Landau level spectroscopy of electron-electron interactions in graphene

Synergistic correlated states and nontrivial topology in coupled graphene-insulator heterostructures

Graphene has aroused great attention due to the intriguing properties associated with its low-energy Dirac Hamiltonian. When graphene is coupled with a correlated insulating substrate, electronic states that cannot be revealed in either individual layer may emerge in a synergistic manner. Here, we theoretically study the correlated and topological states in Coulomb-coupled and gate-tunable graphene-insulator heterostructures. By electrostatically aligning the electronic bands, charge carriers transferred between graphene and the insulator can yield a long-wavelength electronic crystal at the interface, exerting a superlattice Coulomb potential on graphene and generating topologically nontrivial subbands. This coupling can further boost electron-electron interaction effects in graphene, leading to a spontaneous bandgap formation at the Dirac point and interaction-enhanced Fermi velocity. Reciprocally, the electronic crystal at the interface is substantially stabilized with the help of cooperative interlayer Coulomb coupling. We propose a number of substrate candidates for graphene to experimentally demonstrate these effects.

Square-Net Topological Semimetals: How Spectroscopy Furthers Understanding and Control

Square-net materials are well positioned to lead optical spectroscopic explorations into the electronic structure, photoinduced dynamics, and phase transitions in topological semimetals. Hundreds of square-net topological semimetals can be prepared that have remarkably different electronic and optical properties despite having similar structures. Here we present what has been gleaned recently from these materials with the whole gamut of optical spectroscopies, ranging from steady-state reflectance and Raman investigations into topological band structures, electronic correlations, and equilibrium phase transitions to time-resolved techniques used to decipher ultrafast relaxation dynamics and nonequilibrium photoinduced phase transitions. We end with a discussion of some major remaining questions and possible future research directions.

Electrical Control over Phonon Polarization in Strained Graphene

We explore the tunability of the phonon polarization in suspended uniaxially strained graphene by magneto-phonon resonances. The uniaxial strain lifts the degeneracy of the LO and TO phonons, yielding two cross-linearly polarized phonon modes and a splitting of the Raman G peak. We utilize the strong electron-phonon coupling in graphene and the off-resonant coupling to a magneto-phonon resonance to induce a gate-tunable circular phonon dichroism. This, together with the strain-induced splitting of the G peak, allows us to controllably tune the two linearly polarized G mode phonons into circular phonon modes. We are able to achieve a circular phonon polarization of up to 40% purely by electrostatic fields and can reverse its sign by tuning from electron to hole doping. This provides unprecedented electrostatic control over the angular momentum of phonons, which paves the way toward phononic applications.

Interacting chiral electrons at the 2D Dirac points: a review

The pseudo-relativistic chiral electrons in 2D graphene and 3D topological semimetals, known as the massless Dirac or Weyl fermions, constitute various intriguing issues in modern condensed-matter physics. In particular, the issues linked to the Coulomb interaction between the chiral electrons attract great attentions due to their unusual features, namely, the interaction is not screened and has a long-ranged property near the charge-neutrality point, in clear contrast to its screened and short-ranged properties in the conventional correlated materials. In graphene, this long-range interaction induces an anomalous logarithmic renormalization of the Fermi velocity, which causes a nonlinear reshaping of its Dirac cone. In addition, for strong interactions, it even leads to the predictions of an excitonic condensation with a spontaneous mass generation. The interaction, however, would seem to be not that large in graphene, so that the latter phenomenon appears to have not yet been observed. Contrastingly, the interaction is probably large in the pressurized organic materialα-(BEDT-TTF)₂I₃, where a 2D massless-Dirac-fermion phase emerges next to a correlated insulating phase. Therefore, an excellent testing ground would appear in this material for the studies of both the velocity renormalization and the mass generation, as well as for those of the short-range electronic correlations. In this review, we give an overview of the recent progress on the understanding of such interacting chiral electrons in 2D, by placing particular emphasis on the studies in graphene andα-(BEDT-TTF)₂I₃. In the first half, we briefly summarize our current experimental and theoretical knowledge about the interaction effects in graphene, then turn attentions to the understanding inα-(BEDT-TTF)₂I₃, and highlight its relevance to and difference from graphene. The second half of this review focusses on the studies linked to the nuclear magnetic resonance experiments and the associated model calculations inα-(BEDT-TTF)₂I₃. These studies allow us to discuss the anisotropic reshaping of a tilted Dirac cone together with various electronic correlations, and the precursor excitonic dynamics growing prior to a condensation. We see these provide unique opportunities to resolve the momentum dependence of the spin excitations and fluctuations that are strongly influenced by the long-range interaction near the Dirac points.

