Long-range Coulomb interaction in bilayer graphene

The asymmetric Wigner bilayer

We present a comprehensive discussion of the so-called asymmetric Wigner bilayer system, where mobile point charges, all of the same sign, are immersed into the space left between two parallel, homogeneously charged plates (with possibly different charge densities). At vanishing temperatures, the particles are expelled from the slab interior; they necessarily stick to one of the two plates and form there ordered sublattices. Using complementary tools (analytic and numerical), we study systematically the self-assembly of the point charges into ordered ground state configurations as the inter-layer separation and the asymmetry in the charge densities are varied. The overwhelming plethora of emerging Wigner bilayer ground states can be understood in terms of the competition of two strategies of the system: net charge neutrality on each of the plates on the one hand and particles' self-organization into commensurate sublattices on the other hand. The emerging structures range from simple, highly commensurate (and thus very stable) lattices (such as staggered structures, built up by simple motives) to structures with a complicated internal structure. The combined application of our two approaches (whose results agree within remarkable accuracy) allows us to study on a quantitative level phenomena such as over- and underpopulation of the plates by the mobile particles, the nature of phase transitions between the emerging phases (which pertain to two different universality classes), and the physical laws that govern the long-range behaviour of the forces acting between the plates. Extensive, complementary Monte Carlo simulations in the canonical ensemble, which have been carried out at small, but finite temperatures along selected, well-defined pathways in parameter space confirm the analytical and numerical predictions within high accuracy. The simple setup of the Wigner bilayer system offers an attractive possibility to study and to control complex scenarios and strategies of colloidal self-assembly, via the variation of two system parameters.

Unveiling the Superconducting Mechanism of Ba_{0.51}K_{0.49}BiO_{3}

The mechanism of high superconducting transition temperatures (T_{c}) in bismuthates remains under debate despite more than 30 years of extensive research. Our angle-resolved photoemission spectroscopy studies on Ba_{0.51}K_{0.49}BiO_{3} reveal an unexpectedly 34% larger bandwidth than in conventional density functional theory calculations. This can be reproduced by calculations that fully account for long-range Coulomb interactions-the first direct demonstration of bandwidth expansion due to the Fock exchange term, a long-accepted and yet uncorroborated fundamental effect in many body physics.Furthermore, we observe an isotropic superconducting gap with 2Δ_{0}/k_{B}T_{c}=3.51±0.05, and strong electron-phonon interactions with a coupling constant λ∼1.3±0.2. These findings solve a long-standing mystery-Ba_{0.51}K_{0.49}BiO_{3} is an extraordinary Bardeen-Cooper-Schrieffer superconductor, where long-range Coulomb interactions expand the bandwidth, enhance electron-phonon coupling, and generate the high T_{c}. Such effects will also be critical for finding new superconductors.

Rich Polymorphic Behavior of Wigner Bilayers

Self-assembly into target structures is an efficient material design strategy. Combining analytical calculations and computational techniques of evolutionary and Monte Carlo types, we report about a remarkable structural variability of Wigner bilayer ground states, when charges are confined between parallel charged plates. Changing the interlayer separation, or the plate charge asymmetry, a cascade of ordered patterns emerges. At variance with the symmetric case phenomenology, the competition between commensurability features and charge neutralization leads to long range attraction, appearance of macroscopic charges, exotic phases, and nonconventional phase transitions with distinct critical indices, offering the possibility of a subtle, but precise and convenient control over patterns.

Excitation gap of fractal quantum hall states in graphene

In the presence of a magnetic field and an external periodic potential the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter's butterfly. In this work, we develop a Hartree-Fock theory to deal with the electron-electron interaction in the Hofstadter's butterfly state in a finite-size graphene with periodic boundary conditions, where we include both spin and valley degrees of freedom. We then treat the butterfly state as an electron crystal so that we could obtain the order parameters of the crystal in the momentum space and also in an infinite sample. A phase transition between the liquid phase and the fractal crystal phase can be observed. The excitation gaps obtained in the infinite sample is comparable to those in the finite-size study, and agree with a recent experimental observation.

Alternating current-driven graphene superlattices: Kinks, dissipative solitons, dynamic chaotization

The possibility of the solitary electromagnetic wave formation in graphene superlattice subjected to the electromagnetic radiation is discussed. The chaotic behavior of the electron subsystem in graphene superlattice is studied by Melnikov method. Dynamic chaos of electrons is shown to appear for certain intervals of frequencies of incident electromagnetic radiation. The frequency dependence of the radiation critical amplitude which determines the bound of chaos appearance is investigated. The values of radiation frequency at which the critical amplitude increases indefinitely were found.

Fractional quantum Hall effect in Hofstadter butterflies of Dirac fermions

We report on the influence of a periodic potential on the fractional quantum Hall effect (FQHE) states in monolayer graphene. We have shown that for two values of the magnetic flux per unit cell (one-half and one-third flux quantum) an increase of the periodic potential strength results in a closure of the FQHE gap and appearance of gaps due to the periodic potential. In the case of one-half flux quantum this causes a change of the ground state and consequently the change of the momentum of the system in the ground state. While there is also crossing between low-lying energy levels for one-third flux quantum, the ground state does not change with the increase of the periodic potential strength and is always characterized by the same momentum. Finally, it is shown that for one-half flux quantum the emergent gaps are due entirely to the electron-electron interaction, whereas for the one-third flux quantum per unit cell these are due to both non-interacting electrons (Hofstadter butterfly pattern) and the electron-electron interaction.

