High-energy limit of massless Dirac fermions in multilayer graphene using magneto-optical transmission spectroscopy

Evidence for Local Spots of Viscous Electron Flow in Graphene at Moderate Mobility

Dominating electron-electron scattering enables viscous electron flow exhibiting hydrodynamic current density patterns, such as Poiseuille profiles or vortices. The viscous regime has recently been observed in graphene by nonlocal transport experiments and mapping of the Poiseuille profile. Herein, we probe the current-induced surface potential maps of graphene field-effect transistors with moderate mobility using scanning probe microscopy at room temperature. We discover micrometer-sized large areas appearing close to charge neutrality that show current-induced electric fields opposing the externally applied field. By estimating the local scattering lengths from the gate dependence of local in-plane electric fields, we find that electron-electron scattering dominates in these areas as expected for viscous flow. Moreover, we suppress the inverted fields by artificially decreasing the electron-disorder scattering length via mild ion bombardment. These results imply that viscous electron flow is omnipresent in graphene devices, even at moderate mobility.

Novel electric field effects on magneto-optical conductivity in eight-Pmmnborophene

We theoretically study the Landau levels and the magneto-optical conductivity of eight-Pmmnborophene in the presence of a perpendicular magnetic field and an inplane electric field. We find that in the absence of the inplane electric field, the magneto-optical conductivity of eight-Pmmnborophene presents a series of striking single resonance peaks as functions of the frequencyω, and the longitudinal conductivities are found to be anisotropic due to its anisotropic tilted Dirac cones. In the presence of the inplane electric field, some novel effects are predicted on the Landau levels and the magneto-optical conductivity. The Landau level spacings in the two tilted Dirac cones are different, which lifts the degeneracy of the twofold valley, and the magneto-optical conductivity appears a double peak structure. We also discuss the influence of the chemical potential between different Landau levels on the double peak of the magneto-optical response. The valley related magneto-optical properties in the anisotropic structure may make eight-Pmmnborophene a candidate for the new optical devices.

Peculiar optical properties of bilayer silicene under the influence of external electric and magnetic fields

We conduct a comprehensive investigation of the effect of an applied electric field on the optical and magneto-optical absorption spectra for AB-bt (bottom-top) bilayer silicene. The generalized tight-binding model in conjunction with the Kubo formula is efficiently employed in the numerical calculations. The electronic and optical properties are greatly diversified by the buckled lattice structure, stacking configuration, intralayer and interlayer hopping interactions, spin-orbital couplings, as well as the electric and magnetic fields (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{z}\hat{z}$$\end{document}Ezzˆ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\& $$\end{document}&\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{z}\hat{z}$$\end{document}Bzzˆ). An electric field induces spin-split electronic states, a semiconductor-metal phase transitions and the Dirac cone formations in different valleys, leading to the special absorption features. The E_z-dependent low-lying Landau levels possess lower degeneracy, valley-created localization centers, peculiar distributions of quantum numbers, well-behaved and abnormal energy spectra in B_z-dependencies, and the absence of anti-crossing behavior. Consequently, the specific magneto-optical selection rules exist for diverse excitation categories under certain critical electric fields. The optical gaps are reduced as E_z is increased, but enhanced by B_z, in which the threshold channel might dramatically change in the former case. These characteristics are in sharp contrast with those for layered graphene.

The diverse magneto-optical selection rules in bilayer black phosphorus

The magneto-optical properties of bilayer phosphorene is investigated by the generalized tight-binding model and the gradient approximation. The vertical inter-Landau-level transitions, being sensitive to the polarization directions, are mainly determined by the spatial symmetries of sub-envelope functions on the distinct sublattices. The anisotropic excitations strongly depend on the electric and magnetic fields. A uniform perpendicular electric field could greatly diversify the selection rule, frequency, intensity, number and form of symmetric absorption peaks. Specifically, the unusual magneto-optical properties appear beyond the critical field as a result of two subgroups of Landau levels with the main and side modes. The rich and unique magnetoabsorption spectra arise from the very close relations among the geometric structures, multiple intralayer and interlayer hopping integrals and composite external fields.

