Quasiparticles In Graphene Research Articles

Chiral tunneling through double barrier structure in twisted graphene bilayer

The paper discusses the chiral tunneling of charge carriers through double barrier structure in twisted graphene bilayer. The theoretical analysis investigates the transmission probability for various system parameters under both symmetric and asymmetric barrier conditions. The results reveal that the transmission probability of quasiparticles in the K cone is mirror symmetric to that of Kθ cone about φ=0. Furthermore, the study shows that the transmission changes gradually from perfect transmission to perfect reflection in the normal direction by increasing the incident energy and the barrier height, which is different from the case of monolayer and AB-stacked bilayer graphene. It is also found that the double barrier structure remains, only in certain cases, perfectly transparent for normal or near-normal incidence. The chiral nature of the quasiparticles in graphene causes the tunneling to be highly dependent on the direction and also on the double barrier structure. Interestingly, this characteristic provides additional parameter that allows us to tune the electronic properties of the twisted graphene bilayer. Additionally, we found that the transmission exhibits some sharp resonance peaks, the number and amplitude of which depend on the system parameters. Our results provide a better understanding of chiral tunneling in twisted graphene bilayers through double barrier structures, which may thus offer efficient tools to control the transport properties in future graphene-based nanodevices like transistors and photodetectors.

Glass encapsulation of molecular-doped epitaxial graphene for quantum resistance metrology

The large Landau energy spacing, stemming from the linear energy-momentum dispersion of quasi-particles in graphene, allows an efficient realization of the quantum Hall effect at a small density of charge carriers. Promising scalable epitaxial graphene on silicon carbide (SiC), however, requires molecular doping, which is generally unstable under ambient conditions, to compensate for electron transfer from the SiC substrate. Here, we employed classical glass encapsulation common in organic electronics to passivate molecular-doped epitaxial graphene against water and oxygen molecules in air. We have investigated the stability of Hall quantization in a glass-encapsulated device for almost 1 year. The Hall quantization is maintained above a threshold magnetic field within 2 nΩ Ω−1 smaller than the measurement uncertainty of 3.5 nΩ Ω−1 through multiple thermal cycles for almost 1 year, while the ordinary unencapsulated device in air distinctly shows a relative deviation larger than 0.05% from the nominal quantized Hall resistance in 1 month.

Surface charge-transfer doping a quantum-confined silver monolayer beneath epitaxial graphene

Recently the graphene/SiC interface has emerged as a versatile platform for the epitaxy of otherwise unstable, monoelemental, two-dimensional (2D) layers via intercalation. Intrinsically capped into a van der Waals heterostructure with overhead graphene, they compose a new class of quantum materials with striking properties contrasting their parent bulk crystals. Intercalated silver presents a prototypical example where 2D quantum confinement and inversion symmetry breaking entail a metal-to-semiconductor transition. However, little is known about the associated unoccupied states, and control of the Fermi level position across the bandgap would be desirable. Here, we n-type dope a graphene/2D-Ag/SiC heterostack via in situ potassium deposition and probe its band structure by means of synchrotron-based angle-resolved photoelectron spectroscopy. While the induced carrier densities on the order of $10^{14}$ cm$^{-2}$ are not yet sufficient to reach the onset of the silver conduction band, the band alignment of graphene changes relative to the rigidly shifting Ag valence band and substrate core levels. We further demonstrate an ordered potassium adlayer ($2\times 2$ relative to graphene) with free-electron-like dispersion, suppressing plasmaron quasiparticles in graphene via enhanced metalization of the heterostack. Our results establish surface charge-transfer doping as an efficient handle to modify band alignment and electronic properties of a van der Waals heterostructure assembled from graphene and a novel type of monolayered quantum material.

Dynamics of quasi-particles in graphene with impurities and sharp edges from the kp-method standpoint

Dynamics of quasi-particles in graphene with an impurity and a sharp edge is considered with the kp-method that allows an unified approach without usage of any models. Dirac and Weyl equations are derived by the above-mentioned method. The wave function and its envelope function together with the scattering amplitude are found in the Born approximation. The wave functions are shown to be a superposition of virtual Bloch functions which exponential decay outward from the impurity and the edge. At distances much greater that the atomic spacing the wave functions are explicitly presented. Green’s functions for Shrödinger and Dirac equations are derived as well. Boundary conditions for the Dirac equation for graphene with a sharp edge are also derived.

