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Electrons most often organize into Fermi-liquid states in which electron-electron interactions play an inessential role. A well known exception is the case of one-dimensional (1D) electron systems (1DES). In 1D the electron Fermi-surface consists of points, and divergences associated with low-energy particle-hole excitations abound when electron-electron interactions are described perturbatively. In higher space dimensions, the corresponding divergences occur only when Fermi lines or surfaces satisfy idealized nesting conditions. In this article we discuss electron-electron interactions in 2D graphene bilayer systems which behave in many ways as if they were one-dimensional, because they have Fermi points instead of Fermi lines and because their particle-hole energies have a quadratic dispersion which compensates for the difference between 1D and 2D phase space. We conclude, on the basis of a perturbative RG calculation similar to that commonly employed in 1D systems, that interactions in neutral graphene bilayers can drive the system into a strong-coupling broken symmetry state with layer-pseudospin ferromagnetism and an energy gap., Comment: 4 pages, 2 figures and supplementary information

A two-dimensional gas of massless Dirac fermions (MDFs) is a very useful model to describe low-energy electrons in monolayer graphene. Because the MDF current operator is directly proportional to the (sublattice) pseudospin operator, the MDF current-current response function, which describes the response to a vector potential, happens to coincide with the pseudospin-pseudospin response function. In this work we present analytical results for the wavevector- and frequency-dependent longitudinal and transverse pseudospin-pseudospin response functions of noninteracting MDFs. The transverse response in the static limit is then used to calculate the noninteracting orbital magnetic susceptibility. These results are a starting point for the construction of approximate pseudospin-pseudospin response functions that would take into account electron-electron interactions (for example at the random-phase-approximation level). They also constitute a very useful input for future applications of current-density-functional theory to graphene sheets subjected to time- and spatially-varying vector potentials., Comment: 11 pages, 5 figures, submitted

Bilayer graphene (BLG) has recently attracted a great deal of attention because of its electrically tunable energy gaps and its unusual electronic structure. In this Letter we present analytical and semi-analytical expressions, based on the four-band continuum model, for the layer-sum and layer-difference density response functions of neutral and doped BLG. These results demonstrate that BLG density-fluctuations can exhibit either single-component massive-chiral character or standard two-layer character, depending on energy and doping., Comment: 4 + epsilon pages, 4 figures, submitted

In single-layer graphene sheets non-local interband exchange leads to a renormalized Fermi-surface effective mass which vanishes in the low carrier-density limit. We report on a comparative study of Fermi surface effective mass renormalization in single-layer and AB-stacked bilayer graphene. We explain why the mass does not approach zero in the bilayer case, although its value is still strongly suppressed., Comment: 8 pages, 5 figures, submitted to the proceedings of the ICTP Conference `Graphene Week 2008' (Trieste, Italy)

Plasmons in ordinary electron liquids are collective excitations whose long-wavelength limit is rigid center-of-mass motion with a dispersion relation that is, as a consequence of Galileian invariance, unrenormalized by many-body effects. The long-wavelength plasmon frequency is related by the f-sum rule to the integral of the conductivity over the electron-liquid's Drude peak, implying that transport properties also tend not to have important electron-electron interaction renormalizations. In this article we demonstrate that the plasmon frequency and Drude weight of the electron liquid in a doped graphene sheet, which is described by a massless Dirac Hamiltonian and not invariant under ordinary Galileian boosts, are strongly renormalized even in the long-wavelength limit. This effect is not captured by the Random Phase Approximation (RPA), commonly used to describe electron fluids. It is due primarily to non-local inter-band exchange interactions, which, as we show, reduce both the plasmon frequency and the Drude weight relative to the RPA value. Our predictions can be checked using inelastic light scattering or infrared spectroscopy., Comment: 7 pages, 4 figures, submitted

At low energies, electrons in doped graphene sheets are described by a massless Dirac fermion Hamiltonian. In this work we present a semi-analytical expression for the dynamical density-density linear-response function of noninteracting massless Dirac fermions (the so-called "Lindhard" function) at finite temperature. This result is crucial to describe finite-temperature screening of interacting massless Dirac fermions within the Random Phase Approximation. In particular, we use it to make quantitative predictions for the specific heat and the compressibility of doped graphene sheets. We find that, at low temperatures, the specific heat has the usual normal-Fermi-liquid linear-in-temperature behavior, with a slope that is solely controlled by the renormalized quasiparticle velocity., Comment: 9 pages, 5 figures, Submitted to J. Phys. A

We study Andreev reflection in graphene nanoribbon/superconductor hybrid junctions. By using a tight-binding approach and the scattering formalism we show that finite-size effects lead to notable differences with respect to the bulk graphene case. At subgap voltages, conservation of pseudoparity, a quantum number characterizing the ribbon states, yields either a suppression of Andreev reflection when the ribbon has an even number of sites in the transverse direction or perfect Andreev reflection when the ribbon has an odd number of sites. In the former case the suppression of Andreev reflection induces an insulating behavior even when the junction is biased; electron conduction can however be restored by applying a gate voltage., Comment: 6 pages, 6 figures

