Cyclotron resonance in bilayer graphene

Unique electronic and optical properties of stacking-modulated bilayer graphene under external magnetic fields

This study delves into the magneto-electronic and magneto-optical properties of stacking-modulated bilayer graphene. By manipulating domain walls (DWs) across AB-BA domains periodically, we unveil oscillatory Landau subbands and the associated optical excitations. The DWs act as periodic potentials, yielding fascinating 1D spectral features. Our exploration reveals 1D phenomena localized to Bernal stacking, DW regions, and stacking boundaries, highlighting the intriguing formation of Landau state quantization influenced by the commensuration between the magnetic length and the system. The stable quantized localization within different regions leads to the emergence of unconventional quantized subbands. This study provides valuable insights into the essential properties of stacking-modulated bilayer graphene.

Transient lensing from a photoemitted electron gas imaged by ultrafast electron microscopy

Understanding and controlling ultrafast charge carrier dynamics is of fundamental importance in diverse fields of (quantum) science and technology. Here, we create a three-dimensional hot electron gas through two-photon photoemission from a copper surface in vacuum. We employ an ultrafast electron microscope to record movies of the subsequent electron dynamics on the picosecond-nanosecond time scale. After a prompt Coulomb explosion, the subsequent dynamics is characterized by a rapid oblate-to-prolate shape transformation of the electron gas, and periodic and long-lived electron cyclotron oscillations inside the magnetic field of the objective lens. In this regime, the collective behavior of the oscillating electrons causes a transient, mean-field lensing effect and pronounced distortions in the images. We derive an analytical expression for the time-dependent focal length of the electron-gas lens, and perform numerical electron dynamics and probe image simulations to determine the role of Coulomb self-fields and image charges. This work inspires the visualization of cyclotron dynamics inside two-dimensional electron-gas materials and enables the elucidation of electron/plasma dynamics and properties that could benefit the development of high-brightness electron and X-ray sources.

Unconventional valley-dependent optical selection rules and landau level mixing in bilayer graphene

Selection rules are of vital importance in determining the basic optical properties of atoms, molecules and semiconductors. They provide general insights into the symmetry of the system and the nature of relevant electronic states. A two-dimensional electron gas in a magnetic field is a model system where optical transitions between Landau levels (LLs) are described by simple selection rules associated with the LL index N. Here we examine the inter-LL optical transitions of high-quality bilayer graphene by photocurrent spectroscopy measurement. We observed valley-dependent optical transitions that violate the conventional selection rules Δ|N| = ± 1. Moreover, we can tune the relative oscillator strength by tuning the bilayer graphene bandgap. Our findings provide insights into the interplay between magnetic field, band structure and many-body interactions in tunable semiconductor systems, and the experimental technique can be generalized to study symmetry-broken states and low energy magneto-optical properties of other nano and quantum materials.

Electrical Control of Cyclotron Resonance in Dual-Gated Trilayer Graphene

Landau levels (LLs) of ABA-stacked trilayer graphene (TLG) are described as the combination of monolayer graphene-like LLs and bilayer graphene-like LLs. They are extremely sensitive to the applied perpendicular electric displacement field D. Here, we demonstrate the electrical control of cyclotron resonance (CR) in a dual-gated ABA-stacked TLG. Under the irradiation of mid-infrared light, we observed the photovoltage induced by the CR absorption through the photothermoelectric effect. The resonant magnetic field in CR is changed by applying D while keeping the carrier density constant. Numerical simulations based on the tight-binding model complement the experimental observations. We believe that the present study provides a boost to graphene-based photodetectors and photoemitters with an electrically tunable wavelength in mid-infrared to terahertz spectral ranges.