Fundamental solution of the stationary Dirac equation with a linear potential

We explicitly express the fundamental solution of the stationary two-dimensional massless Dirac equation with a constant electric field in terms of Fourier transforms of parabolic cylinder functions. This solution describes the flux of quasiparticles in graphene emitted by a pointlike source of electrons that are partially converted into holes (antiparticles). Using our explicit formula, we calculate its semiclassical asymptotic behavior in the hole region.

Kinetic description of vacuum e+e− production in strong electric fields of arbitrary polarization

We present a detailed analysis of the self-consistent system of kinetic equations (KEs) describing electron-positron pair production from vacuum under the action of a spatially homogeneous time-dependent electric field of arbitrary polarization. The physical significance of all the basic functions of the kinetic theory is ascertained. It is demonstrated that the total system of the KEs consists of two coupled quasiparticle and spin subsystems with their integrals of motion. A projection method is proposed in order to obtain the KE system in two particular cases: linearly polarized external electric field and (2+1)-dimensional description of quasiparticles in graphene. We also address the energy conservation law taking into account the internal plasma field and describe an alternative rigorous derivation of the KE system.

Quantum Confinement of Dirac Quasiparticles in Graphene Patterned with Sub-Nanometer Precision.

Quantum confinement of graphene Dirac-like electrons in artificially crafted nanometer structures is a long sought goal that would provide a strategy to selectively tune the electronic properties of graphene, including bandgap opening or quantization of energy levels. However, creating confining structures with nanometer precision in shape, size, and location remains an experimental challenge, both for top-down and bottom-up approaches. Moreover, Klein tunneling, offering an escape route to graphene electrons, limits the efficiency of electrostatic confinement. Here, a scanning tunneling microscope (STM) is used to create graphene nanopatterns, with sub-nanometer precision, by the collective manipulation of a large number of H atoms. Individual graphene nanostructures are built at selected locations, with predetermined orientations and shapes, and with dimensions going all the way from 2 nm up to 1 µm. The method permits the patterns to be erased and rebuilt at will, and it can be implemented on different graphene substrates. STM experiments demonstrate that such graphene nanostructures confine very efficiently graphene Dirac quasiparticles, both in 0D and 1D structures. In graphene quantum dots, perfectly defined energy bandgaps up to 0.8 eV are found that scale as the inverse of the dot's linear dimension, as expected for massless Dirac fermions.

Valley current in graphene through electron-phonon interaction

We discuss valley current, which is carried by quasiparticles in graphene. We show that the valley current arises owing to a peculiar term in the electron-phonon collision integral that mixes the scalar and vector gauge-field-like vertices in the electron-phonon interaction. This mixing makes collisions of phonons with electrons sensitive to their chirality, which is opposite in two valleys. As a result of collisions with phonons, electrons of the different valleys deviate in opposite directions. Breaking the spatial inversion symmetry is not needed for a valley-dependent deviation of the quasiparticle current. The effect exists both in pristine graphene or bilayer graphene samples, and it increases with temperature owing to a higher rate of collisions with phonons at higher temperatures. The valley current carried by quasiparticles could be detected by measuring the electric current using a nonlocal transformer of a suitable design.

Effect of torus-shape curved space on energy spectrum and magnetization of Dirac fermions in graphene

In this paper, the dynamical properties of charge carriers in the two-dimensional atomic layer of graphene lattice with torus-shape geometry is studied in the presence of a gauge field. The curved space considerations involves Dirac equation along with a magnetic field for relativistic quasiparticles in graphene. By using the Heun’s differential equation, we are able to analytically find discrete Landau levels of graphene in torus-like curved space. The magnetization of energy states is investigated.

