Electrical resistivity near Pomeranchuk instability in two dimensions

We analyze the DC charge transport in the quantum critical regime near a d-wave Pomeranchuk instability in two dimensions. The transport decay rate is linear in temperature everywhere on the Fermi surface except at cold spots on the Brillouin zone diagonal. For pure systems, this leads to a DC resistivity proportional to T^{3/2} in the low-temperature limit. In the presence of impurities the residual impurity resistance at T=0 is approached linearly at low temperatures.Comment: 9 pages, no figure

Renormalized mean-field t-J model of high-Tc superconductivity: comparison with experiment

Using an advanced version of the renormalized mean-field theory (RMFT) for the t-J model, we examine spin-singlet superconducting (SC) state of $d_{x^2 - y^2}$-symmetry. Overall doping dependence of the SC gap magnitude is in good agreement with experimental results for $\text{Bi}_{2}\text{Sr}_{2}\text{Ca} \text{Cu}_2 \text{O}_{8 + \delta}$ (BSCCO) and $\text{La}_{2-x}\text{Sr}_{x}\text{Cu} \text{O}_{4}$ (LSCO) compounds at the optimal doping and in the overdoped regime. We also calculate the dispersion relation for the Bogoliubov quasiparticles and compare our findings both with the angle resolved photoemission data for the cuprates, as well as with the variational Monte Carlo and other mean-field studies. Within the method proposed by Fukushima [cf. Phys. Rev. B \textbf{78}, 115105 (2008)], we analyze different forms of the t-J Hamiltonian, i.e. modifications caused by the form of exchange interaction, and by the presence of three-site terms. It is shown that although the former has a small influence, the latter suppresses strongly the superconductivity. We also analyze the temperature dependence of the gap magnitude and compare the results with those of the recently introduced finite-temperature renormalized mean-field theory (TRMFT) of Wang et al. [cf. Phys. Rev. B \textbf{82}, 125105 (2010)].Comment: 7 pages, 6 figures, 2 tables. Submitted to Physical Review

Kohn's theorem in a superfluid Fermi gas with a Feshbach resonance

We investigate the dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential. According to Kohn's theorem, the frequency of this collective mode is not affected by an interaction between the atoms and is always equal to the trap frequency. This remarkable property, however, does not necessarily hold in an approximate theory. We explicitly prove that the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA), including a coupling between fluctuations in the density and Cooper channels, is consistent with both Kohn's theorem as well as Goldstone's theorem. This proof can be immediately extended to the strong-coupling superfluid theory developed by Nozi\'eres and Schmitt-Rink (NSR), where the effect of superfluid fluctuations is included within the Gaussian level. As a result, the NSR-GRPA formalism can be used to study collective modes in the BCS-BEC crossover region in a manner which is consistent with Kohn's theorem. We also include the effect of a Feshbach resonance and a condensate of the associated molecular bound states. A detailed discussion is given of the unusual nature of the Kohn mode eigenfunctions in a Fermi superfluid, in the presence and absence of a Feshbach resonance. When the molecular bosons feel a different trap frequency from the Fermi atoms, the dipole frequency is shown to {\it depend} on the strength of effective interaction associated with the Feshbach resonance.Comment: 29 pages, 1 figure

Zeeman response of d-wave superconductors: Born approximation for impurity and spin-orbit scattering potentials

The effects of impurity and spin-orbit scattering potentials can strongly affect the Zeeman response of a d-wave superconductor. Here, both the phase diagram and the quasiparticle density of states are calculated within the Born approximation and it is found that the spin-orbit interaction influences in a qualitatively different way the Zeeman response of d-wave and s-wave superconductors.Comment: 19 pages, 6 eps figures, submitted to Physica

Local Spectral Weight of a Luttinger Liquid: Effects from Edges and Impurities

We calculate the finite-temperature local spectral weight (LSW) of a Luttinger liquid with an "open" (hard wall) boundary. Close to the boundary the LSW exhibits characteristic oscillations indicative of spin-charge separation. The line shape of the LSW is also found to have a Fano-like asymmetry, a feature originating from the interplay between electron-electron interaction and scattering off the boundary. Our results can be used to predict how edges and impurities influence scanning tunneling microscopy (STM) of one-dimensional electron systems at low temperatures and voltage bias. Applications to STM on single-walled carbon nanotubes are discussed.Comment: 15 pages, 10 figues, The latest version in pdf format is available at http://www.physik.uni-kl.de/eggert/papers/LSW-LL.pd

Gapped optical excitations from gapless phases: imperfect nesting in unconventional density waves

