Transport Spectroscopy of Symmetry-Broken Insulating States in Bilayer Graphene

The flat bands in bilayer graphene(BLG) are sensitive to electric fields E\bot directed between the layers, and magnify the electron-electron interaction effects, thus making BLG an attractive platform for new two-dimensional (2D) electron physics[1-5]. Theories[6-16] have suggested the possibility of a variety of interesting broken symmetry states, some characterized by spontaneous mass gaps, when the electron-density is at the carrier neutrality point (CNP). The theoretically proposed gaps[6,7,10] in bilayer graphene are analogous[17,18] to the masses generated by broken symmetries in particle physics and give rise to large momentum-space Berry curvatures[8,19] accompanied by spontaneous quantum Hall effects[7-9]. Though recent experiments[20-23] have provided convincing evidence of strong electronic correlations near the CNP in BLG, the presence of gaps is difficult to establish because of the lack of direct spectroscopic measurements. Here we present transport measurements in ultra-clean double-gated BLG, using source-drain bias as a spectroscopic tool to resolve a gap of ~2 meV at the CNP. The gap can be closed by an electric field E\bot \sim13 mV/nm but increases monotonically with a magnetic field B, with an apparent particle-hole asymmetry above the gap, thus providing the first mapping of the ground states in BLG.Comment: 4 figure

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

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

Magnetic Catalysis and Quantum Hall Ferromagnetism in Weakly Coupled Graphene

We study the realization in a model of graphene of the phenomenon whereby the tendency of gauge-field mediated interactions to break chiral symmetry spontaneously is greatly enhanced in an external magnetic field. We prove that, in the weak coupling limit, and where the electron-electron interaction satisfies certain mild conditions, the ground state of charge neutral graphene in an external magnetic field is a quantum Hall ferromagnet which spontaneously breaks the emergent U(4) symmetry to U(2)XU(2). We argue that, due to a residual CP symmetry, the quantum Hall ferromagnet order parameter is given exactly by the leading order in perturbation theory. On the other hand, the chiral condensate which is the order parameter for chiral symmetry breaking generically obtains contributions at all orders. We compute the leading correction to the chiral condensate. We argue that the ensuing fermion spectrum resembles that of massive fermions with a vanishing U(4)-valued chemical potential. We discuss the realization of parity and charge conjugation symmetries and argue that, in the context of our model, the charge neutral quantum Hall state in graphene is a bulk insulator, with vanishing longitudinal conductivity due to a charge gap and Hall conductivity vanishing due to a residual discrete particle-hole symmetry.Comment: 35 page

Microscopic Polarization in Bilayer Graphene

Bilayer graphene has drawn significant attention due to the opening of a band gap in its low energy electronic spectrum, which offers a promising route to electronic applications. The gap can be either tunable through an external electric field or spontaneously formed through an interaction-induced symmetry breaking. Our scanning tunneling measurements reveal the microscopic nature of the bilayer gap to be very different from what is observed in previous macroscopic measurements or expected from current theoretical models. The potential difference between the layers, which is proportional to charge imbalance and determines the gap value, shows strong dependence on the disorder potential, varying spatially in both magnitude and sign on a microscopic level. Furthermore, the gap does not vanish at small charge densities. Additional interaction-induced effects are observed in a magnetic field with the opening of a subgap when the zero orbital Landau level is placed at the Fermi energy

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

Dirac cones reshaped by interaction effects in suspended graphene

We report measurements of the cyclotron mass in graphene for carrier concentrations n varying over three orders of magnitude. In contrast to the single-particle picture, the real spectrum of graphene is profoundly nonlinear so that the Fermi velocity describing the spectral slope reaches ~3x10^6 m/s at n <10^10 cm^-2, three times the value commonly used for graphene. The observed changes are attributed to electron-electron interaction that renormalizes the Dirac spectrum because of weak screening. Our experiments also put an upper limit of ~0.1 meV on the possible gap in graphene

Assessment of pain during rest and during activities in the postoperative period of cardiac surgery

OBJECTIVE: to assess the intensity and site of pain after Cardiac Surgery through sternotomy during rest and while performing five activities. METHOD: descriptive study with a prospective cohort design. A total of 48 individuals participated in the study. A Multidimensional Scale for Pain Assessment was used. RESULTS: postoperative pain from cardiac surgery was moderate during rest and decreased over time. Pain was also moderate during activities performed on the 1st and 2nd postoperative days and decreased from the 3rd postoperative day, with the exception of coughing, which diminished only on the 6th postoperative day. Coughing, turning over, deep breathing and rest are presented in decreased order of intensity. The region of the sternum was the most frequently reported site of pain. CONCLUSION: the assessment of pain in the individuals who underwent cardiac surgery during rest and during activities is extremely important to adapt management and avoid postoperative complications and delayed surgical recovery

Properties of Graphene: A Theoretical Perspective

In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties. Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.Comment: 189 pages. submitted in Advances in Physic