Electronic and optical properties of graphene nanoribbons in external fields

A review work is done for the electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields. Effects due to the lateral confinement, curvature, stacking, non-uniform subsystems and hybrid structures are taken into account. The special electronic properties, induced by complex competitions between external fields and geometric structures, include many one-dimensional parabolic subbands, standing waves, peculiar edge-localized states, width- and field-dependent energy gaps, magnetic-quantized quasi-Landau levels, curvature-induced oscillating Landau subbands, crossings and anti-crossings of quasi-Landau levels, coexistence and combination of energy spectra in layered structures, and various peak structures in the density of states. There exist diverse absorption spectra and different selection rules, covering edge-dependent selection rules, magneto-optical selection rule, splitting of the Landau absorption peaks, intragroup and intergroup Landau transitions, as well as coexistence of monolayer-like and bilayer-like Landau absorption spectra. Detailed comparisons are made between the theoretical calculations and experimental measurements. The predicted results, the parabolic subbands, edge-localized states, gap opening and modulation, and spatial distribution of Landau subbands, have been identified by various experimental measurements.

Rich magneto-absorption spectra of AAB-stacked trilayer graphene

A generalized tight-binding model is developed to investigate the feature-rich magneto-optical properties of AAB-stacked trilayer graphene. Three intragroup and six intergroup inter-Landau-level (inter-LL) optical excitations largely enrich magneto-absorption peaks. In general, the former are much higher than the latter, depending on the phases and amplitudes of LL wavefunctions. The absorption spectra exhibit single- or twin-peak structures which are determined by quantum modes, LL energy spectra and Fermion distribution. The splitting LLs, with different localization centers (2/6 and 4/6 positions in a unit cell), can generate very distinct absorption spectra. There exist extra single peaks because of LL anti-crossings. AAB, AAA, ABA, and ABC stackings considerably differ from one another in terms of the inter-LL category, frequency, intensity, and structure of absorption peaks. The main characteristics of LL wavefunctions and energy spectra and the Fermi-Dirac function are responsible for the configuration-enriched magneto-optical spectra.

Magneto-electronic properties of multilayer graphenes

This article reviews the rich magneto-electronic properties of multilayer graphene systems. Multilayer graphenes are built from graphene sheets attracting one another by van der Waals forces; the magneto-electronic properties are diversified by the number of layers and the stacking configurations. For an N-layer system, Landau levels are divided into N groups, with each identified by a dominant sublattice associated with the stacking configuration. We focus on the main characteristics of Landau levels, including the degeneracy, wave functions, quantum numbers, onset energies, field-dependent energy spectra, semiconductor-metal transitions, and crossing patterns, which are reflected in the magneto-optical spectroscopy, scanning tunneling spectroscopy, and quantum transport experiments. The Landau levels in AA-stacked graphene are responsible for multiple Dirac cones, while in AB-stacked graphene the Dirac properties depend on the number of graphene layers, and in ABC-stacked graphene the low-lying levels are related to surface states. The Landau-level mixing leads to anticrossings patterns in energy spectra, which are seen for intergroup Landau levels in AB-stacked graphene, while in particular, a formation of both intergroup and intragroup anticrossings is observed in ABC-stacked graphene. The aforementioned magneto-electronic properties lead to diverse optical spectra, plasma spectra, and transport properties when the stacking order and the number of layers are varied. The calculations are in agreement with optical and transport experiments, and novel features that have not yet been verified experimentally are presented.

Electric-field-induced rich magneto-absorption spectra of ABC-stacked trilayer graphene

The magneto-optical spectra of ABC-stacked trilayer graphene are enriched by an electric field, providing a way to experimentally identify the stacking order of few layer graphene systems.

Magneto-optical properties of ABC-stacked trilayer graphene

The generalized tight-binding model is developed to investigate the magneto-optical absorption spectra of ABC-stacked trilayer graphene.

