Renormalization of the graphene dispersion velocity determined from scanning tunneling spectroscopy

Absence of edge reconstruction for quantum Hall edge channels in graphene devices

Quantum Hall (QH) edge channels propagating along the periphery of two-dimensional (2D) electron gases under perpendicular magnetic field are a major paradigm in physics. However, groundbreaking experiments that could use them in graphene are hampered by the conjecture that QH edge channels undergo a reconstruction with additional nontopological upstream modes. By performing scanning tunneling spectroscopy up to the edge of a graphene flake on hexagonal boron nitride, we show that QH edge channels are confined to a few magnetic lengths at the crystal edges. This implies that they are ideal 1D chiral channels defined by boundary conditions of vanishing electronic wave functions at the crystal edges, hence free of electrostatic reconstruction. We further evidence a uniform charge carrier density at the edges, incompatible with the existence of upstream modes. This work has profound implications for electron and heat transport experiments in graphene-based systems and other 2D crystalline materials.

A non-perturbative study of the interplay between electron-phonon interaction and Coulomb interaction in undoped graphene

In condensed-matter systems, electrons are subjected to two different interactions under certain conditions. Even if both interactions are weak, it is difficult to perform perturbative calculations due to the complexity caused by the interplay of two interactions. When one or two interactions are strong, ordinary perturbation theory may become invalid. Here we consider undoped graphene as an example and provide a non-perturbative quantum-field-theoretic analysis of the interplay of electron-phonon interaction and Coulomb interaction. We treat these two interactions on an equal footing and derive the exact Dyson-Schwinger (DS) integral equation of the full Dirac-fermion propagator. This equation depends on several complicated correlation functions and thus is difficult to handle. Fortunately, we find that these correlation functions obey a number of exact identities, which allows us to prove that the DS equation of full fermion propagator is self-closed. After solving this self-closed equation, we obtain the renormalized fermion velocity and show that its energy (momentum) dependence of renormalized fermion velocity is dominantly determined by the electron-phonon (Coulomb) interaction. In particular, the renormalized velocity exhibits a logarithmic momentum dependence and a non-monotonic energy dependence.

Tunneling Spectroscopy of Two-Dimensional Materials Based on Via Contacts

We introduce a novel planar tunneling architecture for van der Waals heterostructures based on via contacts, namely, metallic contacts embedded into through-holes in hexagonal boron nitride (hBN). We use the via-based tunneling method to study the single-particle density of states of two different two-dimensional (2D) materials, NbSe₂ and graphene. In NbSe₂ devices, we characterize the barrier strength and interface disorder for barrier thicknesses of 0, 1, and 2 layers of hBN and study the dependence on the tunnel-contact area down to (44 ± 14)² nm². For 0-layer hBN devices, we demonstrate a crossover from diffusive to point contacts in the small-contact-area limit. In graphene, we show that reducing the tunnel barrier thickness and area can suppress effects due to phonon-assisted tunneling and defects in the hBN barrier. This via-based architecture overcomes limitations of other planar tunneling designs and produces high-quality, ultraclean tunneling structures from a variety of 2D materials.

Imaging tunable quantum Hall broken-symmetry orders in graphene

ABSTARCT

When electrons populate a flat band their kinetic energy becomes negligible, forcing them to organize in exotic many-body states to minimize their Coulomb energy^1-5. The zeroth Landau level of graphene under a magnetic field is a particularly interesting strongly interacting flat band because interelectron interactions are predicted to induce a rich variety of broken-symmetry states with distinct topological and lattice-scale orders^6-11. Evidence for these states stems mostly from indirect transport experiments that suggest that broken-symmetry states are tunable by boosting the Zeeman energy¹² or by dielectric screening of the Coulomb interaction¹³. However, confirming the existence of these ground states requires a direct visualization of their lattice-scale orders¹⁴. Here we image three distinct broken-symmetry phases in graphene using scanning tunnelling spectroscopy. We explore the phase diagram by tuning the screening of the Coulomb interaction by a low- or high-dielectric-constant environment, and with a magnetic field. In the unscreened case, we find a Kekulé bond order, consistent with observations of an insulating state undergoing a magnetic-field driven Kosterlitz-Thouless transition^15,16. Under dielectric screening, a sublattice-unpolarized ground state¹³ emerges at low magnetic fields, and transits to a charge-density-wave order with partial sublattice polarization at higher magnetic fields. The Kekulé and charge-density-wave orders furthermore coexist with additional, secondary lattice-scale orders that enrich the phase diagram beyond current theory predictions^6-10. This screening-induced tunability of broken-symmetry orders may prove valuable to uncover correlated phases of matter in other quantum materials.

Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet

The interaction between electrons in graphene under high magnetic fields drives the formation of a rich set of quantum Hall ferromagnetic (QHFM) phases with broken spin or valley symmetry. Visualizing atomic-scale electronic wave functions with scanning tunneling spectroscopy (STS), we resolved microscopic signatures of valley ordering in QHFM phases and spectral features of fractional quantum Hall phases of graphene. At charge neutrality, we observed a field-tuned continuous quantum phase transition from a valley-polarized state to an intervalley coherent state, with a Kekulé distortion of its electronic density. Mapping the valley texture extracted from STS measurements of the Kekulé phase, we could visualize valley skyrmion excitations localized near charged defects. Our techniques can be applied to examine valley-ordered phases and their topological excitations in a wide range of materials.

Robust Quantum Oscillation of Dirac Fermions in a Single-Defect Resonant Transistor

The massless nature of Dirac Fermions produces large energy gaps between Landau levels (LLs), which is promising for topological devices. While the energy gap between the zeroth and first LLs reaches 36 meV in a magnetic field of 1 T in graphene, exploiting the quantum Hall effect at room temperature requires large magnetic fields (∼30 T) to overcome the energy level broadening induced by charge inhomogeneities in the device. Here, we report a way to use the robust quantum oscillations of Dirac Fermions in a single-defect resonant transistor, which is based on local tunneling through a thin (∼1.4 nm) hexagonal boron nitride (h-BN) between lattice-orientation-aligned graphene layers. A single point defect in the h-BN, selected by the orientation-tuned graphene layers, probes local LLs in its proximity, minimizing the energy broadening of the LLs by charge inhomogeneity at a moderate magnetic field and ambient conditions. Thus, the resonant tunneling between lattice-orientation-aligned graphene layers highlights the potential to spectroscopically locate the atomic defects in the h-BN, which contributes to the study on electrically tunable single photon source via defect states in h-BN.

Experimental Determination of the Energy per Particle in Partially Filled Landau Levels

We describe an experimental technique to measure the chemical potential μ in atomically thin layered materials with high sensitivity and in the static limit. We apply the technique to a high quality graphene monolayer to map out the evolution of μ with carrier density throughout the N=0 and N=1 Landau levels at high magnetic field. By integrating μ over filling factor ν, we obtain the ground state energy per particle, which can be directly compared to numerical calculations. In the N=0 Landau level, our data show exceptional agreement with numerical calculations over the whole Landau level without adjustable parameters as long as the screening of the Coulomb interaction by the filled Landau levels is accounted for. In the N=1 Landau level, a comparison between experimental and numerical data suggests the importance of valley anisotropic interactions and reveals a possible presence of valley-textured electron solids near odd filling.

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.

Quantum-dot assisted spectroscopy of degeneracy-lifted Landau levels in graphene

Energy spectroscopy of strongly interacting phases requires probes which minimize screening while retaining spectral resolution and local sensitivity. Here, we demonstrate that such probes can be realized using atomic sized quantum dots bound to defects in hexagonal Boron Nitride tunnel barriers, placed at nanometric distance from graphene. With dot energies capacitively tuned by a planar graphite electrode, dot-assisted tunneling becomes highly sensitive to the graphene excitation spectrum. The spectra track the onset of degeneracy lifting with magnetic field at the ground state, and at unoccupied excited states, revealing symmetry-broken gaps which develop steeply with magnetic field - corresponding to Landé g factors as high as 160. Measured up to B = 33 T, spectra exhibit a primary energy split between spin-polarized excited states, and a secondary spin-dependent valley-split. Our results show that defect dots probe the spectra while minimizing local screening, and are thus exceptionally sensitive to interacting states.