Valley and Zeeman Splittings in Multilayer Epitaxial Graphene Revealed by Circular Polarization Resolved Magneto-infrared Spectroscopy

Circular-polarization-resolved magneto-infrared studies of multilayer epitaxial graphene (MEG) are performed using tunable quantum cascade lasers in high magnetic fields up to 17.5 T. Landau level (LL) transitions in the monolayer and bilayer graphene inclusions of MEG are resolved, and considerable electron-hole asymmetry is observed in the extracted electronic band structure. For monolayer graphene, a four-fold splitting of the n = 0 to n = 1 LL transition is evidenced and attributed to the lifting of the valley and spin degeneracy of the zeroth LL and the broken electron-hole symmetry. The magnetic field dependence of the splitting further reveals its possible mechanisms. The best fit to experimental data yields effective g-factors, g_VS^* = 6.7 and g_ZS^* = 4.8, for the valley and Zeeman splittings, respectively.

Effects of site asymmetry and valley mixing on Hofstadter-type spectra of bilayer graphene in a square-scatter array potential

Under a magnetic field perpendicular to an monolayer graphene, the existence of a two-dimensional periodic scatter array can not only mix Landau levels of the same valley for displaying split electron-hole Hofstadter-type energy spectra, but also couple two sets of Landau subbands from different valleys in a bilayer graphene. Such a valley mixing effect with a strong scattering strength has been found observable and studied thoroughly in this paper by using a Bloch-wave expansion approach and a projected [Formula: see text] effective Hamiltonian including interlayer effective mass, interlayer coupling and asymmetrical on-site energies due to a vertically-applied electric field. For bilayer graphene, we find two important characteristics, i.e. mixing and interference of intervalley scatterings in the presence of a scatter array, as well as a perpendicular-field induced site-energy asymmetry which deforms severely or even destroys completely the Hofstadter-type band structures due to the dependence of Bloch-wave expansion coefficients on the applied electric field.

Spin-polarized magneto-electronic properties in buckled monolayer GaAs

We develop the generalized tight-binding model to fully explore the magneto-electronic properties of monolayer GaAs, where the buckled structure, multi-orbital chemical bondings, spin-orbit coupling, electric field, and magnetic field are considered simultaneously. The diverse magnetic quantization covers three groups of spin-polarized Landau levels (LLs) near the Fermi level, with the unique initial energies, LL degeneracy, energy spacings, magnetic-field-dependence, and spin splitting. Furthermore, the Landau state probabilities exhibit specific oscillation patterns, being composed of the localization centers, node regularities, and energy-dependent variations of the dominating orbitals. The density of states directly reflects the main features of the LL energy spectra in the form, height, number, and frequency of the spin-split delta-function-like prominent peaks. The electric field leads to the monotonous/nonmonotonous LL energy dispersions, LL crossing behavior, gap modulation, phase transition and enhancement of spin splitting. The complex gap modulations and even semiconductor-semimetal transitions are attributed to the strong competition among the intrinsic interactions, magnetic field, and electric field. Such predicted magneto-electronic properties could be verified by scanning tunneling spectroscopy and are helpful in designing the top-gated and phase-change electronic devices.

Visualization and Control of Single-Electron Charging in Bilayer Graphene Quantum Dots

Graphene p-n junctions provide an ideal platform for investigating novel behavior at the boundary between electronics and optics that arise from massless Dirac Fermions, such as whispering gallery modes and Veselago lensing. Bilayer graphene also hosts Dirac Fermions, but they differ from single-layer graphene charge carriers because they are massive, can be gapped by an applied perpendicular electric field, and have very different pseudospin selection rules across a p-n junction. Novel phenomena predicted for these massive Dirac Fermions at p-n junctions include anti-Klein tunneling, oscillatory Zener tunneling, and electron cloaked states. Despite these predictions there has been little experimental focus on the microscopic spatial behavior of massive Dirac Fermions in the presence of p-n junctions. Here we report the experimental manipulation and characterization of massive Dirac Fermions within bilayer graphene quantum dots defined by circular p-n junctions through the use of scanning tunneling microscopy-based (STM) methods. Our p-n junctions are created via a flexible technique that enables realization of exposed quantum dots in bilayer graphene/hBN heterostructures. These quantum dots exhibit sharp spectroscopic resonances that disperse in energy as a function of applied gate voltage. Spatial maps of these features show prominent concentric rings with diameters that can be tuned by an electrostatic gate. This behavior is explained by single-electron charging of localized states that arise from the quantum confinement of massive Dirac Fermions within our exposed bilayer graphene quantum dots.

