Session N6: Focus Session: Graphene - Electronic Properties, Gap Formation

Interaction-induced gapped state in charge neutral bilayer graphene

Bilayer graphene (BLG) at the charge neutrality point (CNP) possess instability to electronic interactions, and is expected to host a ground state with spontaneously broken symmetries. Within this regime, I will discuss our transport spectroscopy measurements using high quality suspended BLG samples. We observe an insulating state at CNP with a gap $\sim$ 2 meV, which can be closed by finite doping or a perpendicular electric field of either polarity. For magnetic field B \textgreater\ 1T, the gap increases linearly with B. Our work contributes towards understanding the rich interaction-driven physics in BLG. Finally, latest progress on transport spectroscopy measurements of Landau level gaps in these high quality samples will also be discussed.   

Electron-electron interactions in non-equilibrium bilayer graphene

The charge conductivity of doped bilayer graphene can be understood as a net steady-state pseudospin polarization. Due to the chirality inherent in the Hamiltonian, electron-electron interactions renormalize this polarization even at zero temperature, when the phase space for electron-electron scattering vanishes. Nevertheless, at usual transport densities the electron-electron interaction contribution displays only a weak density dependence and has a negligible effect on the conductivity. This smallness is due to the large value of the interlayer tunneling parameter. Interestingly, the effect of interactions in transport vanishes as the carrier number density tends to zero, in contrast to single-layer graphene and topological insulators. The vanishing is attributed to the fact that the pseudospin winds twice around the Fermi surface. Our study relies on the quantum Liouville equation in the first Born approximation with respect to the scattering potential, with electron-electron interactions taken into account self-consistently in the Hartree-Fock approximation, and screening in the random phase approximation.   

Ab initio quasiparticle bandstructure of ABA and ABC-stacked graphene trilayers

We obtain the quasiparticle band structure of ABA and ABC-stacked graphene trilayers through ab initio density functional theory (DFT) and many-body quasiparticle calculations within the GW approximation. To interpret our results, we fit the DFT and GW $\pi$ bands to a low energy tight-binding model, which is found to reproduce very well the observed features near the K point. The values of the extracted hopping parameters are reported and compared with available theoretical and experimental data. For both stackings, the quasiparticle corrections lead to a renormalization of the Fermi velocity, an effect also observed in previous calculations on monolayer graphene. They also increase the separation between the higher energy bands, which is proportional to the nearest neighbor interlayer hopping parameter $\gamma_1$. Both features are brought to closer agreement with experiment through the quasiparticle corrections. Finally, other effects, such as trigonal warping, electron-hole assymetry and energy gaps are discussed in terms of the associated parameters. This work was supported by the Brazilian funding agencies: CAPES, CNPq, FAPERJ and INCT-Nanomateriais de Carbono. It was also supported by NSF grant No. DMR10-1006184 and U.S. DOE under Contract No. DE-AC02-05CH11231.   

Magneto-Coulomb Drag in Double Layer Graphene

We report on our theoretical investigations on the Coulomb drag in double-layer graphene in strong magnetic fields. Using diagrammatic perturbation theory, we obtain explicit analytical expressions for the nonlinear susceptibility and the drag conductivity. At low temperatures $T$, the drag conductivity behaves as $\mathrm{exp}(-\Delta/T)/T$, where $\Delta$ is the inter-Landau level transition energy nearest to the Fermi level. For full filling at the zeroth Landau level, we find a non-vanishing drag that arises from the intrinsic contribution of filled Landau levels below the Dirac point.   

Structural, electronic, and mechanical properties of superlattices of interlayer-bonded domains in twisted bilayer graphene

We present a comprehensive computational analysis of the atomic and electronic structure and mechanical properties of a novel class of carbon nanostructures, formed due to interlayer covalent $sp^{3}$ C-C bonding in twisted bilayer graphene as a result of controlled chemical functionalization (hydrogenation or fluorination). Depending on the twist angle and local stacking of layers, these nanostructures are superlattices of diamond-like nanocrystals or caged fullerene-like configurations embedded within the bilayer. According to density functional theory calculations, the electronic behavior of these $sp^{2}/sp^{3}$ hybrid configurations ranges from semi-metallic, characterized by linear dispersion around the K point in the first Brillouin zone, to semi-conducting/insulating with electronic band gaps ranging from a few meV to $\sim$4 eV; this electronic character depends on the symmetry and periodicity of the superlattices and on the type of chemisorbed species. We have also studied the mechanical response of these superlattices to tensile and shear strain based on molecular dynamics simulations; their interlayer shear modulus increases strongly and their Young's modulus and tensile strength and strain decrease moderately compared to those of pristine bilayer graphene.   

