Session B12: Graphene: Electronic Structure and Interactions - Bilayer Graphene

Berry phase and pseudospin winding number in bilayer graphene

In 2006, two seminal studies on the novel quantum Hall effect of bilayer graphene [K. S. Novoselov et al., Nat. Phys. {\bf 2}, 177 (2006); E. McCann and V. I. Fal'ko, Phys. Rev. Lett. {\bf 96}, 086805 (2006)] appeared. Those papers claim that a non-trivial Berry phase of $2\pi$ in bilayer graphene is responsible for the novel quantum Hall effect described. Since then, it has become widely accepted by people working on the novel physics of graphene nanostructures that bilayer graphene has a non-trivial Berry phase of $2\pi$ (different from 0, as for conventional two-dimensional electron gas). In this talk, we show that (i) the relevant Berry phase for bilayer graphene is the same as that for a conventional two-dimensional electron gas and especially that (ii) what is actually obtained in the quantum Hall measurements is not the absolute value of the Berry phase of graphene multilayers but the pseudospin winding number. The results of our study ask for a re-interpretation of the numerous works related to the Berry phase in graphene multilayers.   

Electron-hole asymmetry and band mass renormalization in bilayer graphene: elucidating the role of electron-electron interactions with first-principles GW calculations

The electron-hole asymmetry and the band masses of bilayer graphene are fundamental quantities in various phenomena and in the applications of this material. \textit{A priori}, both of these quantities can depend on a number of microscopic mechanisms, including single-particle effects such as next-nearest neighbor hopping amplitude, as well as many-body effects such as the electron-electron interaction. We calculate the low energy electronic structure of bilayer graphene from first-principles, within the GW approximation. Our results indicate that both the electron-hole asymmetry and the band mass are strongly renormalized by electron-electron interactions. Our results are in good agreement with recent Shubnikov-de Haas experiments on bilayer graphene.   

Spontaneous broken time reversal symmetry and persistent current states in bilayer graphene

We report on the possibility of electron interaction driven spontaneously broken time reversal symmetry states in bilayer graphene through Fermi surface instability (aka Pomeranchuk instability) in both $\ell =0$ and $\ell =1$ channels. The conditions for spontaneous current carrying equilibrium states are most favorable in the regime of high interlayer potential difference and finite doping. These states are accompanied by valley polarization, which leads to a finite Hall conductivity that is approximately proportional to carrier density. Ref. cond-mat arXiv:1111.1765   

Time-reversal symmetry breaking states in bilayer graphene

The time-reversal symmetry breaking states in bilayer graphene which do not break translational symmetry can be classified by the spatial symmetry of the spontaneous current patterns. Among the four possible states, only one has anomalous Hall effect. In a simple model with near-neighbor interactions, we compare their energies in the mean-field approximation. We also compare which of the states is compatible with the observed gapped state in bilayer graphene.   

Spontaneous symmetry breaking in bilayer graphene

Recent experiments [1-4] provided compelling evidence for the correlated electron behavior in undoped bilayer graphene at both zero and finite magnetic field. The key question concerns the nature of the broken-symmetry phases realized experimentally. I will present the phase diagram for the zero-density state in the quantum Hall regime ($\nu=0$ state) obtained within the framerwork of quantum Hall ferromagnetism. Comparing these results with the experimental data of Refs. [1,4], I will argue that the $\nu=0$ insulating state realized in bilayer graphene is the canted antiferromagnetic phase. I will also show that the (canted) antiferromagnetic phase can persist at all magnetic fields down to zero and argue that this is the most likely scenario for the insulating state observed in Ref. [4]. \\[4pt] [1] R. T. Weitz {\em et al.}, Science 330, 812 (2010). \\[0pt] [2] F. Freitag {\em et al.}, arXiv:1104.3816 (2011). \\[0pt] [3] A. S. Mayorov, {\em et al.}, Science 333, 860 (2011). \\[0pt] [4] J. Velasco Jr. {\em et al.}, arXiv:1108.1609 (2011). \\[0pt] [5] M. Kharitonov, arXiv:1103.6285, arXiv:1105.5386, arxiv:1109.1553 (2011).   