Tunable excitons in bilayer graphene

Excitons, the bound states of an electron and a hole in a solid material, play a key role in the optical properties of insulators and semiconductors. Here, we report the observation of excitons in bilayer graphene (BLG) using photocurrent spectroscopy of high-quality BLG encapsulated in hexagonal boron nitride. We observed two prominent excitonic resonances with narrow line widths that are tunable from the mid-infrared to the terahertz range. These excitons obey optical selection rules distinct from those in conventional semiconductors and feature an electron pseudospin winding number of 2. An external magnetic field induces a large splitting of the valley excitons, corresponding to a g-factor of about 20. These findings open up opportunities to explore exciton physics with pseudospin texture in electrically tunable graphene systems​.

Layer Polarizability and Easy-Axis Quantum Hall Ferromagnetism in Bilayer Graphene

We report magnetotransport measurements of graphene bilayers at large perpendicular electric displacement fields, up to ∼1.5 V/nm, where we observe crossings between Landau levels with different orbital quantum numbers. The displacement fields at the studied crossings are primarily determined by energy shifts originating from the Landau level layer polarizability or polarization. Despite decreasing Landau level spacing with energy, successive crossings occur at larger displacement fields, resulting from decreasing polarizability with orbital quantum number. For particular crossings we observe resistivity hysteresis in displacement field, indicating the presence of a first-order transition between states exhibiting easy-axis quantum Hall ferromagnetism.

Direct Observation of Landau Level Resonance and Mass Generation in Dirac Semimetal Cd3As2 Thin Films

Three-dimensional topological Dirac semimetals have hitherto stimulated unprecedented research interests as a new class of quantum materials. Breaking certain types of symmetries has been proposed to enable the manipulation of Dirac fermions, and that was soon realized by external modulations such as magnetic fields. However, an intrinsic manipulation of Dirac states, which is more efficient and desirable, remains a significant challenge. Here, we report a systematic study of quasi-particle dynamics and band evolution in Cd₃As₂ thin films with controlled chromium (Cr) doping by both magneto-infrared spectroscopy and electrical transport. We observe the √B relation of inter-Landau-level resonance in Cd₃As₂, an important signature of ultrarelativistic massless state inaccessible in previous optical experiments. A crossover from quantum to quasi-classical behavior makes it possible to directly probe the mass of Dirac fermions. Importantly, Cr doping allows for a Dirac mass acquisition and topological phase transition enabling a desired dynamic control of Dirac fermions. Corroborating with the density-functional theory calculations, we show that the mass generation can be explained by the explicit C₄ rotation symmetry breaking and the resultant Dirac gap engineering through Cr substitution for Cd atoms. The manipulation of the system symmetry and Dirac mass in Cd₃As₂ thin films provides a tuning knob to explore the exotic states stemming from the parent phase of Dirac semimetals.

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.

Faraday rotation in bilayer graphene-based integrated microcavity

Bernal-stacked bilayer graphene has rich ground states with various broken symmetries, allowing the existence of magneto-optical (MO) effects even in the absence of an external magnetic field. Here we report controllable Faraday rotation (FR) of bilayer graphene induced by electrostatic gate voltage, whose value is 10 times smaller than the case of single layer graphene with a magnetic field. A proposed bilayer graphene-based microcavity configuration enables the enhanced FR angle due to the large localized electromagnetic field. Our results offer unique opportunities to apply bilayer graphene for MO devices.

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.

Anomalous spectral features of a neutral bilayer graphene

Graphene and its bilayer are two-dimensional systems predicted to show exciting many-body effects near the neutrality point. The ideal tool to investigate spectrum reconstruction effects is angle-resolved photoemission spectroscopy (ARPES) as it probes directly the band structure with information about both energy and momentum. Here we reveal, by studying undoped exfoliated bilayer graphene with ARPES, two essential aspects of its many-body physics: the electron-phonon scattering rate has an anisotropic k-dependence and the type of electronic liquid is non-Fermi liquid. The latter behavior is evident from an observed electron-electron scattering rate that scales linearly with energy from 100 meV to 600 meV and that is associated with the proximity of bilayer graphene to a two-dimensional quantum critical point of competing orders.

