Undoped Bilayer Graphene Research Articles

Half-metal and other fractional metal phases in doped AB bilayer graphene

We argue theoretically that, in doped $AB$ bilayer graphene, electron-electron coupling can give rise to the spontaneous formation of fractional metal phases. These states, being generalizations of a more common half-metal, have a Fermi surface that is perfectly polarized not only in terms of a spin-related quantum number, but also in terms of the valley index. The proposed mechanism assumes that the ground state of undoped bilayer graphene is a spin-density-wave insulator, with a finite gap in the single-electron spectrum. Upon doping, the insulator is destroyed and replaced by a fractional metal phase. As doping increases, transitions between various types of fractional metal (half-metal, quarter-metal, etc.) are triggered. Our findings are consistent with recent experiments on doped $AB$ bilayer graphene, in which a cascade of phase transitions between different isospin states was observed.

Optical properties of biased bilayer graphene due to gap parameter effects

We address the optical conductivity of undoped bilayer graphene in the presence of a finite bias voltage at finite temperature. The effects of gap parameter and stacking type on optical conductivity are discussed in the context of tight binding model Hamiltonian. Green’s function approach has been implemented to find the behavior of optical conductivity of bilayer graphene within linear response theory. We have found the frequency dependence of optical conductivity for different values of gap parameter and bias voltage. Also the dependence of optical conductivity on the temperature has been investigated in details. A peak appears in the plot of optical conductivity versus frequency for different values of temperatures and bias voltage. Furthermore we find the frequency position of broad peak in optical conductivity goes to higher values with increase of gap parameter for both bernal and simple stacked bilayer graphenes.

Electrical conductivity of undoped bilayer Graphene: Beyond nearest neighbor approximation

We have addressed density of states and electrical conductivity of undoped biased bilayer graphene for both AA and AB stacking in the context of tight binding model hamiltonian. The effects of next nearest neighbor hopping amplitude for electrons and gap parameter on electronic density of states and electrical conductivity have been investigated. Green’s function approach has been implemented to find the behavior of electrical conductivity of bilayer graphene within linear response theory. We have found the temperature dependence of electrical conductivity for different values of gap parameter and bias voltage in the presence of neat nearest neighbor hopping integral. Our results for density of states of bilayer graphene in the presence of gap parameter show the increase of bias voltage reduces the band gap width. Also a peak in the dependence of thermal conductivity on temperature has been observed for all physical parameters. An anisotropic behavior for electrical conductivity of unbiased simple bilayer graphene in the presence of gap parameter has been resulted.

Simple synthesis of highly uniform bilayer-carbon nanocages

A simple, highly scalable method of obtaining densely-packed, three-dimensional structures of interconnected, bilayer, hollow carbon nanocages, is reported. High-quality nanocages with well controlled wall thickness are synthesized via catalytic templating on densely-packed, mono-sized nickel nanoparticles, nucleating in situ during short, mid-temperature annealing of an inexpensive precursor obtained from nickel acetate and citric acid. Following nickel dissolution, large monolithic grains of densely packed networks of carbon nanocages are obtained and extensively characterized. In situ TEM experiments are conducted to elucidate the mechanism of nanostructure formation, and a geometrical model is proposed to explain the high specific surface area and its relation to the nanocages' diameter and wall thickness. These nanocages, with their bilayer structure, unimodal pore size distribution and pore size of ∼2.5 nm, approach the theoretical capacity of undoped bilayer graphene when tested in an electrochemical double-layer capacitor system. Our synthesis approach provides a facile method for tuning nanocages' morphology and efficiently doping them, creating an effective enhancement of capacity and properties suitable for a broad range of new energy and environmental applications.

Space charge and screening in bilayer graphene

Undoped bilayer graphene is a two-dimensional semimetal with a low-energy excitation spectrum that is parabolic in the momentum. As a result, the screening of an arbitrary external charge Ze is accompanied by a reconstruction of the ground state: valence band electrons (for Z > 0) are promoted to form a space charge around the charge while the holes leave the physical picture. The outcome is a flat neutral object resembling the regular atom except that for it is described by a strictly linear Thomas–Fermi theory. This theory also predicts that the bilayer’s static dielectric constant is the same as that of a two-dimensional electron gas in the long-wavelength limit.

