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

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.

Two-dimensional open quantum system in dissipative bosonic heat bath, external magnetic field, and two time-dependent electric fields

Non-Markovian dynamics of a charged particle in a two-dimensional harmonic oscillator linearly coupled to a neutral bosonic heat bath is investigated in an external uniform magnetic field and two perpendicular time-dependent electric fields. The analytical expressions for the time-dependent and asymptotic angular momentum are derived for the Markovian and non-Markovian dynamics. The dependence of the angular momentum on the frequency of the electric field, cyclotron frequency, collective frequency, and anisotropy of the heat bath is studied. The angular momentum (or magnetization) of a charged particle can be ruled by varying the frequency of the electric field.

Tunable Terahertz Plasmons in Graphite Thin Films

Tunable terahertz plasmons are essential for reconfigurable photonics, which have been demonstrated in graphene through gating, though with relatively weak responses. Here we demonstrate strong terahertz plasmons in graphite thin films via infrared spectroscopy, with dramatic tunability by even a moderate temperature change or an in situ bias voltage. Meanwhile, through magnetoplasmon studies, we reveal that massive electrons and massless Dirac holes make comparable contributions to the plasmon response. Our study not only sets up a platform for further exploration of two-component plasmas, but also opens an avenue for terahertz modulation through electrical bias or all-optical means.

Surface functionalization of twisted graphene C32H15 and C104H52 derivatives with alkalis and superalkalis for NLO response; a DFT study

Herein, we present the detailed comparative study on geometric, electronic, optical and non-linear optical response of alkalis and superalkalis doped twisted graphene. The results illustrate that alkali metals and superalkalis interact with the central ring of the twisted graphene through non-covalent interactions which demonstrate the stability of the resultant complexes. NBO charges indicate the transfer of electrons from dopant (alkali metal atoms and superalkalis) towards twisted graphene sheet. Superalkalis doped twisted graphene complexes exhibit higher first hyperpolarizability values compared to alkali metals analogues. Among superalkalis doped complexes, K₃O@C₁₀₄H₅₂ shows the highest β_o value of 1.68 × 10⁵ au. In frequency dependent first hyperpolarizability analysis, strong second harmonic generation (SHG) response of K₃O@C₃₂H₁₅ complex is observed at both selected resonance frequency values (532 nm and1064 nm) whereas EOPE value of K₃O@C₃₂H₁₅ complex shows higher induced response at 1064 nm wavelength. The static hyperpolarizability (β_o) further increases under the influence of applied electric field. Among all complexes, Li₃O@C₃₂H₁₅ graphene complex has the highest β_o value (1.40 × 10⁵ au) under applied electric field along x axis when sheet is in y-z plane. This analysis will be an important guideline for future studies on twisted graphene based NLO materials.

Intersubband Landau Level Couplings Induced by In-Plane Magnetic Fields in Trilayer Graphene

We observed broken-symmetry quantum Hall effects and level crossings between spin- and valley- resolved Landau levels (LLs) in Bernal stacked trilayer graphene. When the magnetic field was tilted with respect to the sample normal from 0° to 66°, the LL crossings formed at intersections of zeroth and second LLs from monolayer-graphene-like and bilayer-graphene-like subbands, respectively, exhibited a sequence of transitions. The results indicate the LLs from different subbands are coupled by in-plane magnetic fields (B_{∥}), which was explained by developing the tight-binding model Hamiltonian of trilayer graphene under B_{∥}.

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.

Optical magnetoplasmons in rhombohedral graphite with a three-dimensional Dirac cone structure

Rhombohedral graphite has a three-dimensional Dirac cone structure, differing only perturbatively from the bulk stack of independent graphene layers, so that the three-dimensional integer quantum Hall effect can be well exhibited in this system. In this paper, optical magnetoplasmons are obtained by using the random phase approximation. Such collective excitations do not exist in monolayer graphene but are shown to originate from Landau level mixing due to interlayer Coulomb interaction in the quantum Hall effect regime. The three-dimensional character of rhombohedral graphite is thus demonstrated. The results should be realized in response to a longitudinal external electric field or an incident infrared electromagnetic wave.

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.

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.

An analytical approach for the energy spectrum and optical properties of gated bilayer graphene

An analytical approach is developed to access the exact energy spectrum, wave functions, dipole matrix element (M_fi) and absorption spectra (A(ω)) of gated Bernal bilayer graphene.

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.

Generation of entangled photons in graphene in a strong magnetic field

Entangled photon states attract tremendous interest as the most vivid manifestation of nonlocality of quantum mechanics and also for emerging applications in quantum information. Here we propose a mechanism of generation of polarization-entangled photons, which is based on the nonlinear optical interaction (four-wave mixing) in graphene placed in a magnetic field. Unique properties of quantized electron states in a magnetized graphene and optical selection rules near the Dirac point give rise to a giant optical nonlinearity and a high rate of photon production in the mid- or far-infrared range. A similar mechanism of photon entanglement may exist in topological insulators where the surface states have a Dirac-cone dispersion and demonstrate similar properties of magneto-optical absorption.

Nonlinear optics of graphene in a strong magnetic field

Graphene placed in a magnetic field possesses an extremely high mid/far-infrared optical nonlinearity originating from its unusual band structure and selection rules for the optical transitions near the Dirac point. Here, we study the linear and nonlinear optical response of graphene in strong magnetic and optical fields using a quantum-mechanical density-matrix formalism. We calculate the power of the coherent terahertz radiation generated as a result of the four-wave mixing in graphene. We show that even one monolayer of graphene gives rise to an appreciable nonlinear frequency conversion efficiency and Raman gain for modest intensities of the incident infrared radiation.

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.

Cyclotron motion in the vicinity of a Lifshitz transition in graphite

Graphite, a model (semi)metal with trigonally warped bands, is investigated with a magnetoabsorption experiment and viewed as an electronic system in the vicinity of the Lifshitz transition. A characteristic pattern of up to 20 cyclotron resonance harmonics has been observed. This large number of resonances, their relative strengths and characteristic shapes trace the universal properties of the electronic states near a separatrix in momentum space. Quantum-mechanical perturbative methods with respect to the trigonal warping term hardly describe the data which are, on the other hand, fairly well reproduced within a quasiclassical approach and conventional band structure model. Trigonal symmetry is preserved in graphite in contrast to a similar system, bilayer graphene.

Magneto-Raman scattering of graphene on graphite: electronic and phonon excitations

Magneto-Raman-scattering experiments from the surface of graphite reveal novel features associated to purely electronic excitations which are observed in addition to phonon-mediated resonances. Graphene-like and graphite domains are identified through experiments with ∼1  μm spatial resolution performed in magnetic fields up to 32 T. Polarization resolved measurements emphasize the characteristic selection rules for electronic transitions in graphene. Graphene on graphite displays the unexpected hybridization between optical phonon and symmetric across the Dirac point inter Landau level transitions. The results open new experimental possibilities--to use light scattering methods in studies of graphene under quantum Hall effect conditions.

Observation of magnetophonon resonance of Dirac fermions in graphite

Coherent coupling of Dirac fermion magnetoexcitons with an optical phonon is observed in graphite as marked magnetic-field dependent splittings and anticrossing behavior of the two coupled modes. The sharp magnetophonon resonance occurs in regions of the graphite sample with properties of superior single-layer graphene having enhanced lifetimes of Dirac fermions. The greatly reduced carrier broadening to values below the graphene electron-phonon coupling constant explains the appearance of sharp resonances that reveal a fundamental interaction of Dirac fermions.