Ising Phase in AA Stacked Bilayer Graphene

AA stacked bilayer graphene bears a close resemblance to biased, double layer graphene (in which a strong barrier separates the two layers), with layer bonding and anti-bonding states of the AA system playing the roles of layer states in the double layer system. The latter has a U(1) symmetry which can break, to form a condensed exciton groundstate. The AA system however has only Ising symmetry. In this presentation we analyze the possibility that electron-electron interactions break this to open a gap in the energy spectrum. We find that, in the mean field approximation, the ground state has a charge density wave character, with the charge modulation of each layer out of phase. We calculate the gap and the mean field critical temperature as a function of the strength of the Coulomb interaction, taking screening into account self-consistently with the calculation of the gap. We also analyze the transition between ordered and thermally disordered phases based on a continuum model, and find that the transition is controlled by an effective U(1) stiffness. We argue that in the limit of zero layer separation, for which the full U(1) symmetry of the Hamiltonian is restored, the Ising transition continuously goes into a Kosterlitz-Thouless transition.   

Electronic Properties of Curved Graphene-Ring Structures

We have undertaken a theoretical investigation of electronic properties of a curved graphene ring in the Dirac approximation making use of elasticity theory. This study is motivated by experimental reports that indicate the existence of gauge-fields in graphene when it is under tension and also by the recent possibility of controlling deformations in its surface in a variety of shapes on different substrates [1]. We discuss how an Aharonov-Bohm field can be used to design new responses obtained by adding real magnetic fluxes and pseudomagnetic fields. We show that the persistent current tends to be inhomogeneous in the same way that the Fermi velocity has a spatial-dependent character[2]. We also discuss the role of strain in the position of the Dirac points that have been the source of recent controversies. [1] T. Georgiou et al., Appl. Phys. Lett. 99, 093103 (2011). [2] F. de Juan et al., PRL 108, 227205 (2012). [3] A. Kitt et al., Phys. Rev. B 85, 115432 (2012)   

Morphology and electronic transport study of suspended graphene

This presentation will first describe our recent electrical transport studies of suspended bilayer and trilayer graphene devices at low temperature: Bilayer graphene at the charge neutrality point is unstable to electronic interactions, and expected to host a ground state with spontaneously broken symmetries, whereas in trilayer graphene stacking order provides another important degree of freedom for tuning its electronic properties. For instance, at the Dirac point, Bernal-stacked TLG remains metallic but r-TLG becomes insulating with an intrinsic interaction-driven gap around 6 meV. Our results underscore the rich interaction-induced phenomena in both bilayer and trilayer graphene with different stacking orders, and its potential towards electronic applications. Next we will discuss the manipulation of the morphology of suspended graphene via electrostatic and thermal control: We observe significant deflections of single-, bi-, and trilayer graphene sheets in response to electrostatic force. At low temperature, wide graphene sheets ripple and butterfly features form at its two free edges. These observations have important applications for understanding electrical, mechanical, and thermal properties as well as strain engineering in suspended graphene devices.   

Field-induced Energy Gaps in Bilayer Graphene under Shear

Using the first-principles calculations method, we study the effects of shear on field-induced insulating states of bilayer graphene (BLG). It is shown that the low energy bands near the charge neutral point of BLG change significantly upon application of shear. We also find that the energy gap of BLG under transverse electric field sensitively depend on both direction and amount of shear. Generally, the field-induced energy gap decreases as the sliding increases under shear. For BLG with the specific direction of shear, the shear can quench the energy gap to zero completely even in the presence of electric field thus realizing insulator-to-metal transition just by sliding. We discuss origins of these interesting phenomena and suggest some experimental methods to detect the transition.   

Kekule-induced band-gap opening in graphene in contact with ZrO2

We have studied pressure-dependent atomic and electronic structure of graphene in contact with (111) surface of zirconium dioxide (ZrO2) using first-principles calculations. The atomic structures are optimized by relaxation, and we found that the lowest-energy configuration shows a band gap at the Dirac point at ambient pressure and the band gap increases as pressure increases. Our analysis shows that the band-gap opening is due to overlap of wavefunctions, change in potential energy, and in-plane distortion of graphene lattice. This in-plane distortion of graphene is found to be the Kekule distortion, which generates intervalley coupling. As pressure increases, the Kekule distortion in graphene increases and the band gap at the Dirac point is proportional to the size of the distortion. This work was supported by the NRF of Korea (Grant No. 2011-0018306) and KISTI Supercomputing Center (Project No. KSC-2012-C2-14).   

Quantum phase transitions to Kondo states in bilayer graphene

We study a magnetic impurity intercalated in Bernal-stacked bilayer graphene described by a multiband Anderson Hamiltonian. Through a properly generalized Schrieffer-Wolff transformation, it reduces to a single-channel Kondo model with a strongly energy-dependent exchange coupling. The form of this effective Kondo Hamiltonian suggests the possibility of driving the system through quantum phase transitions via tuning of the chemical potential through doping or electrical means. The microscopic coupling of the impurity to the graphene layers determines symmetries and details of the various phases. We use the numerical renormalization group to accurately access the many-body physics of this system. Our calculations reveal zero-temperature transitions under variation of the band filling and/or the energy of the impurity level between a local-moment phase and a pair of singlet strong-coupling phases. The latter have conventional Kondo, pseudogap Kondo, and local-singlet regimes that can be distinguished through their thermodynamic and spectral properties, as well as their different rates of variation of the Kondo temperature with the chemical potential.