Manipulating electronic structure of graphene for producing ferromagnetic graphene particles by Leidenfrost effect-based method

First isolation of graphene, as a great achievement, opens a new horizon in a broad range of science. Graphene is one of the most promising materials for spintronic fields whose application is limited due to its weak magnetic property. Despite many experimental and theoretical efforts for obtaining ferromagnetic graphene, still, a high degree of magnetization is an unsolved challenge. Even, in most observations, graphene magnetization is reported at extremely low temperatures rather than room temperature. In principle, the magnetic property of graphene is created by manipulation of its electronic structure. Removing or adding bonds of graphene such as creating vacancy defects, doping, adatom, edges, and functionalization can change the electronic structure and the external perturbation, such as external magnetic field, temperature, and strain can either. Recently, single and few-layer graphene have been investigated in the presence of these perturbations, and also the electronic changes have been determined by Raman spectroscopy. Here, we successfully could develop a simple and novel Leidenfrost effect-based method for graphene magnetization at room temperature with the external perturbations which apply simultaneously in the graphene flakes inside the Leidenfrost droplets. Macroscale ferromagnetic graphene particles are produced by this method. Briefly, the graphene is obtained by the liquid-phase exfoliation method in the ethanol solution media and also evaporates on the hot surface as a Leidenfrost droplet in the magnetic fields. Then, the floated graphene flakes circulate inside the droplets. Due to the strain and temperature inside the droplets and external magnetic field (the magnet in heater-stirrer), the electronic structure of graphene is instantly changed. The changes are extremely rapid that the graphene flakes behave as a charged particle and also produce an internal magnetic field during their circulation. The internal magnetic field is measured by sensors. As the main accomplishment of this study, we could develop a simple method for inducing magnetism obtained 0.4 emu/g in the graphene, as magnetization saturation at room temperature, which is higher than the reported values. Another achievement of this work is the detection of the Leidenfrost droplets magnetic field, as an internal one which has obtained for the first time. To investigate magnetic graphene particles, the magnetization process, and the electronic structure of the vibrating sample magnetometer (VSM), magnetic field sensor, and Raman spectroscopy are used, respectively.

Energy Spectrum of Two-Dimensional Excitons in a Nonuniform Dielectric Medium

We demonstrate that, in monolayers (MLs) of semiconducting transition metal dichalcogenides, the s-type Rydberg series of excitonic states follows a simple energy ladder: ε_{n}=-Ry^{*}/(n+δ)^{2}, n=1,2,…, in which Ry^{*} is very close to the Rydberg energy scaled by the dielectric constant of the medium surrounding the ML and by the reduced effective electron-hole mass, whereas the ML polarizability is accounted for only by δ. This is justified by the analysis of experimental data on excitonic resonances, as extracted from magneto-optical measurements of a high-quality WSe_{2} ML encapsulated in hexagonal boron nitride (hBN), and well reproduced with an analytically solvable Schrödinger equation when approximating the electron-hole potential in the form of a modified Kratzer potential. Applying our convention to other MoSe_{2}, WS_{2}, MoS_{2} MLs encapsulated in hBN, we estimate an apparent magnitude of δ for each of the studied structures. Intriguingly, δ is found to be close to zero for WSe_{2} as well as for MoS_{2} monolayers, what implies that the energy ladder of excitonic states in these two-dimensional structures resembles that of Rydberg states of a three-dimensional hydrogen atom.