Cooperative Motion of Electrons on the Graphene Surface

Introduction. Today, the development of the graphene theory to control its physical and mechanical properties is a relevant objective. The paper deals with the conducting properties of graphene. In particular, the paper investigates the linear law of electron dispersion and traces its corollaries. Materials and Methods. The development of the theory is based on the verified experimental data and on the foundamental principles of the solid body theory and quantum mechanics. The study follows the universal synergetic principle according to which, there have been developed two split-level mathematical models of the quasi-particle motion in graphene on exposure to the electric field. On the macroscopic level, we suggest that graphene should be analyzed as a crystal consisting of three parallel planes. Two of them are electron gas. The remaining one is the main body of the crystal. On the microscopic level, the quasi-particle motion of the electron wave is described through the Schroedinger equation. Results. The study has developed the alternative method for the explanation of the linear dispersion law in graphene on the macroscopic level. Basing on the analysis of the model, the paper provides a hypothesis of the cooperative motion of the electron pairs, which make up a boson particle. The given hypothesis is different from the traditional one. In accordance with the latter, quasi-particles in graphene are Dirac fermions. To prove the hypothesis consilience, the study examines Hall’s effect in grapheme. The linear dispersion law for a pair of electrons is also deduced from the Schroedinger equation. Both the macroscopic and microscopic models are in a reasonable agreement with the experimental data. Discussion and Conclusion. The main result of the research is the development of the multi-level mathematical model which properly features the conducting properties of graphene (linear dispersion law, anomalous Hall effect). The practical relevance consists in revealing the possibility to control the conducting properties of graphene through impacts on electron pairs.

Chemical-potential flow equations for graphene with Coulomb interactions

We calculate the chemical potential dependence of the renormalized Fermi velocity and static dielectric function for Dirac quasiparticles in graphene nonperturbatively at finite temperature. By reinterpreting the chemical potential as a flow parameter in the spirit of the functional renormalization group (fRG) we obtain a set of flow equations, which describe the change of these functions upon varying the chemical potential. In contrast to the fRG the initial condition of the flow is nontrivial and has to be calculated separately. Our results confirm that the charge carrier density dependence of the Fermi velocity is negligible, validating the comparison of the fRG calculation at zero density of Bauer et al., Phys. Rev. B 92, 121409 (2015) with the experiment of Elias et al., Nat. Phys. 7, 701 (2011).

Graphene through the looking glass of QFT

This paper is aimed to review and promote the main applications of the methods of quantum field theory (QFT) to description of quantum effects in graphene. We formulate the effective electromagnetic action following from the Dirac model for the quasi-particles in graphene and apply it for derivation of different observable effects like the induced mean charge, quantized conductivity, Faraday effect and Casimir interaction involving graphene samples.

Landau levels in graphene in the presence of emergent gravity

We consider graphene in the presence of external magnetic field and elastic deformations that cause emergent magnetic field. The total magnetic field results in the appearance of Landau levels in the spectrum of quasiparticles. In addition, the quasiparticles in graphene experience the emergent gravity. We consider the particular choice of elastic deformation, which gives constant emergent magnetic field and vanishing torsion. Emergent gravity may be considered as perturbation. We demonstrate that the corresponding first order approximation affects the energies of the Landau levels only through the constant renormalization of Fermi velocity. The degeneracy of each Landau level receives correction, which depends essentially on the geometry of the sample. There is the limiting case of the considered elastic deformation, that corresponds to the uniformly stretched graphene. In this case in the presence of the external magnetic field the degeneracies of the Landau levels remain unchanged.

Plasmon-drag-assisted terahertz generation in a graphene layer incorporating an asymmetric plasmon nanostructure

This Rapid Communication presents a structure and full theoretical analysis to exploit the photon drag effect for THz signal generation in a graphene layer integrated with a plasmonic structure. The plasmonic structure is composed of a periodic array of asymmetric nanoparticles patterned over a graphene layer. The nanoparticles are designed to accomplish two goals: field localization due to the plasmonic resonance and manipulating the phase of the near field to effectively drag the quasiparticles in graphene. Combining the asymmetry with the plasmon resonances of nanoparticles, we show that an enhancement as large as three orders of magnitude is attainable in the power of the generated THz wave. This level of unprecedented enhancement mostly stems from the phase manipulation of the near field caused by asymmetric nanoparticles. Using the achieved enhancement, it is demonstrated that an ultra-wideband THz signal carrying the power of $1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{W}$ can be generated using a commercially available femtosecond pulsed laser.