The selection rule of graphene in a composite magnetic field

The generalized tight-binding model with exact diagonalization method is developed to calculate the optical properties of monolayer graphene in the presence of composite magnetic fields. The ratio of the uniform magnetic field and the modulated one accounts for a strong influence on the structure, number, intensity and frequency of absorption peaks, and thus the extra selection rules that are subsequently induced can be explained. When the modulated field increases, each symmetric peak, under a uniform magnetic field, splits into a pair of asymmetric peaks with lower intensities. The threshold absorption frequency exhibits an obvious evolution in terms of a redshift. These absorption peaks obey the same selection rule that is followed by Landau level transitions. Moreover, at a sufficiently strong modulation strength, the extra peaks in the absorption spectrum might arise from different selection rules.

Magneto-optical fingerprints of distinct graphene multilayers using the giant infrared Kerr effect

The remarkable electronic properties of graphene strongly depend on the thickness and geometry of graphene stacks. This wide range of electronic tunability is of fundamental interest and has many applications in newly proposed devices. Using the mid-infrared, magneto-optical Kerr effect, we detect and identify over 18 interband cyclotron resonances (CR) that are associated with ABA and ABC stacked multilayers as well as monolayers that coexist in graphene that is epitaxially grown on 4H-SiC. Moreover, the magnetic field and photon energy dependence of these features enable us to explore the band structure, electron-hole band asymmetries, and mechanisms that activate a CR response in the Kerr effect for various multilayers that coexist in a single sample. Surprisingly, we find that the magnitude of monolayer Kerr effect CRs is not temperature dependent. This unexpected result reveals new questions about the underlying physics that makes such an effect possible.

Valley-spin polarization in the magneto-optical response of silicene and other similar 2D crystals

We calculate the magneto-optical conductivity and electronic density of states for silicene, the silicon equivalent of graphene, and similar crystals such as germanene. In the presence of a perpendicular magnetic field and electric field gating, we note that four spin- and valley-polarized levels can be seen in the density of states, and transitions between these levels lead to similarly polarized absorption lines in the longitudinal, transverse Hall, and circularly polarized dynamic conductivity. While previous spin and valley polarization predicted for the conductivity is only present in the response to circularly polarized light, we show that distinct spin and valley polarization can also be seen in the longitudinal magneto-optical conductivity at experimentally attainable energies. The frequency of the absorption lines may be tuned by the electric and magnetic field to onset in a range varying from THz to the infrared. This potential to isolate charge carriers of definite spin and valley label may make silicene a promising candidate for spin- and valleytronic devices.

Time-resolved spectroscopy on epitaxial graphene in the infrared spectral range: relaxation dynamics and saturation behavior

We present the results of pump–probe experiments on multilayer graphene samples performed in a wide spectral range, namely from the near infrared (photon energy 1.5 eV) to the terahertz (photon energy 8 meV) spectral range. In the near infrared, exciting carriers and probing at higher photon energies provides direct evidence for a hot carrier distribution. Furthermore, spectroscopic signatures of the highly doped graphene layers at the interface to SiC are observed in the near-infrared range. In the mid-infrared range, the various relaxation mechanisms, in particular scattering via optical phonons and Auger-type processes, are identified by comparing the experimental results to microscopic modeling. Changes from induced transmission to induced absorption are attributed to probing above or below the Fermi edge of the graphene layers. This effect occurs for certain photon energies in the near-infrared range, where it is related to highly doped graphene layers at the interface to SiC, and in the far-infrared range for the quasi-intrinsic graphene layers. In addition to the relaxation dynamics, the saturation of pump-induced bleaching of graphene is studied. Here a quadratic dependence of the saturation fluence on the pump photon energy in the infrared spectral range is revealed.

Semiconducting states and transport in metallic armchair-edged graphene nanoribbons

Based on the nonequilibrium Green's function method within the tight-binding approximation scheme, through a scanning tunneling microscopy (STM) model, we study the low-energy electronic states and transport properties of carbon chains in armchair-edged graphene nanoribbons (AGNRs). We show that semiconducting AGNRs possess only semiconducting chains, while metallic ones possess not only metallic chains but also unconventional semiconducting chains located at the 3 jth (j ≠ 0) column from the edge (the first chain) due to the vanishing of the metallic component in the electron wavefunction. The two types of states for carbon chains in a metallic AGNR system are demonstrated by different density of states and STM tunneling currents. Moreover, a similar phenomenon is predicted in the edge region of very wide AGNRs. However, there is remarkable difference in the tunneling current between narrow and wide ribbons.