Effects of Landau level mixing on the fractional quantum Hall effect in monolayer graphene

We report results of exact diagonalization studies of the spin- and valley-polarized fractional quantum Hall effect in the N = 0 and N = 1 Landau levels in graphene. We use an effective model that incorporates Landau level mixing to lowest order in the parameter κ = ((e(2)/εℓ)/(ħv(F)/ℓ)) = (e(2)/εv(F)ħ), which is magnetic field independent and can only be varied through the choice of substrate. We find Landau level mixing effects are negligible in the N = 0 Landau level for κ ≲ 2. In fact, the lowest Landau level projected Coulomb Hamiltonian is a better approximation to the real Hamiltonian for graphene than it is for semiconductor based quantum wells. Consequently, the principal fractional quantum Hall states are expected in the N = 0 Landau level over this range of κ. In the N = 1 Landau level, fractional quantum Hall states are expected for a smaller range of κ and Landau level mixing strongly breaks particle-hole symmetry, producing qualitatively different results compared to the N = 0 Landau level. At half filling of the N = 1 Landau level, we predict the anti-Pfaffian state will occur for κ ∼ 0.25-0.75.

Layer anti-ferromagnetism on bilayer honeycomb lattice

Bilayer honeycomb lattice, with inter-layer tunneling energy, has a parabolic dispersion relation, and the inter-layer hopping can cause the charge imbalance between two sublattices. Here, we investigate the metal-insulator and magnetic phase transitions on the strongly correlated bilayer honeycomb lattice by cellular dynamical mean-field theory combined with continuous time quantum Monte Carlo method. The procedures of magnetic spontaneous symmetry breaking on dimer and non-dimer sites are different, causing a novel phase transition between normal anti-ferromagnet and layer anti-ferromagnet. The whole phase diagrams about the magnetism, temperature, interaction and inter-layer hopping are obtained. Finally, we propose an experimental protocol to observe these phenomena in future optical lattice experiments.

Gap structure of the Hofstadter system of interacting Dirac fermions in graphene

The effects of mutual Coulomb interactions between Dirac fermions in monolayer graphene on the Hofstadter energy spectrum are investigated. For two flux quanta per unit cell of the periodic potential, interactions open a gap in each Landau level with the smallest gap in the n=1 Landau level. For more flux quanta through the unit cell, where the noninteracting energy spectra have many gaps in each Landau level, interactions enhance the low-energy gaps and strongly suppress the high-energy gaps and almost close a high-energy gap for n=1. The signature of the interaction effects in the Hofstadter system can be probed through magnetization, which is governed by the mixing of the Landau levels and is enhanced by the Coulomb interaction.

Renormalization group aspects of graphene

Graphene is a two-dimensional crystal of carbon atoms with fascinating electronic and morphological properties. The low-energy excitations of the neutral, clean system are described by a massless Dirac Hamiltonian in (2+1) dimensions, which also captures the main electronic and transport properties. A renormalization group analysis sheds light on the success of the free model: owing to the special form of the Fermi surface that reduces to two single points in momentum space, short-range interactions are irrelevant and only gauge interactions such as long-range Coulomb or effective disorder can play a role in the low-energy physics. We review these features and briefly discuss other aspects related to disorder and to the bilayer material along the same lines.

Bandgap opening in oxygen plasma-treated graphene

We report a change in the semimetallic nature of single-layer graphene after exposure to oxygen plasma. The resulting transition from semimetallic to semiconducting behavior appears to depend on the duration of the exposure to the plasma treatment. The observation is confirmed by electrical, photoluminescence and Raman spectroscopy measurements. We explain the opening of a bandgap in graphene in terms of functionalization of its pristine lattice with oxygen atoms. Ab initio calculations show more details about the interaction between carbon and oxygen atoms and the consequences on the optoelectronic properties, that is, on the extent of the bandgap opening upon increased functionalisation density.

Controllable driven phase transitions in fractional quantum Hall states in bilayer graphene

Here we report from our theoretical studies that, in biased bilayer graphene, one can induce phase transitions from an incompressible fractional quantum Hall state to a compressible state by tuning the band gap at a given electron density. The nature of such phase transitions is different for weak and strong interlayer coupling. Although for strong coupling more levels interact there is a lesser number of transitions than for the weak coupling case. The intriguing scenario of tunable phase transitions in the fractional quantum Hall states is unique to bilayer graphene and has never before existed in conventional semiconductor systems.

Dynamical screening and excitonic instability in bilayer graphene

Electron interactions in undoped bilayer graphene lead to an instability of the gapless state, "which-layer" symmetry breaking, and energy gap opening at the Dirac point. In contrast with single-layer graphene, the bilayer system exhibits instability even for an arbitrarily weak interaction. A controlled theory of this instability for realistic dynamically screened Coulomb interactions is developed, with full account of the dynamically generated ultraviolet cutoff. This leads to an energy gap that scales as a power law of the interaction strength, making the excitonic instability readily observable.