Dirac Fermions In Graphene Research Articles

Spatial and magnetic confinement of massless Dirac fermions

The massless Dirac fermions and the ease to introduce spatial and magnetic confinement in graphene provide us unprecedented opportunity to explore confined relativistic matter in this condensed-matter system. Here we report the interplay between the confinement induced by external electric fields and magnetic fields of the massless Dirac fermions in graphene. When the magnetic length lB is larger than the characteristic length of the confined electric potential lV, the spatial confinement dominates and a relatively small critical magnetic field splits the spatial-confinement-induced atomic-like shell states by switching on a pi Berry phase of the quasiparticles. When the lB becomes smaller than the lV, the transition from spatial confinement to magnetic confinement occurs and the atomic-like shell states condense into Landau levels (LLs) of the Fock-Darwin states in graphene. Our experiment demonstrates that the spatial confinement dramatically changes the energy spacing between the LLs and generates large electron-hole asymmetry of the energy spacing between the LLs. These results shed light on puzzling observations in previous experiments, which hitherto remained unaddressed.

Reduction scheme for coupled Dirac systems

We analyze a class of coupled quantum systems whose dynamics can be understood via two uncoupled, lower-dimensional quantum settings with auxiliary interactions. The general reduction scheme, based on algebraic properties of the potential term, is discussed in detail for two-dimensional Dirac Hamiltonian. We discuss its possible application in description of Dirac fermions in graphene or bilayer graphene in presence of distortion scattering or spin–orbit interaction. We illustrate the general results on the explicit examples where the involved interactions are non-uniform in space and time.

Manipulation of Dirac Fermions in Nanochain-Structured GrapheneSupported by the National Key Research and Development Program of China (Grant Nos. 2020YFA0308800 and 2016YFA0202300), the National Natural Science Foundation of China (Grant Nos. 11974045 and 61888102), Chinese Academy of Sciences (Grant No. XDB30000000), Beijing Institute of Technology Research Fund Program for Young Scholars (Grant No. 3050011181909), and China Postdoctoral Science Foundation (Grant

Graphene has afforded an ideal 2D platform for investigating a rich and fascinating behavior of Dirac fermions. Here, we develop a theoretical mechanism for manipulating the Dirac fermions in graphene, such as from type-I to type-II and type-III, by a top-down nanopatterning approach. We demonstrate that by selective chemical adsorption to pattern the 2D graphene into coupled 1D armchair chains (ACs), the intrinsic isotropic upright Dirac cone becomes anisotropic and strongly tilted. Based on model analyses and first-principles calculations, we show that both the shape and tilt of Dirac cone can be tuned by the species of chemisorption, e.g., halogen vs hydrogen, which modifies the strength of inter-AC coupling. Furthermore, the topological edge states and transport properties of the engineered Dirac fermions are investigated. Our work sheds lights on understanding the Dirac fermions in a nanopatterned graphene platform, and provides guidance for designing nanostructures with novel functionality.

Impact of nitrogen doping on the band structure and the charge carrier scattering in monolayer graphene

The addition of nitrogen as a dopant in monolayer graphene is a flexible approach to tune the electronic properties of graphene as required for applications. Here, we investigate the impact of the doping process that adds N dopants and defects on the key electronic properties, such as the mobility, the effective mass, the Berry phase, and the scattering times of the charge carriers. Measurements at low temperatures and magnetic fields up to 9 T show a decrease of the mobility with increasing defect density due to elastic, short-range scattering. At low magnetic fields weak localization indicates an inelastic contribution depending on both defects and dopants. Analysis of the effective mass shows that the N dopants decrease the slope of the linear bands, which are characteristic for the band structure of graphene around the Dirac point. The Berry phase, however, remains unaffected by the modifications induced through defects and dopants, showing that the overall band structure of the samples is still exhibiting the key properties as expected for Dirac fermions in graphene.

