We theoretically investigate Fano factors arising in local spectroscopy of impurity resonances in graphene. It is demonstrated that Fano line shapes can strongly differ from the antiresonances usually found on metal surfaces. Graphene's highly symmetric Fermi points make this effect particularly sensitive to the detailed atomistic structure and orbital symmetries of the impurity. After a model discussion based on an Anderson impurity coupled to an electron bath with linearly vanishing density of states, we present first-principles calculations of Co adatoms on graphene. For Co above the center of a graphene hexagon, we find that the two-dimensional E 1 representation made of d xz , d yz orbitals is likely responsible for the hybridization and ultimately Kondo screening for cobalt on graphene. Anomalously large Fano q factors depending strongly on the orbitals involved are obtained. For a resonant s-wave impurity, a similarly strong adsorption site dependence of the q factor is demonstrated. These anomalies are striking examples of quantum-mechanical interference related to the Berry phase inherent to the graphene band structure.

Graphene, a single sheet of graphite, has attracted tremendous attention due to recent experiments which demonstrate that carriers in it are described by massless fermions with linear dispersion. In this note, we consider the possibility of Wigner crystallization in graphene in the absence of external magnetic field. We show that the ratio of potential and kinetic energy is independent of the carrier density, the tuning parameter that usually drives Wigner crystallization and find that for given material parameters (dielectric constant and Fermi velocity), Wigner crystallization is not possible. We comment on the how these results change in the presence of a strong external magnetic field. PACS numbers:Graphene is a single sheet of carbon atoms which can be extracted from graphite by micro-mechanical cleavage [1]. Various theoretical and experimental studies of this 2-dimensional system have shown that its properties [2,3,4,5,6,7] are markedly different from those of the conventional 2-dimensional electron gas (2DEG) formed in semiconductor heterostructures. The carriers in such a 2DEG are well described by Fermi liquid theory, and have quadratic dispersion at small momenta, E k =h 2 k 2 /2m * , where m * is the band mass [8]. Carriers in graphene, on the other hand, have a band structure in which electron and hole bands touch at two points in the Broullion zone. This, combined with the hexagonal lattice structure of graphene, lead to linear dispersion at small momenta, E k =hv G k. Therefore the carriers behave as "massless" Dirac particles [5,6,9,10,11] with characteristic velocity v G ∼ 10 6 m/s. This difference in the character of quasiparticles -massive quadratically dispersing vs. massless linearly dispersing -gives rise to a host of remarkable phenomena including unusual quantum Hall effects and π Berry phase [2,3,4,5].Another interesting aspect of graphene is that it is a better realization of two dimensional system. The conventional 2DEG is formed in semiconductor quantum wells where the width of the quantum well is usually around 100 -300Å. Various properties of such a 2DEG have been extensively studied using primarily transport measurements. However, it has not been amenable to local probes such as a scanning tunneling microscope (STM), because the 2DEG is buried about 1000Å from the sample surface. In graphene, on the other hand, the width of the effective quantum well is approximately 5 − 10Å (distance between two graphene sheets in graphite), and the 2DEG is amenable to local probes including those which will allow the study of inhomogeneous states. In addition, the density and the polarity of carriers in graphene can be adjusted simply by changing the gate voltage; something that is not possible in conventional semiconductor heterojunctions.Here, we investigate the possibility of Wigner crystallization in graphene. Following the pioneering work of E. Wigner [12], a Wigner crystal has become one of the extensively studied phases of conventional 2DEG at low densities. This state appears when electron...

The nature of the hidden order (HO) in U Ru2Si2 below THO = 17.5K has been a puzzle for a long time. Neutron scattering studies of this material reveal a rich spin dynamics. We focus on inelastic neutron scattering in U Ru2Si2 and argue that observed gap in the fermion spectrum naturally leads to the spin feature observed at energies ωres = 4 − 6meV at momenta at Q * = (1 ± 0.4, 0, 0). We discuss how spin features seen in U Ru2Si2 can indeed be thought of in terms of spin resonance that develops in HO state and is not related to superconducting transition at 1.5K. In our analysis we assume that the HO gap is due to a particle-hole condensate that connects nested parts of the Fermi surface with nesting vector Q * . Within this approach we can predicted the behavior of the spin susceptibility at Q * and find it to be is strikingly similar to the phenomenology of resonance peaks in high-Tc and heavy fermion superconductors. The energy of the resonance peak scales with THO ωres ≃ 4kBTHO. We discuss observable consequences spin resonance will have on neutron scattering and local density of states. Moreover, we argue how establishment of spin resonance in U Ru2Si2 and better characterization of susceptibility, temperature, pressure and Rh doping dependence would elucidate the nature of the HO.

We revisit the question of nature of odd-frequency superconductors, first proposed by Berezinskii in 1974. 1 We start with the notion that order parameter of odd-frequency superconductors can be thought of as a time derivative of the odd-time pairing operator. It leads to the notion of the composite boson condensate. 2 To elucidate the nature of broken symmetry state in odd-frequency superconductors, we consider a wave function that properly captures the coherent condensate of composite charge 2e bosons in an odd-frequency superconductor. We consider the Hamiltonian which describes the equal-time composite boson condensation as proposed earlier in Phys. Rev. B 52, 1271Rev. B 52, (1995. We propose a BCS-like wave function that describes a composite condensate comprised of a spin-0 Cooper pair and a spin-1 magnon excitation. We derive the quasiparticle dispersion, the self-consistent equation for the order parameter and the density of states. We show that the coherent wave function approach recovers all the known proposerties of odd-frequency superconductors: the quasi-particle excitations are gapless and the superconducting transition requires a critical coupling.