Comprehensive Electrostatic Modeling of Exposed Quantum Dots in Graphene/Hexagonal Boron Nitride Heterostructures

Recent experimental advancements have enabled the creation of tunable localized electrostatic potentials in graphene/hexagonal boron nitride (hBN) heterostructures without concealing the graphene surface. These potentials corral graphene electrons yielding systems akin to electrostatically defined quantum dots (QDs). The spectroscopic characterization of these exposed QDs with the scanning tunneling microscope (STM) revealed intriguing resonances that are consistent with a tunneling probability of 100% across the QD walls. This effect, known as Klein tunneling, is emblematic of relativistic particles, underscoring the uniqueness of these graphene QDs. Despite the advancements with electrostatically defined graphene QDs, a complete understanding of their spectroscopic features still remains elusive. In this study, we address this lapse in knowledge by comprehensively considering the electrostatic environment of exposed graphene QDs. We then implement these considerations into tight binding calculations to enable simulations of the graphene QD local density of states. We find that the inclusion of the STM tip's electrostatics in conjunction with that of the underlying hBN charges reproduces all of the experimentally resolved spectroscopic features. Our work provides an effective approach for modeling the electrostatics of exposed graphene QDs. The methods discussed here can be applied to other electrostatically defined QD systems that are also exposed.

Guiding Dirac Fermions in Graphene with a Carbon Nanotube

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

Accurate Gap Determination in Monolayer and Bilayer Graphene/ h-BN Moiré Superlattices

High mobility single and few-layer graphene sheets are in many ways attractive as nanoelectronic circuit hosts but lack energy gaps, which are essential to the operation of field-effect transistors. One of the methods used to create gaps in the spectrum of graphene systems is to form long period moiré patterns by aligning the graphene and hexagonal boron nitride ( h-BN) substrate lattices. Here, we use planar tunneling devices with thin h-BN barriers to obtain direct and accurate tunneling spectroscopy measurements of the energy gaps in single-layer and bilayer graphene- h-BN superlattice structures at charge neutrality (first Dirac point) and at integer moiré band occupancies (second Dirac point, SDP) as a function of external electric and magnetic fields and the interface twist angle. In single-layer graphene, we find, in agreement with previous work, that gaps are formed at neutrality and at the hole-doped SDP, but not at the electron-doped SDP. Both primary and secondary gaps can be determined accurately by extrapolating Landau fan patterns to a zero magnetic field and are as large as ≈17 meV for devices in near-perfect alignment. For bilayer graphene, we find that gaps occur only at charge neutrality where they can be modified by an external electric field.

Interaction-driven quantum Hall wedding cake-like structures in graphene quantum dots

Quantum-relativistic matter is ubiquitous in nature; however, it is notoriously difficult to probe. The ease with which external electric and magnetic fields can be introduced in graphene opens a door to creating a tabletop prototype of strongly confined relativistic matter. Here, through a detailed spectroscopic mapping, we directly visualize the interplay between spatial and magnetic confinement in a circular graphene resonator as atomic-like shell states condense into Landau levels. We directly observe the development of a "wedding cake"-like structure of concentric regions of compressible-incompressible quantum Hall states, a signature of electron interactions in the system. Solid-state experiments can, therefore, yield insights into the behavior of quantum-relativistic matter under extreme conditions.

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.

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.

Spatial charge inhomogeneity and defect states in topological Dirac semimetal thin films of Na3Bi

Topological Dirac semimetals (TDSs) are three-dimensional analogs of graphene, with carriers behaving like massless Dirac fermions in three dimensions. In graphene, substrate disorder drives fluctuations in Fermi energy, necessitating construction of heterostructures of graphene and hexagonal boron nitride (h-BN) to minimize the fluctuations. Three-dimensional TDSs obviate the substrate and should show reduced E_F fluctuations due to better metallic screening and higher dielectric constants. We map the potential fluctuations in TDS Na₃Bi using a scanning tunneling microscope. The rms potential fluctuations are significantly smaller than the thermal energy room temperature (ΔE_F,rms = 4 to 6 meV = 40 to 70 K) and comparable to the highest-quality graphene on h-BN. Surface Na vacancies produce a novel resonance close to the Dirac point with surprisingly large spatial extent and provide a unique way to tune the surface density of states in a TDS thin-film material. Sparse defect clusters show bound states whose occupation may be changed by applying a bias to the scanning tunneling microscope tip, offering an opportunity to study a quantum dot connected to a TDS reservoir.

2D Raman band splitting in graphene: Charge screening and lifting of the K-point Kohn anomaly

Pristine graphene encapsulated in hexagonal boron nitride has transport properties rivalling suspended graphene, while being protected from contamination and mechanical damage. For high quality devices, it is important to avoid and monitor accidental doping and charge fluctuations. The 2D Raman double peak in intrinsic graphene can be used to optically determine charge density, with decreasing peak split corresponding to increasing charge density. We find strong correlations between the 2D ₁ and 2D ₂ split vs 2D line widths, intensities, and peak positions. Charge density fluctuations can be measured with orders of magnitude higher precision than previously accomplished using the G-band shift with charge. The two 2D intrinsic peaks can be associated with the "inner" and "outer" Raman scattering processes, with the counterintuitive assignment of the phonon closer to the K point in the KM direction (outer process) as the higher energy peak. Even low charge screening lifts the phonon Kohn anomaly near the K point for graphene encapsulated in hBN, and shifts the dominant intensity from the lower to the higher energy peak.

