barrier tilting and scatterers within a barrier on tunneling transport of Dirac electrons in graphene

Dirac-electronic tunneling and transport properties with both finite and zero energy band gap are investigated for graphene with an in-plane tilted potential barrier embedded with scatters. For a tilted barrier, by using Wentzel-Kramers-Brillouin approximation, an analytical solution is obtained first for transmission coefficient of Dirac electrons in gapped graphene in the absence of any scatters. In the presence of either a single or a continuous distribution of scatters embedded within a tilted barrier, however, a numerical scheme based on finite-difference approach is developed for accurately calculating both transmission coefficient and tunneling resistance of Dirac electrons. Here, the combination of a tilted barrier and a scatter potential can be viewed as an effective barrier-potential profile facilitated by a proper gate structure. Meanwhile, a full analysis and detailed comparisons are presented for the interplay between effects of both distributed scatters in a barrier and barrier tilting on tunneling transport of Dirac electrons in graphene. The barrier-tilting field and scatter position are found to play a key role in controlling a peak of tunneling resistance as well as in its switching to a cusp by a mid-barrier-embedded scatter as the incident energy reaches the Dirac point in a barrier. Different from a single scatter, a continuous distribution within a barrier can enhance the unimpeded incoherent tunneling for head-on collision while greatly suppressing skew ones with increasing barrier-tilting field. All these predicted attractive transport properties are expected to be extremely useful for designing both novel electronic and optical graphene-based devices and electronic lenses in ballistic-electron optics.

Spin- and valley-related tunneling time of massive Dirac electrons in a ferromagnetic MoS2 quantum structure

Abstract We investigate the tunneling time of massive Dirac electrons through an electric barrier in a ferromagnetic quantum structure consisting of normal/ferromagnetic/ normal MoS 2 parts. The results show that the dwell time is not only spin-separated but also valley-separated due to the spin-valley coupling of valence-band edges together with the exchange field. When the electric barrier broadens, the spin-dependent and valley-dependent dwell times increase with oscillating behavior. These behaviors are different from the massless Dirac electrons in graphene. Moreover, both the spin- and valley-dependent dwell times can be effectively modulated by the angle of incidence, the width, and the height of the electric barrier.

Dirac Magnons in a Honeycomb Lattice Quantum XY Magnet CoTiO3

The discovery of massless Dirac electrons in graphene and topological Dirac-Weyl materials has prompted a broad search for bosonic analogues of such Dirac particles. Recent experiments have found evidence for Dirac magnons above an Ising-like ferromagnetic ground state in a two-dimensional (2D) kagome lattice magnet and in the van der Waals layered honeycomb crystal CrI$_3$, and in a 3D Heisenberg magnet Cu$_3$TeO$_6$. Here we report on our inelastic neutron scattering investigation on large single crystals of a stacked honeycomb lattice magnet CoTiO$_3$, which is part of a broad family of ilmenite materials. The magnetically ordered ground state of CoTiO$_3$ features ferromagnetic layers of Co$^{2+}$, stacked antiferromagnetically along the $c$-axis. We discover that the magnon dispersion relation exhibits strong easy-plane exchange anisotropy and hosts a clear gapless Dirac cone along the edge of the 3D Brillouin zone. Our results establish CoTiO$_3$ as a model pseudospin-$1/2$ material to study interacting Dirac bosons in a 3D quantum XY magnet.

Dirac electron in graphene with magnetic fields arising from first-order intertwining operators

The behavior of a Dirac electron in graphene, under magnetic fields which are orthogonal to the layer, is studied. The initial problem is reduced to an equivalent one, wherein two one-dimensional Schrödinger Hamiltonians are intertwined by a first-order differential operator. Special magnetic fields are initially chosen, in order that will be shape-invariant, exactly solvable potentials. When looking for more general first-order operators intertwining H− with a not-necessarily shape-invariant Hamiltonian, new magnetic fields associated also with analytic solutions will be generated. The iteration of this procedure is also discussed.

Long-wavelength gauge symmetry and translations in a magnetic field for Dirac electrons in graphene

In two-dimensional (2D) electron systems in a magnetic field, the Coulomb interaction among charge carriers, under Landau quantization, essentially governs a variety of many-body phenomena while there are also phenomena, such as the (integer) quantum Hall effect, that appear unaffected by the interaction. It is pointed out that the response of 2D electrons to spatially-uniform potentials and fields enjoys a long-wavelength gauge symmetry, associated with cyclotron motion of electrons, that leaves the Coulomb interaction invariant and that thus naturally explains why cyclotron resonance (as implied by Kohn’s theorem) and the quantized Hall conductance appear insensitive to the interaction. It is discussed, in the light of this new long-wavelength gauge symmetry, how Dirac electrons in graphene and conventional 2D electrons differ in cyclotron-resonance characteristics and the quantum Hall effect.

Valley-coupled transport in graphene with Y-shaped Kekulé structure

We investigate the valley-coupled transport of Dirac electrons in graphene with a uniform Y-shaped Kekul\'e lattice distortion, in which the original $K$ and ${K}^{\ensuremath{'}}$ valleys of the pristine graphene are folded together due to the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ enlargement of the primitive cell. We show that the Klein tunneling effect of Dirac electrons tunneling through a rectangle potential barrier is significantly enhanced: The perfect transmission is not limited to normal incidence but occurs in a range of oblique incidence angle when the inversion symmetry of the system is broken to form a single Dirac-cone phase. It is also found that the C-C bond-length modulation of the Kekul\'e lattice that keeps the inversion symmetry of the system can be used to manipulate the valley degree of freedom in a similar way to the exchange field precessing spin, and such valley manipulation can be implemented conveniently by a gate voltage controlling the local potential of the device. The disorder and temperature effects are also discussed.