Bound states for massive Dirac fermions in graphene in a magnetic step field

We calculate the spectrum of massive Dirac fermions in graphene in the presence of an inhomogeneous magnetic field modeled by a step function. We find an analytical universal relation between the bandwidths and the propagating velocities of the modes at the border of the magnetic region, showing how, by tuning the mass term, one can control the speed of these traveling edge states.Graphic

Coherent states for dispersive pseudo-Landau-levels in strained honeycomb lattices

Dirac fermions in graphene may experiment dispersive pseudo-Landau levels due to a homogeneous pseudomagnetic field and a position-dependent Fermi velocity induced by strain. In this paper, we study the (semi-classical) dynamics of these particles under such a physical context from an approach of coherent states. For this purpose we use a Landau-like gauge to built Perelomov coherent states by the action of a non-unitary displacement operator $D(\alpha)$ on the fundamental state of the system. We analyze the time evolution of the probability density and the generalized uncertainty principle as well as the Wigner function for the coherent states. Our results show how $x$-momentum dependency affects the motion periodicity and the Wigner function shape in phase space.

Linear and Nonlinear Optical Properties of Graphene: A Review

This article gives a brief overview of the linear and nonlinear optical response of graphene and its applications. Graphene exhibits unique physical properties. The charge carriers in graphene follow the relativistic massless Dirac equation; thus, they are known as the Dirac fermions. These Dirac fermions in graphene exhibit peculiar linear band structure at the Dirac point in the first Brillouin zone. These carriers exhibit novel linear and nonlinear optical properties in the presence of an intense electromagnetic field. The unique optical properties (linear and nonlinear) are a consequence of the unusual low-energy electronic band structure of graphene. The linear and nonlinear optical response of graphene can be tuned in the terahertz regime by the application of magnetic field. The uniqueness of graphene is shown by different findings in nonlinear optics such as four-wave mixing, saturation and reverse saturation absorption, two-photon absorption and optical limiting, among others. Therefore, the present review article describes the recent development in the field of linear and nonlinear optics of graphene. The different applications of graphene in the context of optics have been highlighted.

Systematic THz study of the substrate effect in limiting the mobility of graphene

We explore the substrate-dependent charge carrier dynamics of large area graphene films using contact-free non-invasive terahertz spectroscopy. The graphene samples are deposited on seven distinct substrates relevant to semiconductor technologies and flexible/photodetection devices. Using a Drude model for Dirac fermions in graphene and a fitting method based on statistical signal analysis, we extract transport properties such as the charge carrier density and carrier mobility. We find that graphene films supported by substrates with minimal charged impurities exhibit an enhanced carrier mobility, while substrates with a high surface roughness generally lead to a lower transport performance. The smallest amount of doping is observed for graphene placed on the polymer Zeonor, which also has the highest carrier mobility. This work provides valuable guidance in choosing an optimal substrate for graphene to enable applications where high mobility is required.

Microscopic theory of plasmon-enabled resonant terahertz detection in bilayer graphene

The electron gas hosted in a two-dimensional solid-state matrix, such as a quantum well or a two-dimensional van der Waals heterostructure, supports the propagation of plasma waves. Nonlinear interactions between plasma waves, due to charge conservation and current convection, generate a constant density gradient which can be detected as a dc potential signal at the boundaries of the system. This phenomenon is at the heart of a plasma-wave photodetection scheme which was first introduced by Dyakonov and Shur for electronic systems with a parabolic dispersion and then extended to the massless Dirac fermions in graphene. In this work, we develop the theory of plasma-wave photodetection in bilayer graphene, which has the peculiarity that the dispersion relation depends locally and dynamically on the intensity of the plasma wave. In our analysis, we show how quantum capacitance effects, arising from the local fluctuations of the electronic dispersion, modify the intensity of the photodetection signal. An external electrical bias, e.g. induced by top and bottom gates, can be used to control the strength of the quantum capacitance corrections, and thus the photoresponse.

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.

Dirac fermions in graphene using the position-dependent translation operator formalism

Within the position-dependent translation operator formalism for quantum systems, we obtain analytical expressions for the eigenstates and the Landau level spectrum of Dirac fermions in graphene in the presence of a perpendicularly applied magnetic field and, as a consequence of the formalism, with a generalized form of the momentum operator. Moreover, we explore the behavior of wave packet dynamics in such a system by considering different initial pseudospin polarizations and metric parameters. Our findings show that the Landau levels, the wave packet trajectories, and velocities are significantly affected by the choice of the metric in the non-Euclidean space of the deformed momentum operator, exhibiting a tunable energy level spacing. In the dynamics analysis, one observes an enhancement of the oscillation amplitude of the average positions for all investigated pseudospin polarizations due to the nonsymmetric evolution of the wave packet induced by the different metrics in the system. The present formalism is shown to be a theoretical platform to describe the effects of two scenarios due to (i) a lattice deformation in graphene, giving rise to a natural Fermi velocity renormalization, or even (ii) a nonuniform mass term, induced by a specific substrate, that varies on a length scale much greater than the magnetic field length.