Colossal infrared and terahertz magneto-optical activity in a two-dimensional Dirac material

When two-dimensional electron gases (2DEGs) are exposed to a magnetic field, they resonantly absorb electromagnetic radiation via electronic transitions between Landau levels¹. In 2DEGs with a Dirac spectrum, such as graphene, theory predicts an exceptionally high infrared magneto-absorption, even at zero doping^2-5. However, the measured Landau-level magneto-optical effects in graphene have been much weaker than expected^2,6-12 because of imperfections in the samples available for such experiments. Here, we measure magneto-transmission and Faraday rotation in high-mobility encapsulated monolayer graphene using a custom-designed set-up for magneto-infrared microspectroscopy. Our results show strongly enhanced magneto-optical activity in the infrared and terahertz ranges, characterized by absorption of light near to the 50% maximum allowed, 100% magnetic circular dichroism and high Faraday rotation. Considering that sizeable effects have been already observed at routinely achievable magnetic fields, our findings demonstrate the potential of magnetic tuning in 2D Dirac materials for long-wavelength optoelectronics and plasmonics.

High-Magnetic-Field Tunneling Spectra of ABC-Stacked Trilayer Graphene on Graphite

ABC-stacked trilayer graphene (TLG) was predicted to exhibit novel many-body phenomena due to the existence of almost dispersionless flat bands near the charge neutrality point. Here, using high-magnetic-field scanning tunneling microscopy, we present Landau Level (LL) spectroscopy measurements of high-quality ABC-stacked TLG on graphite. We observe an approximately linear magnetic-field scaling of valley splitting and spin splitting in the ABC-stacked TLG. Our experiment indicates that the spin splitting decreases dramatically with increasing the LL index. When the lowest LL is partially filled, we find an obvious enhancement of the spin splitting, attributing to strong many-body effects. Moreover, we observe linear energy scaling of the inverse lifetime of quasiparticles, providing an additional evidence for the strong electron-electron interactions in the ABC-stacked TLG. These results imply that interesting broken-symmetry states and novel electron correlated effects could emerge in the ABC-stacked TLG in the presence of high magnetic fields.

Stokes and anti-Stokes Raman scattering in mono- and bilayer graphene

Stokes and anti-Stokes Raman spectroscopy associated with the intervalley double resonance process in carbon materials is a unique technique to reveal the relationship between their characteristic electronic band structures and phonon dispersion. In graphene, the dominant resonant behavior for its 2D mode is an intervalley triple resonance Raman process. In this paper, we report the Stokes and anti-Stokes Raman scattering of the 2D mode in pristine graphene. The excitation energy (Eex)-dependent frequency discrepancy between anti-Stokes and Stokes components of the 2D mode (Δω(2D)) is observed, which is in good agreement with the theoretical results. This is attributed to the nonlinear dispersion of the in-plane transverse optical (iTO) phonon branch near the K point, confirmed by the nonlinear Eex-dependent frequency of the 2D mode (ω(2D)) in the range of 1.58-3.81 eV. The wavevector-dependent phonon group velocity of the iTO phonon branch is directly derived from Δω(2D). The Stokes and anti-Stokes Raman scattering of the D mode in defected graphene and the 2D mode in bilayer graphene associated with intervalley double resonance Raman processes is also reported.

Impact of Many-Body Effects on Landau Levels in Graphene

We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier density-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magnetophonon resonances, we extract the charge carrier density dependence of the Landau level transition energies and the associated effective Fermi velocity v_{F}. In contrast to the logarithmic divergence of v_{F} at zero magnetic field, we find a piecewise linear scaling of v_{F} as a function of the charge carrier density, due to a magnetic-field-induced suppression of the long-range Coulomb interaction. We quantitatively confirm our experimental findings by performing tight-binding calculations on the level of the Hartree-Fock approximation, which also allow us to estimate an excitonic binding energy of ≈6  meV contained in the experimentally extracted Landau level transitions energies.

