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.Comment: 4 pages, 6 figure

Spin oscillations of the normal polarized Fermi gas at Unitarity

Using density functional theory in a time dependent approach we determine the frequencies of the compressional modes of the normal phase of a Fermi gas at unitarity as a function of its polarization. Our energy functional accounts for the typical elastic deformations exhibited by Landau theory of Fermi liquids. The comparison with the available experiments is biased by important collisional effects affecting both the {\it in phase} and the {\it out of phase} oscillations even at the lowest temperatures. New experiments in the collisionless regime would provide a crucial test of the applicability of Landau theory to the dynamics of these strongly interacting normal Fermi gases.Comment: 5 pages, 1 figur

Density and spin response function of a normal Fermi gas at unitarity

Using Landau theory of Fermi liquids we calculate the dynamic response of both a polarized and unpolarized normal Fermi gas at zero temperature in the strongly interacting regime of large scattering length. We show that at small excitation energies the {\it in phase} (density) response is enhanced with respect to the ideal gas prediction due to the increased compressibility. Viceversa, the {\it out of phase} (spin) response is quenched as a consequence of the tendency of the system to pair opposite spins. The long wavelength behavior of the static structure factor is explicitly calculated. The results are compared with the predictions in the collisional and superfluid regimes. The emergence of a spin zero sound solution in the unpolarized normal phase is explicitly discussed.Comment: 4 pages, 2 figure

Magnetic scaling in cuprate superconductors

We determine the magnetic phase diagram for the YBa$_2$Cu$_3$O$_{6+x}$ and La$_{2-x}$Sr$_x$CuO$_4$ systems from various NMR experiments. We discuss the possible interpretation of NMR and neutron scattering experiments in these systems in terms of both the non-linear $\sigma$-model of nearly localized spins and a nearly antiferromagnetic Fermi liquid description of magnetically coupled quasiparticles. We show for both the 2:1:4 and 1:2:3 systems that bulk properties, such as the spin susceptibiltiy, and probes at the antiferromagnetic wavevector $(\pi, \pi)$, such as $^{63}T_1$, the $^{63}Cu$ spin relaxation time, both display a crossover at a temperature $T_{cr}$, which increases linearly with decreasing hole concentration, from a non-universal regime to a $z=1$ scaling regime characterized by spin pseudogap behavior. We pursue the consequences of the ansatz that $T_{cr}$ corresponds to a fixed value of the antiferromagnetic correlation length, $\xi$, and show how this enables one to extract the magnitude and temperature dependence of $\xi$ from measurements of $T_1$ alone. We show that like $T_{cr}$, the temperature $T_*$ which marks a crossover at low temperatures from the $z=1$ scaling regime to a quantum disordered regime, exhibits the same dependence on doping for the 2:1:4 and 1:2:3 systems, and so arrive at a unified description of magnetic behavior in the cuprates, in which the determining factor is the planar hole concentration. We apply our quantitative results for YBa$_2$Cu$_3$O$_7$ to the recent neutron scattering experiments of Fong {\em et al}, and show that the spin excitation near $40 meV$ measured by them corresponds to a spin gap excitation, which is overdamped in the normal state, but becomes visible in the superconducting state.Comment: 18 pages, RevTex, 18 figures are available upon request; submitted to Phys. Rev.

Partially suppressed long-range order in the Bose-Einstein condensation of polaritons

We adopt a kinetic theory of polariton non-equilibrium Bose-Einstein condensation, to describe the formation of off-diagonal long-range order. The theory accounts properly for the dominant role of quantum fluctuations in the condensate. In realistic situations with optical excitation at high energy, it predicts a significant depletion of the condensate caused by long-wavelength fluctuations. As a consequence, the one-body density matrix in space displays a partially suppressed long-range order and a pronounced dependence on the finite size of the system

