Graphene as an electronic membrane

Experiments are finally revealing intricate facts about graphene which go beyond the ideal picture of relativistic Dirac fermions in pristine two dimensional (2D) space, two years after its first isolation. While observations of rippling added another dimension to the richness of the physics of graphene, scanning single electron transistor images displayed prevalent charge inhomogeneity. The importance of understanding these non-ideal aspects cannot be overstated both from the fundamental research interest since graphene is a unique arena for their interplay, and from the device applications interest since the quality control is a key to applications. We investigate the membrane aspect of graphene and its impact on the electronic properties. We show that curvature generates spatially varying electrochemical potential. Further we show that the charge inhomogeneity in turn stabilizes ripple formation.Comment: 6 pages, 11 figures. Updated version with new results about the re-hybridization of the electronic orbitals due to rippling of the graphene sheet. The re-hybridization adds the next-to-nearest neighbor hopping effect discussed in the previous version. New reference to recent STM experiments that give support to our theor

Gauss-Bonnet Black Holes and Heavy Fermion Metals

We consider charged black holes in Einstein-Gauss-Bonnet Gravity with Lifshitz boundary conditions. We find that this class of models can reproduce the anomalous specific heat of condensed matter systems exhibiting non-Fermi-liquid behaviour at low temperatures. We find that the temperature dependence of the Sommerfeld ratio is sensitive to the choice of Gauss-Bonnet coupling parameter for a given value of the Lifshitz scaling parameter. We propose that this class of models is dual to a class of models of non-Fermi-liquid systems proposed by Castro-Neto et.al.Comment: 17 pages, 6 figures, pdfLatex; small corrections to figure 10 in this versio

Observation of Van Hove singularities in twisted graphene layers

Electronic instabilities at the crossing of the Fermi energy with a Van Hove singularity in the density of states often lead to new phases of matter such as superconductivity, magnetism or density waves. However, in most materials this condition is difficult to control. In the case of single-layer graphene, the singularity is too far from the Fermi energy and hence difficult to reach with standard doping and gating techniques. Here we report the observation of low-energy Van Hove singularities in twisted graphene layers seen as two pronounced peaks in the density of states measured by scanning tunneling spectroscopy. We demonstrate that a rotation between stacked graphene layers can generate Van Hove singularities, which can be brought arbitrarily close to the Fermi energy by varying the angle of rotation. This opens intriguing prospects for Van Hove singularity engineering of electronic phases.Comment: 21 pages 5 figure

Structural phase transition in IrTe2_2: A combined study of optical spectroscopy and band structure calculations

Ir$_{1-x}$Pt$_x$Te$_2$ is an interesting system showing competing phenomenon between structural instability and superconductivity. Due to the large atomic numbers of Ir and Te, the spin-orbital coupling is expected to be strong in the system which may lead to nonconventional superconductivity. We grew single crystal samples of this system and investigated their electronic properties. In particular, we performed optical spectroscopic measurements, in combination with density function calculations, on the undoped compound IrTe$_2$ in an effort to elucidate the origin of the structural phase transition at 280 K. The measurement revealed a dramatic reconstruction of band structure and a significant reduction of conducting carriers below the phase transition. We elaborate that the transition is not driven by the density wave type instability but caused by the crystal field effect which further splits/separates the energy levels of Te (p$_x$, p$_y$) and Te p$_z$ bands.Comment: 16 pages, 5 figure

Electric Field Effects on Graphene Materials

Understanding the effect of electric fields on the physical and chemical properties of two-dimensional (2D) nanostructures is instrumental in the design of novel electronic and optoelectronic devices. Several of those properties are characterized in terms of the dielectric constant which play an important role on capacitance, conductivity, screening, dielectric losses and refractive index. Here we review our recent theoretical studies using density functional calculations including van der Waals interactions on two types of layered materials of similar two-dimensional molecular geometry but remarkably different electronic structures, that is, graphene and molybdenum disulphide (MoS$_2$). We focus on such two-dimensional crystals because of they complementary physical and chemical properties, and the appealing interest to incorporate them in the next generation of electronic and optoelectronic devices. We predict that the effective dielectric constant ($\varepsilon$) of few-layer graphene and MoS$_2$ is tunable by external electric fields ($E_{\rm ext}$). We show that at low fields ($E_{\rm ext}^{}<0.01$ V/\AA) $\varepsilon$ assumes a nearly constant value $\sim$4 for both materials, but increases at higher fields to values that depend on the layer thickness. The thicker the structure the stronger is the modulation of $\varepsilon$ with the electric field. Increasing of the external field perpendicular to the layer surface above a critical value can drive the systems to an unstable state where the layers are weakly coupled and can be easily separated. The observed dependence of $\varepsilon$ on the external field is due to charge polarization driven by the bias, which show several similar characteristics despite of the layer considered.Comment: Invited book chapter on Exotic Properties of Carbon Nanomatter: Advances in Physics and Chemistry, Springer Series on Carbon Materials. Editors: Mihai V. Putz and Ottorino Ori (11 pages, 4 figures, 30 references