RKKY interaction in bilayer graphene

We study the RKKY interaction between two magnetic impurities located on the same layer (intralayer case) or on different layers (interlayer case) in undoped bilayer graphene (BLG) in the four-bands model, by directly calculating the Green functions in the eigenvalues and eigenvectors representation. Our results show that both intra- and interlayer RKKY interactions between two magnetic impurities located on the same (opposite) sublattice are always ferromagnetic (antiferromagnetic). Furthermore we find unusual long-distance decay of the RKKY interaction in BLG. The intralyer RKKY interactions between two magnetic impurities located on the same sublattice, JAnAn(R) and JBnBn(R), decay closely as 1/R6 and 1/R2 at large impurity distances respectively, but when they are located on opposite sublattices the RKKY interactions exhibit 1/R4 decays approximately. In the interlayer case, the RKKY interactions between two magnetic impurities located on the same sublattice show a decay close to 1/R4 at large impurity distances, but if two magnetic impurities be on opposite sublattices the RKKY interactions, JA1B2(R) and JB1A2(R), decay closely as 1/R6 and 1/R2 respectively. Both intra- and interlayer RKKY interactions have anisotropic oscillatory factors which for intralayer case is equal to that for single layer graphene (SLG). Our results at weak and strong interlayer coupling limits reduce to the RKKY interaction of SLG and that of BLG in the two-bands approximation respectively.

Edge states of bilayer graphene in the quantum Hall regime

We study the low-energy edge states of bilayer graphene in a strong perpendicular magnetic field. Several possible simple boundary geometries related to zigzag edges are considered. Tight-binding calculations reveal three types of edge-state behaviors: weakly, strongly, and nondispersive edge states. These three behaviors may all be understood within a continuum model, and related by nonlinear transformations to the spectra of quantum Hall edge states in a conventional two-dimensional electron system. In all cases, the edge states closest to zero energy include a holelike edge state of one valley and a particlelike state of the other on the same edge, which may or may not cross, depending on the boundary condition. Edge states with the same spin generically have anticrossings that complicate the spectra, but which may be understood within degenerate perturbation theory. The results demonstrate that the number of edge states crossing the Fermi level in clean, undoped bilayer graphene depends both on boundary conditions and the energies of the bulk states.

Publisher’s Note: Intra-Landau-level magnetoexcitons and the transition between quantum Hall states in undoped bilayer graphene [Phys. Rev. B83, 115455 (2011)

Publisher’s Note: Intra-Landau-level magnetoexcitons and the transition between quantum Hall states in undoped bilayer graphene [Phys. Rev. B<b>83</b>, 115455 (2011)

Intra-Landau-level magnetoexcitons and the transition between quantum Hall states in undoped bilayer graphene

We study the collective modes of the quantum Hall states in undoped bilayer graphene in a strong perpendicular magnetic and electric field. Both for the well-known ferromagnetic state that is relevant for small electric field $E_\perp$ and the analogous valley/layer polarized one suitable for large $E_\perp$, the low energy physics is dominated by magnetoexcitons with zero angular momentum that are even combinations of excitons that conserve Landau orbitals. We identify a long wave length instability in both states, and argue that there is an intermediate range of the electric field $E^{(1)}_\text{c} < E_\perp < E^{(2)}_\text{c}$ where a gapless phase interpolates between the incompressible quantum Hall states. The experimental relevance of this crossover via a gapless state is discussed.

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.

Non-Fermi-liquid behavior in neutral bilayer graphene

We calculate the density-density response function and electron self-energy for undoped bilayer graphene within the random phase approximation. We show that the quasiparticle decay rate scales linearly with the quasiparticle energy, and quasiparticle weight vanishes logarithmically in the low-energy limit, indicating non-Fermi-liquid behavior. This is a consequence of the absence of a Fermi surface for neutral bilayer graphene and corresponding larger phase space available for scattering processes. Experimental consequences of our results as well as their differences from those of single-layer graphene are discussed.

Anisotropic minimal conductivity of graphene bilayers

The Fermi line of bilayer graphene at zero energy is transformed into four separated points positioned trigonally at the corner of the hexagonal first Brillouin zone. We show that as a result of this trigonal splitting the minimal conductivity of an undoped bilayer graphene strip becomes anisotropic with respect to the orientation $\ensuremath{\theta}$ of the connected electrodes and finds a dependence on its length $L$ on the characteristic scale $\ensuremath{\ell}=\ensuremath{\pi}/\ensuremath{\Delta}k\ensuremath{\simeq}50\text{ }\text{nm}$ determined by the inverse of $k$-space distance of two Dirac points. The minimum conductivity increases from a universal isotropic value ${\ensuremath{\sigma}}_{\ensuremath{\perp}}^{\text{min}}=(8/\ensuremath{\pi}){e}^{2}/h$ for a short strip $L⪡\ensuremath{\ell}$ to a higher anisotropic value for longer strips, which in the limit of $L⪢\ensuremath{\ell}$ varies from $(7/3){\ensuremath{\sigma}}_{\ensuremath{\perp}}^{\text{min}}$ at $\ensuremath{\theta}=0$ to $3{\ensuremath{\sigma}}_{\ensuremath{\perp}}^{\text{min}}$ over an angle range $\ensuremath{\Delta}\ensuremath{\theta}\ensuremath{\sim}\ensuremath{\ell}/L$.