Time-dependent density-functional theory (TDDFT) is a powerful tool to study the non-equilibrium dynamics of inhomogeneous interacting many-body systems. Here we show that the simple adiabatic local-spin-density approximation for the time-dependent exchange-correlation potential is surprisingly accurate in describing collective density and spin dynamics in strongly correlated one-dimensional ultracold Fermi gases. Our conclusions are based on extensive comparisons between our TDDFT results and accurate results based on the adaptive time-dependent density-matrix renormalization-group method., Comment: 11 pages, 6 figures, submitted

Motivated by the large interest in the non-equilibrium dynamics of low-dimensional quantum many-body systems, we present a fully-microscopic theoretical and numerical study of the "charge" and "spin" dynamics in a one-dimensional ultracold Fermi gas following a quench. Our approach, which is based on time-dependent current-density-functional theory, is applicable well beyond the linear-response regime and produces both spin-charge separation and spin-drag-induced broadening of the spin packets., Comment: 4+epsilon pages, 3 figures, submitted. High-quality figures can be requested to the authors

We outline a Kohn-Sham-Dirac density-functional-theory (DFT) scheme for graphene sheets that treats slowly-varying inhomogeneous external potentials and electron-electron interactions on an equal footing. The theory is able to account for the the unusual property that the exchange-correlation contribution to chemical potential increases with carrier density in graphene. Consequences of this property, and advantages and disadvantages of using the DFT approach to describe it, are discussed. The approach is illustrated by solving the Kohn-Sham-Dirac equations self-consistently for a model random potential describing charged point-like impurities located close to the graphene plane. The influence of electron-electron interactions on these non-linear screening calculations is discussed at length, in the light of recent experiments reporting evidence for the presence of electron-hole puddles in nearly-neutral graphene sheets., Comment: 11 pages, 9 figures, submitted. High-quality figures can be requested to the authors

Spin propagation in systems of one-dimensional interacting fermions at finite temperature is intrinsically diffusive. The spreading rate of a spin packet is controlled by a transport coefficient termed "spin drag" relaxation time $\tau_{\rm sd}$. In this paper we present both numerical and analytical calculations of $\tau_{\rm sd}$ for a two-component spin-polarized cold Fermi gas trapped inside a tight atomic waveguide. At low temperatures we find an activation law for $\tau_{\rm sd}$, in agreement with earlier calculations of Coulomb drag between slightly asymmetric quantum wires, but with a different and much stronger temperature dependence of the prefactor. Our results provide a fundamental input for microscopic time-dependent spin-density functional theory calculations of spin transport in 1D inhomogeneous systems of interacting fermions., Comment: 7 pages, 5 figures

Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected from FFLO theory. However, we also show by numerically computing the mixed spin-charge static structure factor that charge and spin degrees of freedom appear to be coupled already for small imbalance. We discuss the consequences of this coupling for the observation of the FFLO phase, as well as for the stabilization of the quasi-long range order into long-range order by coupling many identical 1D systems, as in quasi-1D optical lattices., Comment: 7 pages, 5 figures, submitted

We present detailed numerical and analytical investigations of the nonequilibrium dynamics of spin-polarized ultracold Fermi gases following a sudden switching-on of the atom-atom pairing coupling strength. Within a time-dependent mean-field approach we show that on increasing the imbalance it takes longer for pairing to develop, the period of the nonlinear oscillations lengthens, and the maximum value of the pairing amplitude decreases. As expected, dynamical pairing is suppressed by the increase of the imbalance. Eventually, for a critical value of the imbalance the nonlinear oscillations do not even develop. Finally, we point out an interesting temperature-reentrant behavior of the exponent characterizing the initial instability., Comment: 10 pages, 6 figures. High-quality figures can be requested to the authors

We report on a theoretical study of the influence of electron-electron interactions on ARPES spectra in graphene that is based on the random-phase-approximation and on graphene's massless Dirac equation continuum model. We find that level repulsion between quasiparticle and plasmaron resonances gives rise to a gap-like feature at small k. ARPES spectra are sensitive to the electron-electron interaction coupling strength $\alpha_{\rm gr}$ and might enable an experimental determination of this material parameter., Comment: 5 Pages, 4 Figures, Submitted

We predict that neutral graphene bilayers are pseudospin magnets in which the charge density-contribution from each valley and spin spontaneously shifts to one of the two layers. The band structure of this system is characterized by a momentum-space vortex which is responsible for unusual competition between band and kinetic energies leading to symmetry breaking in the vortex core. We discuss the possibility of realizing a pseudospin version of ferromagnetic metal spintronics in graphene bilayers based on hysteresis associated with this broken symmetry., Comment: 5 pages, 4 figures; added figure 1, modified introduction and discussion; updated references