Ultrafast Terahertz Nonlinear Optics of Landau Level Transitions in a Monolayer Graphene

We investigated the ultrafast terahertz (THz) nonlinearity in a monolayer graphene under the strong magnetic field using THz pump-THz probe spectroscopy. An ultrafast suppression of the Faraday rotation associated with inter-Landau level (LL) transitions is observed, reflecting the Dirac electron character of nonequidistant LLs with large transition dipole moments. A drastic modulation of electron distribution in LLs is induced by far off-resonant THz pulse excitation in the transparent region. Numerical simulation based on the density matrix formalism without rotating-wave approximation reproduces the experimental results. Our results indicate that the strong light-matter coupling regime is realized in graphene, with the Rabi frequency exceeding the carrier wave frequency and even the relevant energy scale of the inter-LL transition.

Many-Particle Effects in the Cyclotron Resonance of Encapsulated Monolayer Graphene

We study the infrared cyclotron resonance of high-mobility monolayer graphene encapsulated in hexagonal boron nitride, and simultaneously observe several narrow resonance lines due to interband Landau-level transitions. By holding the magnetic field strength B constant while tuning the carrier density n, we find the transition energies show a pronounced nonmonotonic dependence on the Landau-level filling factor, ν∝n/B. This constitutes direct evidence that electron-electron interactions contribute to the Landau-level transition energies in graphene, beyond the single-particle picture. Additionally, a splitting occurs in transitions to or from the lowest Landau level, which is interpreted as a Dirac mass arising from coupling of the graphene and boron nitride lattices.

Bielectron vortices in two-dimensional Dirac semimetals

Searching for new states of matter and unusual quasi-particles in emerging materials and especially low-dimensional systems is one of the major trends in contemporary condensed matter physics. Dirac materials, which host quasi-particles which are described by ultrarelativistic Dirac-like equations, are of a significant current interest from both a fundamental and applied physics perspective. Here we show that a pair of two-dimensional massless Dirac–Weyl fermions can form a bound state independently of the sign of the inter-particle interaction potential, as long as this potential decays at large distances faster than Kepler’s inverse distance law. This leads to the emergence of a new type of energetically favorable quasiparticle: bielectron vortices, which are double-charged and reside at zero-energy. Their bosonic nature allows for condensation and may give rise to Majorana physics without invoking a superconductor. These novel quasi-particles arguably explain a range of poorly understood experiments in gated graphene structures at low doping.

Two-dimensional Dirac semimetals are known to host fermionic excitations which can mimic physics usually found in ultrarelativistic quantum mechanics. Here, the authors unveil the existence of another type of quasiparticle, bielectron vortices, which are bosonic and may give rise to new types of condensates.

Interacting Electrons in Graphene: Fermi Velocity Renormalization and Optical Response

We have developed a Hartree-Fock theory for electrons on a honeycomb lattice aiming to solve a long-standing problem of the Fermi velocity renormalization in graphene. Our model employs no fitting parameters (like an unknown band cutoff) but relies on a topological invariant (crystal structure function) that makes the Hartree-Fock sublattice spinor independent of the electron-electron interaction. Agreement with the experimental data is obtained assuming static self-screening including local field effects. As an application of the model, we derive an explicit expression for the optical conductivity and discuss the renormalization of the Drude weight. The optical conductivity is also obtained via precise quantum Monte Carlo calculations which compares well to our mean-field approach.