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.

Temperature-Dependent Electron-Electron Interaction in Graphene on SrTiO3

The electron band structure of graphene on SrTiO₃ substrate has been investigated as a function of temperature. The high-resolution angle-resolved photoemission study reveals that the spectral width at Fermi energy and the Fermi velocity of graphene on SrTiO₃ are comparable to those of graphene on a BN substrate. Near the charge neutrality, the energy-momentum dispersion of graphene exhibits a strong deviation from the well-known linearity, which is magnified as temperature decreases. Such modification resembles the characteristics of enhanced electron-electron interaction. Our results not only suggest that SrTiO₃ can be a plausible candidate as a substrate material for applications in graphene-based electronics but also provide a possible route toward the realization of a new type of strongly correlated electron phases in the prototypical two-dimensional system via the manipulation of temperature and a proper choice of dielectric substrates.

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.

Direct Probing of the Electronic Structures of Single-Layer and Bilayer Graphene with a Hexagonal Boron Nitride Tunneling Barrier

The chemical and mechanical stability of hexagonal boron nitride (h-BN) thin films and their compatibility with other free-standing two-dimensional (2D) crystals to form van der Waals heterostructures make the h-BN-2D tunnel junction an intriguing experimental platform not only for the engineering of specific device functionalities but also for the promotion of quantum measurement capabilities. Here, we exploit the h-BN-graphene tunnel junction to directly probe the electronic structures of single-layer and bilayer graphene in the presence and the absence of external magnetic fields with unprecedented high signal-to-noise ratios. At a zero magnetic field, we identify the tunneling spectra related to the charge neutrality point and the opening of the electric-field-induced bilayer energy gap. In the quantum Hall regime, the quantization of 2D electron gas into Landau levels (LL) is seen as early as 0.2 T, and as many as 30 well-separated LL tunneling conductance oscillations are observed for both electron- and hole-doped regions. Our device simulations successfully reproduce the experimental observations. Additionally, we extract the relative permittivity of three-to-five layer h-BN and find that the screening capability of thin h-BN films is as much as 60% weaker than bulk h-BN.

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.

Charge Puddles in Graphene near the Dirac Point

The charge carrier density in graphene on a dielectric substrate such as SiO_{2} displays inhomogeneities, the so-called charge puddles. Because of the linear dispersion relation in monolayer graphene, the puddles are predicted to grow near charge neutrality, a markedly distinct property from conventional two-dimensional electron gases. By performing scanning tunneling microscopy and spectroscopy on a mesoscopic graphene device, we directly observe the puddles' growth, both in spatial extent and in amplitude, as the Fermi level approaches the Dirac point. Self-consistent screening theory provides a unified description of both the macroscopic transport properties and the microscopically observed charge disorder.

Nanomesh-Type Graphene Superlattice on Au(111) Substrate

The adherence of graphene to various crystalline substrates often leads to a periodic out-of-plane modulation of its atomic structure due to the lattice mismatch. While, in principle, convex (protrusion) and concave (depression) superlattice geometries are nearly equivalent, convex superlattices have predominantly been observed for graphene on various metal surfaces. Here we report the STM observation of a graphene superlattice with concave (nanomesh) morphology on Au(111). DFT and molecular dynamics simulations confirm the nanomesh nature of the graphene superlattice on Au(111) and also reveal its potential origin as a surface reconstruction, consisting of the imprinting of the nanomesh morphology into the Au(111) surface. This unusual surface reconstruction can be attributed to the particularly large mobility of the Au atoms on Au(111) surfaces and most probably plays an important role in stabilizing the concave graphene superlattice. We report the simultaneous observation of both convex and concave graphene superlattices on herringbone reconstructed Au(111) excluding the contrast inversion as the origin of the observed concave morphology. The observed graphene nanomesh superlattice can provide an intriguing nanoscale template for self-assembled structures and nanoparticles that cannot be stabilized on other surfaces.