The pseudospin degree of freedom in a semiconductor bilayer gives rise to a collective mode analogous to the ferromagnetic resonance mode of a ferromagnet. We present a theory of the dependence of the energy and the damping of this mode on layer separation $d$. Based on these results, we discuss the possibility of realizing transport-current driven pseudospin-transfer oscillators in semiconductors., Comment: 4+ pages, 3 figures, submitted

Doped graphene sheets are pseudochiral two-dimensional Fermi liquids with abnormal electron-electron interaction physics. We address graphene's Fermi liquid properties quantitatively using a microscopic random-phase-approximation theory and comment on the importance of using exchange-correlation potentials based on the properties of a chiral two-dimensional electron gas in density-functional-theory applications to graphene nanostructures., Comment: 15 pages, 4 figures, submitted

Low-energy spin and charge excitations of one-dimensional interacting fermions are completely decoupled and propagate with different velocities. These modes however can decay due to several possible mechanisms. In this paper we expose a new facet of spin-charge separation: not only the speeds but also the damping rates of spin and charge excitations are different. While the propagation of long-wavelength charge excitations is essentially ballistic, spin propagation is intrinsically damped and diffusive. We suggest that cold Fermi gases trapped inside a tight atomic waveguide offer the opportunity to measure the spin-drag relaxation rate that controls the broadening of a spin packet., Comment: 4 pages, 4 figures, submitted

Graphene is described at low-energy by a massless Dirac equation whose eigenstates have definite chirality. We show that the tendency of Coulomb interactions in lightly doped graphene to favor states with larger net chirality leads to suppressed spin and charge susceptibilities. Our conclusions are based on an evaluation of graphene's exchange and random-phase-approximation (RPA) correlation energies. The suppression is a consequence of the quasiparticle chirality switch which enhances quasiparticle velocities near the Dirac point., Comment: 5 pages, 4 figures

The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern., Comment: 10 pages, 3 figures, 1 Table, submitted to Phys. Rev. on July 25th 2006

We present an extensive numerical study of ground-state properties of confined repulsively interacting fermions on one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham density-functional calculations and quantum Monte Carlo simulations. The density-functional calculations employ a Bethe-Ansatz-based local-density approximation for the correlation energy, which accounts for Luttinger-liquid and Mott-insulator physics. Semi-analytical and fully numerical formulations of this approximation are compared with each other and with a cruder Thomas-Fermi-like local-density approximation for the total energy. Precise quantum Monte Carlo simulations are used to assess the reliability of the various local-density approximations, and in conjunction with these allow to obtain a detailed microscopic picture of the consequences of the interplay between particle-particle interactions and confinement in one-dimensional systems of strongly correlated fermions., Comment: 14 pages, 11 figures, 1 table, submitted

Two-component Fermi gases with tunable repulsive or attractive interactions inside quasi-one-dimensional (Q1D) harmonic wells may soon become the cleanest laboratory realizations of strongly correlated Luttiger and Luther-Emery liquids under confinement. We present a microscopic Kohn-Sham density-functional theory of these systems, with specific attention to a gas on the approach to a confinement-induced Feshbach resonance. The theory employs the one-dimensional Gaudin-Yang model as the reference system and transfers the appropriate Q1D ground-state correlations to the confined inhomogeneous gas {\it via} a suitable local-density approximation to the exchange and correlation energy functional. Quantitative understanding of the role of the interactions in the bulk shell structure of the axial density profile is thereby achieved. While repulsive intercomponent interactions depress the amplitude of the shell structure of the noninteracting gas, attractive interactions stabilize atomic-density waves through spin pairing. These should be clearly observable in atomic clouds containing of the order of up to a hundred atoms., Comment: 13 pages, 9 figures, submitted

We present a novel and comprehensive microscopic study of Luther-Emery-paired phases in a strongly interacting atomic Fermi gas inside a parabolic trap and a one-dimensional (1D) optical lattice. Our work is based on a lattice version of density-functional theory, which uses as reference system the 1D homogeneous Hubbard model. We test our approach for repulsive interactions against Quantum Monte Carlo data and show that, for sufficiently strong attractions, an atomic-density wave (ADW) in the central portion of the trap breaks the discrete translational symmetry of the underlying lattice. We demonstrate that the emergence of an ADW has a dramatic impact on experimental observables such as the Fraunhofer diffraction pattern and the momentum distribution., Comment: 4 pages, 4 figures, 1 table, submitted

Fully frustrated Josephson Junction arrays (FF-JJA's) exhibit a subtle compound phase transition in which an Ising transition associated with discrete broken translational symmetry and a Berezinskii-Kosterlitz-Thouless (BKT) transition associated with quasi-long-range phase coherence occur nearly simultaneously. In this Letter we discuss a cold atom realization of the FF-JJA system. We demonstrate that both orders can be studied by standard momentum-distribution-function measurements and present numerical results, based on a successful self-consistent spin-wave approximation, that illustrate the expected behavior of observables., Comment: 5 pages, 3 figures, submitted