Drude weight and optical conductivity of doped graphene Giovanni Vignale, University of Missouri-Columbia, DMR The frequency of long wavelength plasmons (collective oscillations of the electronic density) is usually controlled by classical electrostatics. But in doped graphene sheets it presents strong quantum mechanical corrections due to the fact that the carriers are massless Dirac Fermions. This e ff ect is caused by the coupling between the density oscillations and the pseudospin degree of freedom of the massless Dirac fermions. Making use of diagrammatic perturbation theory to first order in the electron-electron interaction, we have shown that this coupling enhances both the plasmon frequency and the Drude weight D (the strength of the peak in the low-frequency optical conductivity) relative to the conventional weight D 0. D/D 0 is plotted in (a) for different values of the interaction strength  ee. We also calculate a significant enhancement of the optical conductivity  at  frequencies just above the absorption threshold, as shown in (b). Our predictions are consistent with infrared absorption measurements (inset in (b)). (a) (b)  

Many-Body Orbital Paramagnetism of Graphene Giovanni Vignale, University of Missouri-Columbia, DMR The orbital magnetic susceptibility  m of an ordinary electron gas is small and negative (i.e., the magnetic field is expelled from the sample). In contrast, the orbital magnetic susceptibility of massless Dirac fermions in a doped graphene sheet is null when the fermions are treated as non-interacting particles. Making use of diagrammatic perturbation theory, we have calculated  m for doped graphene sheets to first order in the Coulomb interaction, and found that, as a result of interactions,  m acquires a finite positive value. Our formula for  m is given in the box on the right in terms of the velocity v of massless Fermions, their Fermi energy  F and the interaction parameter . The factor N(  ) is plotted in the figure. Doped graphene sheets are thus unique systems in which the orbital magnetic susceptibility is paramagnetic (i.e. the externally applied magnetic field is reinforced) and entirely controlled by many-body effects. N Phys. Rev. Lett. 104, (2010)

Spin drag in a Fermi gas on the verge of ferromagnetism Giovanni Vignale, University of Missouri-Columbia, DMR Recent experiments have presented evidence of ferromagnetism in a two-component ultra-cold Fermi gas with strong repulsive interactions. Motivated by these experiments we have considered spin drag, i.e., frictional drag due to scattering of particles with opposite spin, in such systems. We have found that when the ferromagnetic state is approached from the normal side, the spin drag relaxation rate is strongly enhanced near the critical temperature T F (Fig. (a) – k F a is the parameter that controls the strength of the repulsive interaction between atoms). We have also determined the temperature dependence of the spin diffusion constant (Fig. (b)). In a trapped gas the spin drag relaxation rate determines the damping of the spin dipole mode, which therefore provides a precursor signal of the ferromagnetic phase transition that may be used to experimentally determine the proximity to the ferromagnetic phase. Phys. Rev. Lett. 104, (2010). (a) (b)

D’yakonov-Perel’ spin relaxation for degenerate electrons in the electron-hole liquid Giovanni Vignale, University of Missouri-Columbia, DMR We have completed an analytical study of spin relaxation time,  s, for degenerate electrons in a photo-excited electron-hole liquid (EHL) in intrinsic semiconductors exhibiting a spin-split band structure. The dominant mechanism of spin relaxation of electrons in these materials is spin precession (D’yakonov-Perel’ mechanism) limited by electron-hole scattering, with small corrections from electron-electron scattering and virtually none from electron- impurity scattering. We have obtained simple expressions for the scattering lifetimes (  kF, and  kF *, in different approximations) which enter the spin relaxation time calculation (see Figure). The electron-hole scattering rate is found to be comparable to the scattering rates from impurities in the electron liquid (EL) – a common model for n-type doped semiconductors. As the density of electron-hole pairs decreases, a strong enhancement of the scattering rates and a corresponding slowing down of spin relaxation is predicted due to exchange and correlation e ff ects in the electron-hole liquid. In the opposite limit of high density, the original D’yakonov-Perel’ model fails due to decreasing scattering rates and is eventually superseded by free precession of individual quasiparticle spins.