Bosonization approach for “atomic collapse” in graphene

We study quantum electrodynamics with 2+1 dimensional massless Dirac fermion around a Coulomb impurity. Around a large charge with atomic number Z > 137, the QED vacuum is expected to collapse due to the strong Coulombic force. While the relativistic quantum mechanics fails to make reliable predictions for the fate of the vacuum, the heavy ion collision experiment also does not give clear understanding of this system. Recently, the “atomic collapse” resonances were observed on graphene where an artificial nuclei can be made. In this paper, we present our nonperturbative study of the vacuum structure of the quasiparticles in graphene with a charge impurity which contains multi-body effect using bosonization method.

Sound waves induce Volkov-like states, band structure and collimation effect in graphene

We find exact states of graphene quasiparticles under a time-dependent deformation (sound wave), whose propagation velocity is smaller than the Fermi velocity. To solve the corresponding effective Dirac equation, we adapt the Volkov-like solutions for relativistic fermions in a medium under a plane electromagnetic wave. The corresponding electron-deformation quasiparticle spectrum is determined by the solutions of a Mathieu equation resulting in band tongues warped in the surface of the Dirac cones. This leads to a collimation effect of electron conduction due to strain waves.

Time-dependent massless Dirac fermions in graphene

Using the Lewis–Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent vector potential. The eigenvalue equations for the two spinor components of the Lewis–Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians.

Time-dependent pair creation and the Schwinger mechanism in graphene

The momentum spectrum of positively and negatively charged carriers created in intrinsic graphene submitted to a time-dependent external electric field is evaluated for many external field configurations. Owing to the formal analogy between relativistic quantum mechanics and the description of graphene quasiparticles in terms of the massless Dirac equation, the electron momentum density is evaluated within two-dimensional massless quantum electrodynamics coupled to a strong classical field. This allows the treatment of dynamical effects in electron-hole creation and gives a physical description in terms of the time-dependent Schwinger mechanism. At zero transverse momentum, it is shown that the Fermi bound in the electron-hole momentum spectrum is saturated in a certain momentum window and the pair density depends only on the potential difference between asymptotic potentials before and after the interaction. The pair density for nonzero transverse momenta is evaluated using numerical calculations. The numerical results demonstrate that an important number of pairs can be created by an external field through both tunneling and multiphoton processes. It is argued that these features of the dynamical pair production may facilitate the detection of the Schwinger mechanism using graphene as a condensed matter analog to quantum electrodynamics.

Dynamics of quasiparticles in graphene under intense circularly polarized light

A monolayer of graphene irradiated with circularly polarized light suggests a unique platform for surface electromagnetic wave (plasmon-polariton) manipulation. In fact, the time periodicity of the Hamiltonian leads to a geometric Aharonov-Anandan phase and results in a photovoltaic Hall effect in graphene, creating off-diagonal components of the conductivity tensor. The latter drastically changes the dispersion relation of surface plasmon-polaritons, leading to hybrid wave generation. In this paper we present a systematic and self-contained analysis of the hybrid surface waves obtained from Maxwell equations based on a microscopic formula for the conductivity. We consider a practical example of graphene sandwiched between two dielectric media and show that in the one-photon approximation there is formation of propagating hybrid surface waves. From this analysis emerges the possibility of a reliable experimental realization to study Zitterbewegung of charge carriers of graphene.

Band-anisotropy induced Bloch–Siegert shift in graphene

In this work, we study the well-known phenomenon of the Bloch–Siegert shift, paying special attention to the change in the resonance condition of anomalous Rabi oscillations that are peculiar to graphene. The inclusion of frequency doubling (counter-rotating terms) in the conventional rotating wave approximation leads to a rather small shift in the resonance condition which forms the conventional Bloch–Siegert shift. In case of anomalous Rabi oscillations, however, band anisotropy caused by the inclusion of next-nearest neighbor hopping together with frequency doubling or the Rashba effect leads to a Bloch–Siegert shift which is quite substantial (in percentage terms, actually infinite), lending credence to the claim that the anomalous Rabi oscillation is sensitive to qualitative changes in the low energy band structure of graphene and as such is a useful indicator of the chiral massless Dirac fermion nature of quasiparticles in graphene.