Synthesis of Au/graphene oxide composites for selective and sensitive electrochemical detection of ascorbic acid

In this work, we present a novel ascorbic acid (AA) sensor applied to the detection of AA in human sera and pharmaceuticals. A series of Au nanoparticles (NPs) and graphene oxide sheets (Au NP/GO) composites were successfully synthesized by reduction of gold (III) using sodium citrate. Then the Au NP/GO composites were used to construct nonenzymatic electrodes in practical AA measurement. The electrode that has the best performance presents attractive analytical features, such as a low working potential of +0.15 V, a high sensitivity of 101.86 μA mM(-1) cm(-2) to AA, a low detection limit of 100 nM, good reproducibility and excellent selectivity. And more,it was also employed to accurately and practically detect AA in human serum and clinical vitamin C tablet with the existence of some food additive. The enhanced AA electrochemical properties of the Au NP/GO modified electrode in our work can be attributed to the improvement of electroactive surface area of Au NPs and the synergistic effect from the combination of Au NPs and GO sheets. This work shows that the Au NP/GO/GCEs hold the prospect for sensitive and selective determination of AA in practical clinical application.

Feature-rich magnetic quantization in sliding bilayer graphenes

The generalized tight-binding model, based on the subenvelope functions of distinct sublattices, is developed to investigate the magnetic quantization in sliding bilayer graphenes. The relative shift of two graphene layers induces a dramatic transformation between the Dirac-cone structure and the parabolic band structure, and thus leads to drastic changes of Landau levels (LLs) in the spatial symmetry, initial formation energy, intergroup anti-crossing, state degeneracy and semiconductor-metal transition. There exist three kinds of LLs, i.e., well-behaved, perturbed and undefined LLs, which are characterized by a specific mode, a main mode plus side modes, and a disordered mode, respectively. Such LLs are clearly revealed in diverse magneto-optical selection rules. Specially, the undefined LLs frequently exhibit intergroup anti-crossings in the field-dependent energy spectra, and show a large number of absorption peaks without optical selection rules.

Touching points in the energy band structure of bilayer graphene superlattices

The energy band structure of the bilayer graphene superlattices with zero-averaged periodic δ-function potentials are studied within the four-band continuum model. Using the transfer matrix method, the study is mainly focused on examining the touching points between adjacent minibands. For the zero-energy touching points the dispersion relation derived shows a Dirac-like double-cone shape with the group velocity which is periodic in the potential strength P with the period of π and becomes anisotropic at relatively large P. From the finite-energy touching points we have identified those located at zero wave-number. It was shown that for these finite-energy touching points the dispersion is direction-dependent in the sense that it is linear or parabolic in the direction parallel or perpendicular to the superlattice direction, respectively. We have also calculated the density of states and the conductivity which demonstrates a manifestation of the touching points examined.

Terahertz science and technology of carbon nanomaterials

The diverse applications of terahertz (THz) radiation and its importance to fundamental science makes finding ways to generate, manipulate and detect THz radiation one of the key areas of modern applied physics. One approach is to utilize carbon nanomaterials, in particular, single-wall carbon nanotubes and graphene. Their novel optical and electronic properties offer much promise to the field of THz science and technology. This article describes the past, current, and future of THz science and technology of carbon nanotubes and graphene. We will review fundamental studies such as THz dynamic conductivity, THz nonlinearities and ultrafast carrier dynamics as well as THz applications such as THz sources, detectors, modulators, antennas and polarizers.

Probing electronic excitations in mono- to pentalayer graphene by micro magneto-Raman spectroscopy

We probe electronic excitations between Landau levels in freestanding N-layer graphene over a broad energy range, with unprecedented spectral and spatial resolution, using micro magneto-Raman scattering spectroscopy. A characteristic evolution of electronic bands in up to five Bernal-stacked graphene layers is evidenced and shown to remarkably follow a simple theoretical approach, based on an effective bilayer model. (N > 3)-layer graphenes appear as appealing candidates in the quest for novel phenomena, particularly in the quantum Hall effect regime. Our work paves the way toward minimally invasive investigations of magneto-excitons in other emerging low-dimensional systems, with a spatial resolution down to 1 μm.