Tunable Kondo Resonance at a Pristine Two-Dimensional Dirac Semimetal on a Kondo Insulator.

The proximity of two different materials leads to an intricate coupling of quasiparticles so that an unprecedented electronic state is often realized at the interface. Here, we demonstrate a resonance-type many-body ground state in graphene, a nonmagnetic two-dimensional Dirac semimetal, when grown on SmB6, a Kondo insulator, via thermal decomposition of fullerene molecules. This ground state is typically observed in three-dimensional magnetic materials with correlated electrons. Above the characteristic Kondo temperature of the substrate, the electron band structure of pristine graphene remains almost intact. As temperature decreases, however, the Dirac Fermions of graphene become hybridized with the Sm 4f states. Remarkable enhancement of the hybridization and Kondo resonance is observed with further cooling and increasing charge-carrier density of graphene, evidencing the Kondo screening of the Sm 4f local magnetic moment by the conduction electrons of graphene at the interface. These findings manifest the realization of the Kondo effect in graphene by the proximity of SmB6 that is tuned by the temperature and charge-carrier density of graphene.

High-order minibands and interband Landau level reconstruction in graphene moiré superlattices

The propagation of Dirac fermions in graphene through a long-period periodic potential would result in a band folding together with the emergence of a series of cloned Dirac points (DPs). In highly aligned graphene/hexagonal boron nitride (G/hBN) heterostructures, the lattice mismatch between the two atomic crystals generates a unique kind of periodic structure known as a moir\'e superlattice. Of particular interests is the emergent phenomena related to the reconstructed band-structure of graphene, such as the Hofstadter butterfly, topological currents, gate dependent pseudospin mixing, and ballistic miniband conduction. However, most studies so far have been limited to the lower-order minibands, e.g. the 1st and 2nd minibands counted from charge neutrality, and consequently the fundamental nature of the reconstructed higher-order miniband spectra still remains largely unknown. Here we report on probing the higher-order minibands of precisely aligned graphene moir\'e superlattices by transport spectroscopy. Using dual electrostatic gating, the edges of these high-order minibands, i.e. the 3rd and 4th minibands, can be reached. Interestingly, we have observed interband Landau level (LL) crossinginducing gap closures in a multiband magneto-transport regime, which originates from band overlap between the 2nd and 3rd minibands. As observed high-order minibands and LL reconstruction qualitatively match our simulated results. Our findings highlight the synergistic effect of minibands in transport, thus presenting a new opportunity for graphene electronic devices.

Landau poles in condensed matter systems

The existence or not of Landau poles is one of the oldest open questions in non-asymptotic quantum field theories. We investigate the Landau pole issue in two condensed matter systems whose long-wavelength physics is described by appropriate quantum field theories: the critical quantum magnet and Dirac fermions in graphene with long-range Coulomb interactions. The critical quantum magnet provides a classic example of a quantum phase transition, and it is well described by the $\phi^4$ theory. We find that the irrelevant but symmetry-allowed couplings, such as the $\phi^6$ potential, can significantly change the fate of the Landau pole in the $\phi^4$ theory. We obtain the coupled beta functions of a $\phi^4 + \phi^6$ potential at both small and large orders. Already from the 1-loop calculation, the Landau pole is replaced by an ultraviolet fixed point. A Lipatov analysis at large orders reveals that the inclusion of a $\phi^6$ term also has important repercussions for the high-order expansion of the beta functions. We also investigate the role of the Landau pole in 2+1 dimensional Dirac fermions with Coulomb interactions, e.g., graphene. Both the weak-coupling perturbation theory up to 2 loops and a low-order large-N calculation show the absence of a Landau pole. Furthermore, we calculate the asymptotic expansion coefficients of the beta function. We find that the asymptotic coefficient is bounded by that of a $\phi^4$ theory, so graphene is free from Landau poles if the $\phi^4$ theory does not manifest a Landau pole. We briefly discuss possible experiments that could potentially probe the existence of a Landau pole in these systems. Studying Landau poles in suitable condensed matter systems is of considerable fundamental importance since the relevant Landau pole energy scales in particle physics, whether it is quantum electrodynamics or Higgs physics, are completely unattainable.