Vibrational Properties of h-BN and h-BN-Graphene Heterostructures Probed by Inelastic Electron Tunneling Spectroscopy

Inelastic electron tunneling spectroscopy is a powerful technique for investigating lattice dynamics of nanoscale systems including graphene and small molecules, but establishing a stable tunnel junction is considered as a major hurdle in expanding the scope of tunneling experiments. Hexagonal boron nitride is a pivotal component in two-dimensional Van der Waals heterostructures as a high-quality insulating material due to its large energy gap and chemical-mechanical stability. Here we present planar graphene/h-BN-heterostructure tunneling devices utilizing thin h-BN as a tunneling insulator. With much improved h-BN-tunneling-junction stability, we are able to probe all possible phonon modes of h-BN and graphite/graphene at Γ and K high symmetry points by inelastic tunneling spectroscopy. Additionally, we observe that low-frequency out-of-plane vibrations of h-BN and graphene lattices are significantly modified at heterostructure interfaces. Equipped with an external back gate, we can also detect high-order coupling phenomena between phonons and plasmons, demonstrating that h-BN-based tunneling device is a wonderful playground for investigating electron-phonon couplings in low-dimensional systems.

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.

MoS 2 MoS2: choice substrate for accessing and tuning the electronic properties of graphene

One of the enduring challenges in graphene research and applications is the extreme sensitivity of its charge carriers to external perturbations, especially those introduced by the substrate. The best available substrates to date, graphite and hexagonal boron nitride (h-BN), still pose limitations: graphite being metallic does not allow gating, while both h-BN and graphite, having lattice structures closely matched to that of graphene, may cause significant band structure reconstruction. Here we show that the atomically smooth surface of exfoliated MoS(2) provides access to the intrinsic electronic structure of graphene without these drawbacks. Using scanning tunneling microscopy and Landau-level (LL) spectroscopy in a device configuration that allows tuning of the carrier concentration, we find that graphene on MoS(2) is ultraflat, producing long mean free paths, while avoiding band structure reconstruction. Importantly, the screening of the MoS(2) substrate can be tuned by changing the position of the Fermi energy with relatively low gate voltages. We show that shifting the Fermi energy from the gap to the edge of the conduction band gives rise to enhanced screening and to a substantial increase in the mean free path and quasiparticle lifetime. MoS(2) substrates thus provide unique opportunities to access the intrinsic electronic properties of graphene and to study in situ the effects of screening on electron-electron interactions and transport.

Why does graphene behave as a weakly interacting system?

We address the puzzling weak-coupling perturbative behavior of graphene interaction effects as manifested experimentally, in spite of the effective fine structure constant being large, by calculating the effect of Coulomb interactions on the quasiparticle properties to next-to-leading order in the random phase approximation (RPA). The focus of our work is graphene suspended in vacuum, where electron-electron interactions are strong and the system is manifestly in a nonperturbative regime. We report results for the quasiparticle residue and the Fermi velocity renormalization at low carrier density. The smallness of the next-to-leading order corrections that we obtain demonstrates that the RPA theory converges rapidly and thus, in contrast to the usual perturbative expansion in the bare coupling constant, constitutes a quantitatively predictive theory of graphene many-body physics for any coupling strength.

Graphene on hexagonal boron nitride

The field of graphene research has developed rapidly since its first isolation by mechanical exfoliation in 2004. Due to the relativistic Dirac nature of its charge carriers, graphene is both a promising material for next-generation electronic devices and a convenient low-energy testbed for intrinsically high-energy physical phenomena. Both of these research branches require the facile fabrication of clean graphene devices so as not to obscure its intrinsic physical properties. Hexagonal boron nitride has emerged as a promising substrate for graphene devices as it is insulating, atomically flat and provides a clean charge environment for the graphene. Additionally, the interaction between graphene and boron nitride provides a path for the study of new physical phenomena not present in bare graphene devices. This review focuses on recent advancements in the study of graphene on hexagonal boron nitride devices from the perspective of scanning tunneling microscopy with highlights of some important results from electrical transport measurements.

Charge-carrier screening in single-layer graphene

The effect of charge-carrier screening on the transport properties of a neutral graphene sheet is studied by directly probing its electronic structure. We find that the Fermi velocity, Dirac point velocity, and overall distortion of the Dirac cone are renormalized due to the screening of the electron-electron interaction in an unusual way. We also observe an increase of the electron mean free path due to the screening of charged impurities. These observations help us to understand the basis for the transport properties of graphene, as well as the fundamental physics of these interesting electron-electron interactions at the Dirac point crossing.