We consider the effect of imperfect nesting in quasi-one-dimensional unconventional density waves in the case, when the imperfect nesting and the gap depends on the same wavevector component. The phase diagram is very similar to that in a conventional density wave. The density of states is highly asymmetric with respect to the Fermi energy. The optical conductivity at T=0 remains unchanged for small deviations from perfect nesting. For higher imperfect nesting parameter, an optical gap opens, and considerable amount of spectral weight is transferred to higher frequencies. This makes the optical response of our system very similar to that of a conventional density wave. Qualitatively similar results are expected in d-density waves.Comment: 8 pages, 7 figure

Correlated bosons on a lattice: Dynamical mean-field theory for Bose-Einstein condensed and normal phases

We formulate a bosonic dynamical mean-field theory (B-DMFT) which provides a comprehensive, thermodynamically consistent framework for the theoretical investigation of correlated lattice bosons. The B-DMFT is applicable for arbitrary values of the coupling parameters and temperature and becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In contrast to its fermionic counterpart the construction of the B-DMFT requires different scalings of the hopping amplitudes with Z depending on whether the bosons are in their normal state or in the Bose-Einstein condensate. A detailed discussion of how this conceptual problem can be overcome by performing the scaling in the action rather than in the Hamiltonian itself is presented. The B-DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. It reproduces all previously investigated limits in parameter space such as the Beliaev-Popov and Hartree-Fock-Bogoliubov approximations and generalizes the existing mean-field theories of interacting bosons. The self-consistency equations of the B-DMFT are those of a bosonic single-impurity coupled to two reservoirs corresponding to bosons in the condensate and in the normal state, respectively. We employ the B-DMFT to solve a model of itinerant and localized, interacting bosons analytically. The local correlations are found to enhance the condensate density and the Bose-Einstein condensate (BEC) transition temperature T_{BEC}. This effect may be used experimentally to increase T_{BEC} of bosonic atoms in optical lattices.Comment: 17 pages, 4 figures, extended versio

Anomalous impurity effects in nonadiabatic superconductors

We show that, in contrast with the usual electron-phonon Migdal-Eliashberg theory, the critical temperature Tc of an isotropic s-wave nonadiabatic superconductor is strongly reduced by the presence of diluted non-magnetic impurities. Our results suggest that the recently observed Tc-suppression driven by disorder in K3C60 [Phys. Rev. B vol.55, 3866 (1997)] and in Nd(2-x)CexCuO(4-delta) [Phys. Rev. B vol.58, 8800 (1998)] could be explained in terms of a nonadiabatic electron-phonon coupling. Moreover, we predict that the isotope effect on Tc has an impurity dependence qualitatively different from the one expected for anisotropic superconductors.Comment: 10 pages, euromacr.tex, europhys.sty, 6 figures. Replaced with accepted version (Europhysics Letters

Bulk inhomogeneous phases of anisotropic particles: A fundamental measure functional study of the restricted orientations model

The phase diagram of prolate and oblate particles in the restricted orientations approximation (Zwanzig model) is calculated. Transitions to different inhomogeneous phases (smectic, columnar, oriented, or plastic solid) are studied through minimization of the fundamental measure functional (FMF) of hard parallelepipeds. The study of parallel hard cubes (PHC's) as a particular case is also included motivated by recent simulations of this system. As a result a rich phase behavior is obtained which include, apart from the usual liquid crystal phases, a very peculiar phase (called here discotic smectic) which was already found in the only existing simulation of the model, and which turns out to be stable because of the restrictions imposed on the orientations. The phase diagram is compared at a qualitative level with simulation results of other anisotropic particle systems.Comment: 11 pages, 10 figure

Electrodynamics of superconductors

An alternate set of equations to describe the electrodynamics of superconductors at a macroscopic level is proposed. These equations resemble equations originally proposed by the London brothers but later discarded by them. Unlike the conventional London equations the alternate equations are relativistically covariant, and they can be understood as arising from the 'rigidity' of the superfluid wave function in a relativistically covariant microscopic theory. They predict that an internal 'spontaneous' electric field exists in superconductors, and that externally applied electric fields, both longitudinal and transverse, are screened over a London penetration length, as magnetic fields are. The associated longitudinal dielectric function predicts a much steeper plasmon dispersion relation than the conventional theory, and a blue shift of the minimum plasmon frequency for small samples. It is argued that the conventional London equations lead to difficulties that are removed in the present theory, and that the proposed equations do not contradict any known experimental facts. Experimental tests are discussed.Comment: Small changes following referee's and editor's comments; to be published in Phys.Rev.