Honeycomb Lattice Of Graphene Research Articles

Growth and properties of chemically modified graphene

AbstractChemically modified graphene was synthesized by chemical vapour deposition (CVD) with ammonia gas introduced during the CVD process. The use of two different metal catalyst films [nickel (Ni) or copper (Cu)] results in distinctly different forms of structural defects in the honeycomb lattice of graphene under identical synthesis conditions. The Ni catalyst film gave rise to numerous “flower‐like” defects, where carbon atoms formed core hexagons surrounded by pentagons alternated with heptagons, whilst graphene grown on a Cu catalyst film contained a much higher concentration of substituted nitrogen atoms. The samples were characterized by a variety of spectroscopic and microscopic methods complemented with electrical transport measurements.magnified image

Formulation of 2D Graphene Deformation Based on Chiral‐Tube Base Vectors

The intrinsic feature of graphene honeycomb lattice is defined by its chiral index (n, m), which can be taken into account when using molecular dynamics. However, how to introduce the index into the continuum model of graphene is still an open problem. The present manuscript adopts the continuum shell model with single director to describe the mechanical behaviors of graphene. In order to consider the intrinsic features of the graphene honeycomb lattice—chiral index (n, m), the chiral‐tube vectors of graphene in real space have been used for construction of reference unit base vectors of the shell model; therefore, the formulations will contain the chiral index automatically, or in an explicit form in physical components. The results are quite useful for future studies of graphene mechanics.

Skyrme and Wigner crystals in graphene

At low-energy, the band structure of graphene can be approximated by two degenerate valleys $(K,K^{\prime})$ about which the electronic spectra of the valence and conduction bands have linear dispersion relations. An electronic state in this band spectrum is a linear superposition of states from the $A$ and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing magnetic field, the band spectrum is split into Landau levels with level N=0 having zero weight on the $B(A)$ sublattice for the $% K(K^{\prime})$ valley. Treating the valley index as a pseudospin and assuming the real spins to be fully polarized, we compute the energy of Wigner and Skyrme crystals in the Hartree-Fock approximation. We show that Skyrme crystals have lower energy than Wigner crystals \textit{i.e.} crystals with no pseudospin texture in some range of filling factor $\nu $ around integer fillings. The collective mode spectrum of the valley-skyrmion crystal has three linearly-dispersing Goldstone modes in addition to the usual phonon mode while a Wigner crystal has only one extra Goldstone mode with a quadratic dispersion. We comment on how these modes should be affected by disorder and how, in principle, a microwave absorption experiment could distinguish between Wigner and Skyrme crystals.

Giant phonon-induced conductance in scanning tunnelling spectroscopy of gate-tunable graphene

Scanning tunnelling spectra of a graphene field-effect transistor reveal an unexpected tenfold increase in conductance as a result of phonon-mediated inelastic tunnelling. The honeycomb lattice of graphene is a unique two-dimensional system where the quantum mechanics of electrons is equivalent to that of relativistic Dirac fermions1,2. Novel nanometre-scale behaviour in this material, including electronic scattering3,4, spin-based phenomena5 and collective excitations6, is predicted to be sensitive to charge-carrier density. To probe local, carrier-density-dependent properties in graphene, we have carried out atomically resolved scanning tunnelling spectroscopy measurements on mechanically cleaved graphene flake devices equipped with tunable back-gate electrodes. We observe an unexpected gap-like feature in the graphene tunnelling spectrum that remains pinned to the Fermi level (EF) regardless of graphene electron density. This gap is found to arise from a suppression of electronic tunnelling to graphene states near EF and a simultaneous giant enhancement of electronic tunnelling at higher energies due to a phonon-mediated inelastic channel. Phonons thus act as a ‘floodgate’ that controls the flow of tunnelling electrons in graphene. This work reveals important new tunnelling processes in gate-tunable graphitic layers.

Ripples in epitaxial graphene on the Si-terminated SiC(0001) surface

The interaction with a substrate can modify the graphene honeycomb lattice and, thus, alter its outstanding properties. This could be particularly true for epitaxial graphene where the carbon layers are grown from the SiC substrate. Extensive ab initio calculations supported by the scanning tunneling microscopy experiments demonstrate here that the substrate indeed induces a strong nanostructuration of the interface carbon layer. It generates an apparent $6\ifmmode\times\else\texttimes\fi{}6$ modulation different from the interface $6\sqrt{3}\ifmmode\times\else\texttimes\fi{}6\sqrt{3}R30$ symmetry used for the calculation. The top carbon layer roughly follows the interface layer morphology. This creates soft $6\ifmmode\times\else\texttimes\fi{}6$ ripples in the otherwise graphene-like honeycomb lattice. The wavelength and height of the ripples are much smaller than the one found in exfoliated graphene. Their formation mechanism also differs; they are due to the weak interaction with the interface layer and not to the roughening of the plane due to the instability of a strictly two-dimensional crystal.

Superconducting States of Pure and Doped Graphene

We study the superconducting phases of the two-dimensional honeycomb lattice of graphene. We find two spin singlet pairing states; s wave and an exotic p+ip that is possible because of the special structure of the honeycomb lattice. At half filling, the p+ip phase is gapless and superconductivity is a hidden order. We discuss the possibility of a superconducting state in metal coated graphene.

Spontaneous Parity Breaking of Graphene in the Quantum Hall Regime

We propose that the inversion symmetry of the graphene honeycomb lattice is spontaneously broken via a magnetic-field-dependent Peierls distortion. This leads to valley splitting of the n=0 Landau level but not of the other Landau levels. Compared to Quantum Hall valley ferromagnetism recently discussed in the literature, lattice distortion provides an alternative explanation to all of the currently observed Quantum Hall plateaus in graphene.

Charge density wave in graphene: Magnetic-field-induced Peierls instability

We suggest that a magnetic-field-induced Peierls instability accounts for the recent experiment of Zhang et al. in which unexpected quantum Hall plateaus were observed at high magnetic fields in graphene on a substrate. This Peierls instability leads to an out-of-plane lattice distortion resulting in a charge density wave (CDW) on sublattices A and B of the graphene honeycomb lattice. We also discuss alternative microscopic scenarios proposed in the literature and leading to a similar CDW ground state in graphene.