Invited article: An integrated mid-infrared, far-infrared, and terahertz optical Hall effect instrument

We report on the development of the first integrated mid-infrared, far-infrared, and terahertz optical Hall effect instrument, covering an ultra wide spectral range from 3 cm(-1) to 7000 cm(-1) (0.1-210 THz or 0.4-870 meV). The instrument comprises four sub-systems, where the magneto-cryostat-transfer sub-system enables the usage of the magneto-cryostat sub-system with the mid-infrared ellipsometer sub-system, and the far-infrared/terahertz ellipsometer sub-system. Both ellipsometer sub-systems can be used as variable angle-of-incidence spectroscopic ellipsometers in reflection or transmission mode, and are equipped with multiple light sources and detectors. The ellipsometer sub-systems are operated in polarizer-sample-rotating-analyzer configuration granting access to the upper left 3 × 3 block of the normalized 4 × 4 Mueller matrix. The closed cycle magneto-cryostat sub-system provides sample temperatures between room temperature and 1.4 K and magnetic fields up to 8 T, enabling the detection of transverse and longitudinal magnetic field-induced birefringence. We discuss theoretical background and practical realization of the integrated mid-infrared, far-infrared, and terahertz optical Hall effect instrument, as well as acquisition of optical Hall effect data and the corresponding model analysis procedures. Exemplarily, epitaxial graphene grown on 6H-SiC, a tellurium doped bulk GaAs sample and an AlGaN/GaN high electron mobility transistor structure are investigated. The selected experimental datasets display the full spectral, magnetic field and temperature range of the instrument and demonstrate data analysis strategies. Effects from free charge carriers in two dimensional confinement and in a volume material, as well as quantum mechanical effects (inter-Landau-level transitions) are observed and discussed exemplarily.

Transport measurement of Landau level gaps in bilayer graphene with layer polarization control

Landau level (LL) gaps are important parameters for understanding electronic interactions and symmetry-broken processes in bilayer graphene (BLG). Here we present transport spectroscopy measurements of LL gaps in double-gated suspended BLG with high mobilities in the quantum Hall regime. By using bias as a spectroscopic tool, we measure the gap Δ for the quantum Hall (QH) state at filling factors ν = ±4 and -2. The single-particle Δ(ν=4) scales linearly with magnetic field B and is independent of the out-of-plane electric field E⊥. For the symmetry-broken ν = -2 state, the measured values of Δ(ν=-2) are ∼1.1 meV/T and 0.17 meV/T for singly gated geometry and dual-gated geometry at E⊥ = 0, respectively. The difference between the two values arises from the E⊥. dependence of Δ(ν=-2), suggesting that the ν = -2 state is layer polarized. Our studies provide the first measurements of the gaps of the broken symmetry QH states in BLG with well-controlled E⊥ and establish a robust method that can be implemented for studying similar states in other layered materials.

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.

Ultrahigh magnetic field study of layer split bands in graphite

We report studies of the magnetospectroscopy of graphite into a new regime of high energies and ultrahigh magnetic fields which allows us to perform the first spectroscopic studies of the interlayer split-off bands, E1 and E2. These bands can be well described by an asymmetric bilayer model and have only a small interlayer band gap asymmetry. We show that all of the properties of the electrons and holes can be described by a simple relativistic behavior determined by γ0 and γ1.

Polarization selection rules for inter-Landau-level transitions in epitaxial graphene revealed by the infrared optical Hall effect

We report on the polarization selection rules of inter-Landau-level transitions using reflection-type optical Hall effect measurements from 600 to 4000 cm(-1) on epitaxial graphene grown by thermal decomposition of silicon carbide. We observe symmetric and antisymmetric signatures in our data due to polarization preserving and polarization mixing inter-Landau-level transitions, respectively. From field-dependent measurements, we identify that transitions in coupled graphene monolayers are governed by polarization mixing selection rules, whereas transitions in decoupled graphene monolayers are governed by polarization preserving selection rules. The selection rules may find explanation by different coupling mechanisms of inter-Landau-level transitions with free charge carrier magneto-optic plasma oscillations.