Magnetoplasmons in layered graphene structures

We calculate the dispersion equations for magnetoplasmons in a single layer, a pair of parallel layers, a graphite bilayer and a superlattice of graphene layers in a perpendicular magnetic field. We demonstrate the feasibility of a drift-induced instability of magnetoplasmons. The magnetoplasmon instability in a superlattice is enhanced compared to a single graphene layer. The energies of the unstable magnetoplasmons could be in the terahertz (THz) part of the electromagnetic spectrum. The enhanced instability makes superlattice graphene a potential source of THz radiation.Comment: 5 pages, 4 figure

Self-consistent calculation of particle-hole diagrams on the Matsubara frequency: FLEX approximation

We implement the numerical method of summing Green function diagrams on the Matsubara frequency axis for the fluctuation exchange (FLEX) approximation. Our method has previously been applied to the attractive Hubbard model for low density. Here we apply our numerical algorithm to the Hubbard model close to half filling ($\rho = 0.40$), and for $T/t = 0.03$, in order to study the dynamics of one- and two-particle Green functions. For the values of the chosen parameters we see the formation of three branches which we associate with the a two-peak structure in the imaginary part of the self-energy. From the imaginary part of the self-energy we conclude that our system is a Fermi liquid (for the temperature investigated here), since Im$\Sigma(\vec{k},\omega) \approx w^2$ around the chemical potential. We have compared our fully self-consistent FLEX solutions with a lower order approximation where the internal Green functions are approximated by free Green functions. These two approches, i.e., the fully selfconsistent and the non-selfconsistent ones give different results for the parameters considered here. However, they have similar global results for small densities.Comment: seven pages, nine figures as ps files. Accepted in Int. J. Modern Phys. C (1997

Dynamics of compressible edge and bosonization

We work out the dynamics of the compressible edge of the quantum Hall system based on the electrostatic model of Chklovskii et al.. We introduce a generalized version of Wen's hydrodynamic quantization approach to the dynamics of sharp edge and rederive Aleiner and Glazman's earlier result of multiple density modes. Bosonic operators of density excitations are used to construct fermions at the interface of the compressible and incompressible region. We also analyze the dynamics starting with the second-quantized Hamiltonian in the lowest Landau level and work out the time development of density operators. Contrary to the hydrodynamic results, the density modes are strongly coupled. We argue that the coupling suppresses the propagation of all acoustic modes, and that the excitations with large wavevectors are subject to decay due to coupling to the dissipative acoustic modes.A possible correction to the tunneling density of states is discussed.Comment: 7 pages, Revtex, 1 figur

Valley dependent many-body effects in 2D semiconductors

We calculate the valley degeneracy ($g_v$) dependence of the many-body renormalization of quasiparticle properties in multivalley 2D semiconductor structures due to the Coulomb interaction between the carriers. Quite unexpectedly, the $g_v$ dependence of many-body effects is nontrivial and non-generic, and depends qualitatively on the specific Fermi liquid property under consideration. While the interacting 2D compressibility manifests monotonically increasing many-body renormalization with increasing $g_v$, the 2D spin susceptibility exhibits an interesting non-monotonic $g_v$ dependence with the susceptibility increasing (decreasing) with $g_v$ for smaller (larger) values of $g_v$ with the renormalization effect peaking around $g_v\sim 1-2$. Our theoretical results provide a clear conceptual understanding of recent valley-dependent 2D susceptibility measurements in AlAs quantum wells.Comment: 5 pages, 3 figure

The correlation energy functional within the GW-RPA approximation: exact forms, approximate forms and challenges

In principle, the Luttinger-Ward Green's function formalism allows one to compute simultaneously the total energy and the quasiparticle band structure of a many-body electronic system from first principles. We present approximate and exact expressions for the correlation energy within the GW-RPA approximation that are more amenable to computation and allow for developing efficient approximations to the self-energy operator and correlation energy. The exact form is a sum over differences between plasmon and interband energies. The approximate forms are based on summing over screened interband transitions. We also demonstrate that blind extremization of such functionals leads to unphysical results: imposing physical constraints on the allowed solutions (Green's functions) is necessary. Finally, we present some relevant numerical results for atomic systems.Comment: 3 figures and 3 tables, under review at Physical Review