On the propagation of Dirac fermions in graphene with strain-induced inhomogeneous Fermi velocity

We consider systems described by a two-dimensional Dirac equation where the Fermi velocity is inhomogeneous as a consequence of mechanical deformations. We show that the mechanical deformations can lead to deflection and focusing of the wave packets. The analogy with known reflectionless quantum systems is pointed out. Furthermore, with the use of the qualitative spectral analysis, we discuss how inhomogeneous strains can be used to create waveguides for valley polarized transport of partially dispersionless wave packets.

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.

Switchable crossed spin conductance in a graphene-based junction: The role of spin-orbit coupling

We theoretically investigate the crossed spin conductance (CSC) of a graphene-based heterostructure consists of ferromagnet, Rashba spin-orbit and superconductor regions. Using Dirac Bogoliubov-de Gennes formalism in the ballistic regime, we show that in the presence of Rashba spin-orbit coupling there are an anomalous crossed Andreev reection and spin-ipped co-tunneling in the process of quantum transport. We demonstrate that the CSC can be reversed with respect to charge conductance by tuning the Rashba spin-orbit coupling which experimentally can be adjusted by the applied perpendicular electric field on the graphene sheet. This feature in addition to a long spin relaxation time of Dirac fermions in graphene proposes designing a device with a non-local spin switch which is crucial for spintronics circuits.

Optical Kerr effect and third harmonic generation in topological Dirac/Weyl semimetal.

We study the nonlinear optical response generated by the massless Dirac quasiparticles residing around the topologically-protected Dirac/Weyl nodal points in three-dimensional (3D) topological semimetals. Analytical expressions of third-order interband nonlinear optical conductivities are obtained based on a quantum mechanical formalism which couples 3D Dirac fermions with multiple photons. Our results reveal that the massless Dirac fermions in three dimensions retains strong optical nonlinearity in terahertz frequency regime similar to the case of the two-dimensional Dirac fermions in graphene. At room temperature, the Kerr nonlinear refractive index and the harmonic generation susceptibility are found to be n2 = 10-11 ∼ 10-8 m2W-1 and χ(3) = 10-14 ∼ 10-8 m2V-2, respectively, in the few terahertz frequency regimes, which is comparable to graphene and orders of magnitudes stronger than many nonlinear crystals. Importantly, because 3D topological Dirac/Weyl semimetals possess bulk structural advantage not found in the strictly two-dimensional graphene, greater design flexibility and improved ease-of-fabrication in terms of photonic and optoelectronic device applications can be achieved. Our finding reveals the potential of 3D topological semimetals as a viable alternative to graphene for nonlinear optics applications.

Guiding Dirac Fermions in Graphene with a Carbon Nanotube.

Relativistic massless charged particles in a two-dimensional conductor can be guided by a one-dimensional electrostatic potential, in an analogous manner to light guided by an optical fiber. We use a carbon nanotube to generate such a guiding potential in graphene and create a single mode electronic waveguide. The nanotube and graphene are separated by a few nanometers and can be controlled and measured independently. As we charge the nanotube, we observe the formation of a single guided mode in graphene that we detect using the same nanotube as a probe. This single electronic guided mode in graphene is sufficiently isolated from other electronic states of linear Dirac spectrum continuum, allowing the transmission of information with minimal distortion.

Non-perturbative corrections to the quasiparticle velocity in graphene

Relativistic fermionic systems have physical quantities calculated by well established quantum electrodynamic prescriptions. In the last few years there has been an enormous interest in condensed matter systems in which the fermions exhibit relativistic dispersion, as Dirac fermions in graphene. We employ a non-perturbative method in order to obtain a non-perturbative correction to the quasiparticle velocity in graphene, and compare with the experimental data. We find a better agreement between the quasiparticle velocity corrected with non-perturbative corrections and measurements, when compared with the standard one-loop result. We also investigate the behavior of the beta function of the renormalization group theory, and find that the non-perturbative corrections do not alter the stability of the infrared fixed point found by the standard result.