The electronic properties of bilayer graphene

We review the electronic properties of bilayer graphene, beginning with a description of the tight-binding model of bilayer graphene and the derivation of the effective Hamiltonian describing massive chiral quasiparticles in two parabolic bands at low energies. We take into account five tight-binding parameters of the Slonczewski-Weiss-McClure model of bulk graphite plus intra- and interlayer asymmetry between atomic sites which induce band gaps in the low-energy spectrum. The Hartree model of screening and band-gap opening due to interlayer asymmetry in the presence of external gates is presented. The tight-binding model is used to describe optical and transport properties including the integer quantum Hall effect, and we also discuss orbital magnetism, phonons and the influence of strain on electronic properties. We conclude with an overview of electronic interaction effects.

Tight-binding description of Landau levels of graphite in tilted magnetic fields

The electronic structure of Bernal-stacked graphite subject to tilted magnetic fields is studied theoretically. The minimal nearest-neighbor tight-binding model with the Peierls substitution is employed to describe the structure of Landau levels. We show that, while the orbital effect of the in-plane component of the magnetic field is negligible for massive Dirac fermions in the vicinity of the K point of the graphite Brillouin zone, at the H point it leads to the experimentally observable splitting of Landau levels, which grows approximately linearly with the in-plane field intensity.

Transport spectroscopy of symmetry-broken insulating states in bilayer graphene

Bilayer graphene is an attractive platform for studying new two-dimensional electron physics, because its flat energy bands are sensitive to out-of-plane electric fields and these bands magnify electron-electron interaction effects. Theory predicts a variety of interesting broken symmetry states when the electron density is at the carrier neutrality point, and some of these states are characterized by spontaneous mass gaps, which lead to insulating behaviour. These proposed gaps are analogous to the masses generated by broken symmetries in particle physics, and they give rise to large Berry phase effects accompanied by spontaneous quantum Hall effects. Although recent experiments have provided evidence for strong electronic correlations near the charge neutrality point, the presence of gaps remains controversial. Here, we report transport measurements in ultraclean double-gated bilayer graphene and use source-drain bias as a spectroscopic tool to resolve a gap of ∼2 meV at the charge neutrality point. The gap can be closed by a perpendicular electric field of strength ∼15 mV nm(-1), but it increases monotonically with magnetic field, with an apparent particle-hole asymmetry above the gap. These data represent the first spectroscopic mapping of the ground states in bilayer graphene in the presence of both electric and magnetic fields.

Quantum Hall effect in twisted bilayer graphene

We address the quantum Hall behavior in twisted bilayer graphene transferred from the C face of SiC. The measured Hall conductivity exhibits the same plateau values as for a commensurate Bernal bilayer. This implies that the eightfold degeneracy of the zero energy mode is topologically protected despite rotational disorder as recently predicted. In addition, an anomaly appears. The densities at which these plateaus occur show a magnetic field dependent offset. It suggests the existence of a pool of localized states at low energy, which do not count towards the degeneracy of the lowest band Landau levels. These states originate from an inhomogeneous spatial variation of the interlayer coupling.

Local compressibility measurements of correlated states in suspended bilayer graphene

Bilayer graphene has attracted considerable interest due to the important role played by many-body effects, particularly at low energies. Here we report local compressibility measurements of a suspended graphene bilayer. We find that the energy gaps at filling factors ν= ± 4 do not vanish at low fields, but instead merge into an incompressible region near the charge neutrality point at zero electric and magnetic field. These results indicate the existence of a zero-field ordered state and are consistent with the formation of either an anomalous quantum Hall state or a nematic phase with broken rotational symmetry. At higher fields, we measure the intrinsic energy gaps of broken-symmetry states at ν=0, ± 1, and ± 2, and find that they scale linearly with magnetic field, yet another manifestation of the strong Coulomb interactions in bilayer graphene.

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.