Transport Spectroscopy of Symmetry-Broken Insulating States in Bilayer Graphene

The flat bands in bilayer graphene (BLG) are sensitive to electric fields $E $directed between the layers, and magnify the electron-electron interaction effects, thus making BLG an attractive platform for new two-dimensional (2D) electron physics. Theories 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 in bilayer graphene are analogous to the masses generated by broken symmetries in particle physics and give rise to large momentum-space Berry curvatures accompanied by spontaneous quantum Hall effects. Though recent experiments have provided convincing evidence of strong electronic correlations near the CNP in BLG, the presence of gaps is controversial. Here we present transport measurements in ultra-clean double-gated BLG, using source-drain bias as a spectroscopic tool to resolve a gap of $\sim $2 meV at the CNP. The gap can be closed by an electric field $E\sim $ 15 mV/nm but increases monotonically with a magnetic field $B$, with an apparent particle-hole asymmetry above the gap, thus providing a spectroscopic mapping of the ground states in BLG.   

Transport in Bilayer Graphene at the Charge Neutrality Point

Bilayer graphene (BLG) at the charge neutrality point is strongly susceptible to electronic interactions, and expected to undergo a phase transition into a state with spontaneous broken symmetries. We experimentally investigate transport properties of a large number ultra-clean BLG devices as functions of temperature, disorder, out-of-plane electric field, and charge density. We will discuss the results in terms of various theoretical models and possible phase transitions ~arising from the rich many body physics in this 2D system.   

Unconventional Landau levels in biased bilayer graphene

We utilize a generalized tight-binding model to study how the bias electric field impacts the magneto-electronic properties of graphene bilayer. With the availability of Landau wave function, the distribution among its sublattices enables the detailed observation of the Landau levels. The external electric field induces different electric potential on respective layers, which in turn lifts the inter-valley degeneracy. In addition, in a certain field range, Landau levels are coupled with each other and reveal the anomalous behavior: despite the serious hybridization of wave functions, these states in energy are still well-behaved Landau levels. These significant changes are directly reflected in the magneto-optical spectra, including the splitting of absorption peaks as well as the enhancement or quenching in response to field strength.   

Interaction-Enhanced Coherence in Graphene and Topological Insulator Bilayers

We analyze the interlayer coherence properties of graphene and topological insulator electron-hole bilayers by solving imaginary-axis Dirac-model gap equations in the random phase approximation. By accounting self-consistently for the dynamical screening of Coulomb interactions in the gapped phase, we find that the gap can rise to values of the order of the Fermi energy in the strong interactions regime. For graphene, we comment on the supportive role of remote bands not included in our two-band Dirac model.   

Analysis of fermions on a honeycomb bilayer lattice with finite-range interactions in the weak-coupling limit

We extend previous analyses of fermions on a honeycomb bilayer lattice via weak-coupling renormalization group (RG) methods with extremely short-range and extremely long-range interactions to the case of finite-range interactions. In particular, we consider different types of interactions including screened Coulomb interactions, much like those produced by a point charge placed either above a single infinite conducting plate or exactly halfway between two parallel infinite conducting plates. We map out the phases that the system enters as a function of the range of the interaction. For spin-$\frac{1}{2}$ fermions, we discover that the system enters an antiferromagnetic phase for short ranges of the interaction and a nematic phase at long ranges, in agreement with the previous work. Our results can help reconcile the recent results of two seemingly contradictory experiments. We also consider the effects of an applied magnetic field on the system in the antiferromagnetic phase via variational mean field theory, obtaining results in qualitative agreement with the experimental data. We find that the antiferromagnetic order parameter increases with field, at first quadratically at low fields, then as $B/\ln(B/B_0)$ at higher fields.   