Electronic Liquid Crystal Phases of a Doped Mott Insulator

The character of the ground state of an antiferromagnetic insulator is fundamentally altered upon addition of even a small amount of charge. The added charges agglomerate along domain walls at which the spin correlations, which may or may not remain long-ranged, suffer a $\pi$ phase shift. In two dimensions, these domain walls are ``stripes'' which are either insulating, or conducting, i.e. metallic rivers with their own low energy degrees of freedom. However, quasi one-dimensional metals typically undergo a transition to an insulating ordered charge density wave (CDW) state at low temperatures. Here it is shown that such a transition is eliminated if the zero-point energy of transverse stripe fluctuations is sufficiently large in comparison to the CDW coupling between stripes. As a consequence, there exist novel, liquid-crystalline low-temperature phases -- an electron smectic, with crystalline order in one direction, but liquid-like correlations in the other, and an electron nematic with orientational order but no long-range positional order. These phases, which constitute new states of matter, can be either high temperature supeconductors or two-dimensional anisotropic ``metallic'' non-Fermi liquids. Evidence for the new phases may already have been obtained by neutron scattering experiments in the cuprate superconductor, La_{1.6-x}Nd_{0.4}Sr_xCuO_{4}.Comment: 5 pages in RevTex with two figures in ep

Broken symmetry states and divergent resistance in suspended bilayer graphene

Graphene [1] and its bilayer have generated tremendous excitement in the physics community due to their unique electronic properties [2]. The intrinsic physics of these materials, however, is partially masked by disorder, which can arise from various sources such as ripples [3] or charged impurities [4]. Recent improvements in quality have been achieved by suspending graphene flakes [5,6], yielding samples with very high mobilities and little charge inhomogeneity. Here we report the fabrication of suspended bilayer graphene devices with very little disorder. We observe fully developed quantized Hall states at magnetic fields of 0.2 T, as well as broken symmetry states at intermediate filling factors $\nu = 0$, $\pm 1$, $\pm 2$ and $\pm 3$. The devices exhibit extremely high resistance in the $\nu = 0$ state that grows with magnetic field and scales as magnetic field divided by temperature. This resistance is predominantly affected by the perpendicular component of the applied field, indicating that the broken symmetry states arise from many-body interactions.Comment: 23 pages, including 4 figures and supplementary information; accepted to Nature Physic

Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice

A spin liquid is a novel quantum state of matter with no conventional order parameter where a finite charge gap exists even though the band theory would predict metallic behavior. Finding a stable spin liquid in two or higher spatial dimensions is one of the most challenging and debated issues in condensed matter physics. Very recently, it has been reported that a model of graphene, i.e., the Hubbard model on the honeycomb lattice, can show a spin liquid ground state in a wide region of the phase diagram, between a semi-metal (SM) and an antiferromagnetic insulator (AFMI). Here, by performing numerically exact quantum Monte Carlo simulations, we extend the previous study to much larger clusters (containing up to 2592 sites), and find, if any, a very weak evidence of this spin liquid region. Instead, our calculations strongly indicate a direct and continuous quantum phase transition between SM and AFMI.Comment: 15 pages with 7 figures and 9 tables including supplementary information, accepted for publication in Scientific Report

Single to Double Hump Transition in the Equilibrium Distribution Function of Relativistic Particles

We unveil a transition from single peaked to bimodal velocity distribution in a relativistic fluid under increasing temperature, in contrast with a non-relativistic gas, where only a monotonic broadening of the bell-shaped distribution is observed. Such transition results from the interplay between the raise in thermal energy and the constraint of maximum velocity imposed by the speed of light. We study the Bose-Einstein, the Fermi-Dirac, and the Maxwell-J\"uttner distributions, all exhibiting the same qualitative behavior. We characterize the nature of the transition in the framework of critical phenomena and show that it is either continuous or discontinuous, depending on the group velocity. We analyze the transition in one, two, and three dimensions, with special emphasis on two-dimensions, for which a possible experiment in graphene, based on the measurement of the Johnson-Nyquist noise, is proposed.Comment: 5 pages, 5 figure

Evolution of Landau Levels into Edge States at an Atomically Sharp Edge in Graphene

The quantum-Hall-effect (QHE) occurs in topologically-ordered states of two-dimensional (2d) electron-systems in which an insulating bulk-state coexists with protected 1d conducting edge-states. Owing to a unique topologically imposed edge-bulk correspondence these edge-states are endowed with universal properties such as fractionally-charged quasiparticles and interference-patterns, which make them indispensable components for QH-based quantum-computation and other applications. The precise edge-bulk correspondence, conjectured theoretically in the limit of sharp edges, is difficult to realize in conventional semiconductor-based electron systems where soft boundaries lead to edge-state reconstruction. Using scanning-tunneling microscopy and spectroscopy to follow the spatial evolution of bulk Landau-levels towards a zigzag edge of graphene supported above a graphite substrate we demonstrate that in this system it is possible to realize atomically sharp edges with no edge-state reconstruction. Our results single out graphene as a system where the edge-state structure can be controlled and the universal properties directly probed.Comment: 16 pages, 4 figure