Electronic properties of a biased graphene bilayer

We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system-a biased bilayer. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its four-band and two-band continuum approximations, and the four-band model is shown to always be a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, made out of either SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point for understanding the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, such as the second-nearest-neighbour hopping energies t' (in-plane) and γ(4) (inter-layer), and the on-site energy Δ.

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.

Interaction-induced shift of the cyclotron resonance of graphene using infrared spectroscopy

We report a study of the cyclotron resonance (CR) transitions to and from the unusual n=0 Landau level (LL) in monolayer graphene. Unexpectedly, we find the CR transition energy exhibits large (up to 10%) and nonmonotonic shifts as a function of the LL filling factor, with the energy being largest at half filling of the n=0 level. The magnitude of these shifts, and their magnetic field dependence, suggests that an interaction-enhanced energy gap opens in the n=0 level at high magnetic fields. Such interaction effects normally have a limited impact on the CR due to Kohn's theorem [W. Kohn, Phys. Rev. 123, 1242 (1961)], which does not apply in graphene as a consequence of the underlying linear band structure.

Electrostatically confined quantum rings in bilayer graphene

We propose a new system where electron and hole states are electrostatically confined into a quantum ring in bilayer graphene. These structures can be created by tuning the gap of the graphene bilayer using nanostructured gates or by position-dependent doping. The energy levels have a magnetic field (B(0)) dependence that is strikingly distinct from that of usual semiconductor quantum rings. In particular, the eigenvalues are not invariant under a B(0) --> -B(0) transformation and, for a fixed total angular momentum index m, their field dependence is not parabolic, but displays two minima separated by a saddle point. The spectra also display several anticrossings, which arise due to the overlap of gate-confined and magnetically confined states.

Tuning the graphene work function by electric field effect

We report variation of the work function for single and bilayer graphene devices measured by scanning Kelvin probe microscopy (SKPM). By use of the electric field effect, the work function of graphene can be adjusted as the gate voltage tunes the Fermi level across the charge neutrality point. Upon biasing the device, the surface potential map obtained by SKPM provides a reliable way to measure the contact resistance of individual electrodes contacting graphene.

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.

Long-range Coulomb interaction in bilayer graphene

We report on our studies of interacting electrons in bilayer graphene in a magnetic field. We demonstrate that the long-range Coulomb interactions between electrons in this material are highly important and account for the band asymmetry in recent optical magneto-absorption experiments [E. A. Henriksen, Phys. Rev. Lett. 100, 087403 (2008)10.1103/PhysRevLett.100.087403]. We show that in the unbiased bilayer (where both layers are at the same electrostatic potential), the interactions can cause mixing of Landau levels in moderate magnetic fields. For the biased bilayer (when the two layers are at different potentials), we demonstrate that the interactions are responsible for a change in the total spin of the ground state for half-filled Landau levels in the valence band.

Band structure asymmetry of bilayer graphene revealed by infrared spectroscopy

We report on infrared spectroscopy of bilayer graphene integrated in gated structures. We observe a significant asymmetry in the optical conductivity upon electrostatic doping of electrons and holes. We show that this finding arises from a marked asymmetry between the valence and conduction bands, which is mainly due to the inequivalence of the two sublattices within the graphene layer and the next-nearest-neighbor interlayer coupling. From the conductivity data, the energy difference of the two sublattices and the interlayer coupling energy are directly determined.

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.

Nonlinear electromagnetic response of graphene: frequency multiplication and the self-consistent-field effects

Graphene is a recently discovered carbon-based material with unique physical properties. This is a monolayer of graphite, and the two-dimensional electrons and holes in it are described by the effective Dirac equation with a vanishing effective mass. As a consequence, the electromagnetic response of graphene is predicted to be strongly nonlinear. We develop a quasi-classical kinetic theory of the nonlinear electromagnetic response of graphene, taking into account the self-consistent-field effects. The response of the system to both harmonic and pulse excitation is considered. The frequency multiplication effect, resulting from the nonlinearity of the electromagnetic response, is studied under realistic experimental conditions. The frequency upconversion efficiency is analyzed as a function of the applied electric field and parameters of the samples. Possible applications of graphene in terahertz electronics are discussed.