Optical signatures of parity anomaly in a gapped graphene-like system

Parity anomaly refers to the violation of coordinate reflection symmetry induced by the quantum fluctuations. It is proposed to exist in a graphene-like system with a finite bare mass for Dirac fermions, and manifests itself as a parity-violating quantum correction to the current of each species of fermions. Coulomb interaction greatly increases the fermion mass, and produces various types of excitons. Of particular interest is the ρ-exciton, which is directly connected to parity anomaly and can be generated by absorbing a specific photon. The exciton is a particle-hole bound state, and can be regarded as condensed-matter analogue of meson composed of quark-anti-quark pair. By virtue of this correspondence, we analyze the optical conductivity and calculate the mass of ρ-exciton by employing the Shifman-Vainshtein-Zakharov sum rule method that is widely used in the studies of hadron phenomenology. We show that ρ-exciton leads to a sharp peak in the optical conductivity, which is observable in optical experiments. Moreover, we study the impact of scalar-like excitons on two-photon processes by computing the decay amplitude, and also find peaks in the Raman spectra.

Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor

The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials.

Hofstadter Butterfly and Many-Body Effects in Epitaxial Graphene Superlattice

Graphene placed on hexagonal boron nitride (h-BN) has received a wide range of interest due to the improved electrical performance and rich physics from the interface, especially the emergence of superlattice Dirac points as well as Hofstadter butterfly in high magnetic field. Instead of transferring graphene onto h-BN, epitaxial growth of graphene directly on a single-crystal h-BN provides an alternative and promising way to study these interesting superlattice effects due to their precise lattice alignment. Here we report an electrical transport study on epitaxial graphene superlattice on h-BN with a period of ∼15.6 nm. The epitaxial graphene superlattice is clean, intrinsic, and of high quality with a carrier mobility of ∼27 000 cm(2) V(-1) s(-1), which enables the observation of Hofstadter butterfly features originated from the superlattice at a magnetic field as low as 6.4 T. A metal-insulator transition and magnetic field dependent Fermi velocity were also observed, suggesting prominent electron-electron interaction-induced many-body effects.

Structural and electronic properties of epitaxial multilayer h-BN on Ni(111) for spintronics applications

Hexagonal boron nitride (h-BN) is a promising material for implementation in spintronics due to a large band gap, low spin-orbit coupling, and a small lattice mismatch to graphene and to close-packed surfaces of fcc-Ni(111) and hcp-Co(0001). Epitaxial deposition of h-BN on ferromagnetic metals is aimed at small interface scattering of charge and spin carriers. We report on the controlled growth of h-BN/Ni(111) by means of molecular beam epitaxy (MBE). Structural and electronic properties of this system are investigated using cross-section transmission electron microscopy (TEM) and electron spectroscopies which confirm good agreement with the properties of bulk h-BN. The latter are also corroborated by density functional theory (DFT) calculations, revealing that the first h-BN layer at the interface to Ni is metallic. Our investigations demonstrate that MBE is a promising, versatile alternative to both the exfoliation approach and chemical vapour deposition of h-BN.

Gate-Dependent Electronic Raman Scattering in Graphene

We report the direct observation of polarization resolved electronic Raman scattering in a gated monolayer graphene device. The evolution of the electronic Raman scattering spectra with gate voltage and its polarization dependence are in full agreement with theoretical expectations for nonresonant Raman processes involving interband electron-hole excitations across the Dirac cone. We further show that the spectral dependence of the electronic Raman scattering signal can be simply described by the dynamical polarizability of graphene in the long wavelength limit. The possibility to directly observe Dirac fermion excitations in graphene opens the way to promising Raman investigations of electronic properties of graphene and other 2D crystals.

Biexciton Binding of Dirac fermions Confined in Colloidal Graphene Quantum Dots

We present transient absorption measurements and microscopic theory of biexciton binding in triangular colloidal graphene quantum dots consisting of 168 sp(2)-hybridized C atoms. We observe optical transitions from the lowest orbitally dark singlet exciton states to states below the energy of an unbound dark+bright singlet-exciton pair. Through microscopic calculations of the low-energy exciton and biexciton states via tight-binding, Hartree-Fock, and configuration interaction methods, the spectra reveal a biexciton consisting primarily of a dark-bright singlet-pair bound by ∼0.14 eV.