Wave-packet dynamics in twisted bilayer graphene

It has been shown recently that high-quality epitaxial graphene (EPG) can be grown on the SiC substrate that exhibits interesting physical properties. In particular, the multilayer graphene films grown on the C-face show rotational disorder. It is expected that the twisted layers exhibit unique new physics that is distinct from that of either single layer graphene or graphite. In this work, the time-dependent wave-packet propagation in twisted bilayer graphene (TBG) is studied based on a tight-binding model with parameters derived from density functional theory. Our results demonstrate intriguing dynamical behavior of electrons in TBG, which is related to the specific interlayer coupling. By varying the twist angle and the initial wave packet, we can effectively control the propagation of electrons in TBG.   

Fermi-velocity reduction in twisted bilayer graphene: large-scale density-functional calculations

Twisted bilayer graphene (BLG) in which two graphene layers are rotated with a certain angle has been observed experimentally and its electronic structure has been studied using mainly tight-binding models [1]. We here report large-scale electronic-structure calculations with local-density approximation in the density-functional theory that clarify salient nature of the twisted BLG with the small rotation angles. The calculations have been done using the real-space density-functional theory (RSDFT) scheme which we have developed for the next-generation massively parallel computers. Implementation of the ultrasoft pseudopotential scheme in RSDFT allows us to treat thousands -of-carbon-atom systems in moderate-size computers. We have found that the Fermi velocity of the Dirac electron in the twisted BLG is substantially reduced compared with that in single layer graphene when the twist angle is small enough. This corroborates the observed reduction in the tight-binding models. We have also found that the wave functions at the Fermi level is strongly localized at AA-stacked region in the BLGs, opening a possibility of new magnetic functions.\\[4pt] [1] A. Luican et al., PRL 106, 126802 (2011); G. Trambly et al., Nano letters 10, 804 (2010); S. Shallcross et al., PRB 81, 165105 (2010).   

A Full electric-field tuning of thermoelectric power in a dual-gated Bi-layer graphene device

By using high quality microcrystals of hexagonal boron nitride as top gate dielectric, we fabricated dual-gated bilayer graphene devices. We demonstrate a full electric field tuning of thermoelectric power resulting from the opening of a band-gap by applying a perpendicular electric field on bilayer graphene. We uncover a large enhancement in thermoelectric power at low temperature. At 15 K, the thermoelectric power can be amplified by more than four-fold attaining a value of $\sim$ 50$\mu$V/K at a displacement field of 0.8 V/nm. Our result may open up a new possibility in thermoelectric application using graphene-based device.   

Phase diagram of the honeycomb bilayer from functional renormalization

The phase diagram for interacting electrons on the honeycomb bilayer with Bernal stacking is explored by means of the functional renormalization group. For half-filling and including a range of repulsive onsite, nearest-neighbor and next-to-nearest neighbor interactions we analyze the emergent instabilities and find antiferromagnetic, two types of charge-density-waves and quantum spin Hall order. The presented phase diagram covers the relevant region for the bilayer graphene parameters which overlaps with the phase boundary between the antiferromagnetic state and the quantum spin Hall state. We comment on the effect of small dopings.   

The Hubbard model on the bilayer honeycomb lattice with Bernal stacking

Using a combination of quantum Monte Carlo, the functional renormalization group and mean-field theory we study the Hubbard model on the bilayer honeycomb as a model for interacting electrons on bilayer graphene. The free bands consisting of two Fermi points with quadratic dispersions lead to a finite density of states, which triggers the antiferromagnetic instability and spontaneously breaks sublattice and spin rotational symmetry once a local Coulomb repulsion is introduced. We show that the antiferromagnetic instability is insensitive to the inclusion of extended Coulomb interactions and discuss effects on the sublattice magnetization and of finite size systems in numerical approaches.