Substrate-induced topological minibands in graphene

The honeycomb lattice sets the basic arena for numerous ideas to implement electronic, photonic, or phononic topological bands in (meta-)materials. Novel opportunities to manipulate Dirac electrons in graphene through band engineering arise from superlattice potentials as induced by a substrate such as hexagonal boron-nitride. Making use of the general form of a weak substrate potential as dictated by symmetry, we analytically derive the low-energy minibands of the superstructure, including a characteristic 1.5 Dirac cone deriving from a three-band crossing at the Brillouin zone edge. Assuming a large supercell, we focus on a single Dirac cone (or valley) and find all possible arrangements of the low-energy electron and hole bands in a complete six-dimensional parameter space. We identify the various symmetry planes in parameter space inducing gap closures and find the sectors hosting topological minibands, including also complex band crossings that generate a valley Chern number atypically larger than one. Our map provides a starting point for the systematic design of topological bands by substrate engineering.

Valley switch in a graphene superlattice due to pseudo-Andreev reflection

Dirac electrons in graphene have a valley degree of freedom that is being explored as a carrier of information. In that context of "valleytronics" one seeks to coherently manipulate the valley index. Here we show that reflection from a superlattice potential can provide a valley switch: Electrons approaching a pristine-graphene--superlattice-graphene interface near normal incidence are reflected in the opposite valley. We identify the topological origin of this valley switch, by mapping the problem onto that of Andreev reflection from a topological superconductor, with the electron-hole degree of freedom playing the role of the valley index. The valley switch is ideal at a symmetry point of the superlattice potential, but remains close to 100% in a broad parameter range.

Graphene coherent states

In this paper, we will construct the coherent states for a Dirac electron in graphene placed in a constant homogeneous magnetic field which is orthogonal to the graphene surface. First of all, we will identify the appropriate annihilation and creation operators. Then, we will derive the coherent states as eigenstates of the annihilation operator, with complex eigenvalues. Several physical quantities, as the Heisenberg uncertainty product, probability density and mean energy value, will be as well explored.

Tuning a circular p-n junction in graphene from quantum confinement to optical guiding.

The photon-like propagation of the Dirac electrons in graphene, together with its record-high electronic mobility, can lead to applications based on ultrafast electronic response and low dissipation. However, the chiral nature of the charge carriers that is responsible for the high mobility also makes it difficult to control their motion and prevents electronic switching. Here, we show how to manipulate the charge carriers by using a circular p-n junction whose size can be continuously tuned from the nanometre to the micrometre scale. The junction size is controlled with a dual-gate device consisting of a planar back gate and a point-like top gate made by decorating a scanning tunnelling microscope tip with a gold nanowire. The nanometre-scale junction is defined by a deep potential well created by the tip-induced charge. It traps the Dirac electrons in quantum-confined states, which are the graphene equivalent of the atomic collapse states (ACSs) predicted to occur at supercritically charged nuclei. As the junction size increases, the transition to the optical regime is signalled by the emergence of whispering-gallery modes, similar to those observed at the perimeter of acoustic or optical resonators, and by the appearance of a Fabry-Pérot interference pattern for junctions close to a boundary.

Effects of optical polarization on hybridization of radiative and evanescent field modes

A back action from Dirac electrons in graphene on the hybridization of radiative and evanescent fields is found as an analogy to Newton's third law. Here, the back action appears as a localized polarization field which greatly modifies an incident surface-plasmon-polariton (SPP) field. This yields a high sensitivity to local dielectric environments and provides a scrutiny tool for molecules or proteins selectively bounded with carbons. A scattering matrix is shown with varied frequencies nearby the surface-plasmon (SP) resonance for the increase, decrease and even a full suppression of the polarization field, which enables accurate effective-medium theories to be constructed for Maxwell-equation finite-difference time-domain methods. Moreover, double peaks in the absorption spectra for hybrid SP and graphene-plasmon modes are significant only with a large conductor plasma frequency, but are overshadowed by a round SPP peak at a small plasma frequency as the graphene is placed close to conductor surface. These resonant absorptions facilitate the polariton-only excitations, leading to polariton condensation for a threshold-free laser.

Ultrafast momentum imaging of pseudospin-flip excitations in graphene

The pseudospin of Dirac electrons in graphene manifests itself in a peculiar momentum anisotropy for photo-excited electron-hole pairs. These interband excitations are in fact forbidden along the direction of the light polarization, and are maximum perpendicular to it. Here, we use time- and angle-resolved photoemission spectroscopy to investigate the resulting unconventional hot carrier dynamics, sampling carrier distributions as a function of energy and in-plane momentum. We first show that the rapidly-established quasi-thermal electron distribution initially exhibits an azimuth-dependent temperature, consistent with relaxation through collinear electron-electron scattering. Azimuthal thermalization is found to occur only at longer time delays, at a rate that depends on the substrate and the static doping level. Further, we observe pronounced differences in the electron and hole dynamics in n-doped samples. By simulating the Coulomb- and phonon-mediated carrier dynamics we are able to disentangle the influence of excitation fluence, screening, and doping, and develop a microscopic picture of the carrier dynamics in photo-excited graphene. Our results clarify new aspects of hot carrier dynamics that are unique to Dirac materials, with relevance for photo-control experiments and optoelectronic device applications.