Electronic and optical properties of monolayer and bilayer graphene

The electronic and optical properties of monolayer and bilayer graphene are investigated to verify the effects of interlayer interactions and external magnetic field. Monolayer graphene exhibits linear bands in the low-energy region. Then the interlayer interactions in bilayers change these bands into two pairs of parabolic bands, where the lower pair is slightly overlapped and the occupied states are asymmetric with respect to the unoccupied ones. The characteristics of zero-field electronic structures are directly reflected in the Landau levels. In monolayer and bilayer graphene, these levels can be classified into one and two groups, respectively. With respect to the optical transitions between the Landau levels, bilayer graphene possesses much richer spectral features in comparison with monolayers, such as four kinds of absorption channels and double-peaked absorption lines. The explicit wave functions can further elucidate the frequency-dependent absorption rates and the complex optical selection rules. These numerical calculations would be useful in identifying the optical measurements on graphene layers.

Magneto-optical Selection Rules in Bilayer Bernal Graphene

The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with the four most important interlayer interactions taken into account. Since the main features of the wave functions are well-depicted, the Landau levels can be divided into two groups based on the characteristics of the wave functions. These Landau levels lead to four categories of absorption peaks in the optical absorption spectra. Such absorption peaks own complex optical selection rules, and these rules can be reasonably explained by the characteristics of the wave functions. In addition, twin-peak structures, regular frequency-dependent absorption rates, and complex field-dependent frequencies are also obtained in this work. The main features of the absorption peaks are very different from those in monolayer graphene and have their origin in the interlayer interactions.

Tuning the electron-phonon coupling in multilayer graphene with magnetic fields

Magneto-Raman scattering study of the E2g optical phonons in multilayer epitaxial graphene grown on a carbon face of SiC is presented. At 4.2 K in magnetic field up to 33 T, we observe a series of well-pronounced avoided crossings each time the optically active inter-Landau level transition is tuned in resonance with the E2g phonon excitation (at 196 meV). The width of the phonon Raman scattering response also shows pronounced variations and is enhanced in conditions of resonance. The experimental results are well reproduced by a model that gives directly the strength of the electron-phonon interaction.

On spectral properties of bilayer graphene: the effect of an SiC substrate and infrared magneto-spectroscopy

We investigate the effect of asymmetry in bilayer graphene induced by a diatomic substrate (such as SiC) and its influence on the bilayer spectrum in zero and strong magnetic fields. We also determine selection rules for inter-Landau level transitions, taking into account all four π bands.

Graphite from the viewpoint of Landau level spectroscopy: an effective graphene bilayer and monolayer

We describe an infrared transmission study of a thin layer of bulk graphite in magnetic fields up to B=34 T. Two series of absorption lines whose energy scales as sqrt[B] and B are present in the spectra and identified as contributions of massless holes at the H point and massive electrons in the vicinity of the K point, respectively. We find that the optical response of the K point electrons corresponds, over a wide range of energy and magnetic field, to a graphene bilayer with an effective interlayer coupling 2gamma_{1}, twice the value for a real graphene bilayer, which reflects the crystal ordering of bulk graphite along the c axis. The K point electrons thus behave as massive Dirac fermions with a mass enhanced twice in comparison to a true graphene bilayer.

Approaching the dirac point in high-mobility multilayer epitaxial graphene

Multilayer epitaxial graphene is investigated using far infrared transmission experiments in the different limits of low magnetic fields and high temperatures. The cyclotron-resonance-like absorption is observed at low temperature in magnetic fields below 50 mT, probing the nearest vicinity of the Dirac point. The carrier mobility is found to exceed 250,000 cm2/(V x s). In the limit of high temperatures, the well-defined Landau level quantization is observed up to room temperature at magnetic fields below 1 T, a phenomenon unusual in solid state systems. A negligible increase in the width of the cyclotron resonance lines with increasing temperature indicates that no important scattering mechanism is thermally activated.