Feynman path-integral approach to the QED3 theory of the pseudogap

In this work the connection between vortex condensation in a d-wave superconductor and the QED$_3$ gauge theory of the pseudogap is elucidated. The approach taken circumvents the use of the standard Franz-Tesanovic gauge transformation, borrowing ideas from the path-integral analysis of the Aharonov-Bohm problem. An essential feature of this approach is that gauge-transformations which are prohibited on a particular multiply-connected manifold (e.g. a superconductor with vortices) can be successfully performed on the universal covering space associated with that manifold.Comment: 15 pages, 1 Figure. Int. J. Mod. Phys. B 17, 4509 (2003). Minor changes from previous versio

Level crossing in the three-body problem for strongly interacting fermions in a harmonic trap

We present a solution of the three-fermion problem in a harmonic potential across a Feshbach resonance. We compare the spectrum with that of the two-body problem and show that it is energetically unfavorable for the three fermions to occupy one lattice site rather than two. We also demonstrate the existence of an energy level crossing in the ground state with a symmetry change of its wave function, suggesting the possibility of a phase transition for the corresponding many-body case.Comment: 5 pages, 6 figures, typos corrected, references adde

Optical transparency of graphene as determined by the fine-structure constant

The observed 97.7% optical transparency of graphene has been linked to the value 1/137 of the fine structure constant, by using results for noninteracting Dirac fermions. The agreement in three significant figures requires an explanation for the apparent unimportance of the Coulomb interaction. Using arguments based on Ward identities, the leading corrections to the optical conductivity due to the Coulomb interactions are correctly computed (resolving a subtle theoretical issue) and shown to amount to only 1-2%, corresponding to 0.03-0.04% in the transparency.Comment: 5 pages, 2 figures, Minor changes, published version with a new titl

Using off-diagonal confinement as a cooling method

In a recent letter [Phys. Rev. Lett. 104, 167201 (2010)] we proposed a new confining method for ultracold atoms on optical lattices, based on off-diagonal confinement (ODC). This method was shown to have distinct advantages over the conventional diagonal confinement (DC) that makes use of a trapping potential, including the existence of pure Mott phases and highly populated condensates. In this paper we show that the ODC method can also lead to temperatures that are smaller than with the conventional DC method, depending on the control parameters. We determine these parameters using exact diagonalizations for the hard-core case, then we extend our results to the soft-core case by performing quantum Monte Carlo (QMC) simulations for both DC and ODC systems at fixed temperatures, and analysing the corresponding entropies. We also propose a method for measuring the entropy in QMC simulations.Comment: 6 pages, 6 figure

Induced superfluidity of imbalanced Fermi gases near unitarity

The induced intraspecies interactions among the majority species, mediated by the minority species, is computed for a population-imbalanced two-component Fermi gas. Although the Feshbach-resonance mediated interspecies interaction is dominant for equal populations, leading to singlet s-wave pairing, we find that in the strongly imbalanced regime the induced intraspecies interaction leads to p-wave pairing and superfluidity of the majority species. Thus, we predict that the observed spin-polaron Fermi liquid state in this regime is unstable to p-wave superfluidity, in accordance with the results of Kohn and Luttinger, below a temperature that, near unitarity, we find to be within current experimental capabilities. Possible experimental signatures of the p-wave state using radio-frequency spectroscopy as well as density-density correlations after free expansion are presented.Comment: 15 pages, 13 figures, submitted to Phys. Rev.

Pairing of a trapped resonantly-interacting fermion mixture with unequal spin populations

We consider the phase separation of a trapped atomic mixture of fermions with unequal spin populations near a Feshbach resonance. In particular, we determine the density profile of the two spin states and compare with the recent experiments of Partridge et al. (cond-mat/0511752). Overall we find quite good agreement. We identify the remaining discrepancies and pose them as open problems.Comment: 4 figures, 4+ pages, revtex

Atom-molecule coherence in a one-dimensional system

We study a model of one-dimensional fermionic atoms that can bind in pairs to form bosonic molecules. We show that at low energy, a coherence develops between the molecule and fermion Luttinger liquids. At the same time, a gap opens in the spin excitation spectrum. The coherence implies that the order parameters for the molecular Bose-Einstein Condensation and the atomic BCS pairing become identical. Moreover, both bosonic and fermionic charge density wave correlations decay exponentially, in contrast with a usual Luttinger liquid. We exhibit a Luther-Emery point where the systems can be described in terms of noninteracting pseudofermions. At this point, we provide closed form expressions for the density-density response functions.Comment: 5 pages, no figures, Revtex 4; (v2) added a reference to cond-mat/0505681 where related results are reported; (v3) Expression of correlation functions given in terms of generalized hypergeometric function

Survival of the d-wave superconducting state near the edge of antiferromagnetism in the cuprate phase diagram

In the cuprate superconductor $YBa_2Cu_3O_{6+x}$, hole doping in the $CuO_2$ layers is controlled by both oxygen content and the degree of oxygen-ordering. At the composition $\rm YBa_2Cu_3O_{6.35}$, the ordering can occur at room temperature, thereby tuning the hole doping so that the superconducting critical temperature gradually rises from zero to 20 K. Here we exploit this to study the c-axis penetration depth as a function of temperature and doping. The temperature dependence shows the d-wave superconductor surviving to very low doping, with no sign of another ordered phase interfering with the nodal quasiparticles. The only apparent doping dependence is a smooth decline of superfluid density as Tc decreases.Comment: 4 pages, 3 figure

Density of states in d-wave superconductors disordered by extended impurities

The low-energy quasiparticle states of a disordered d-wave superconductor are investigated theoretically. A class of such states, formed via tunneling between the Andreev bound states that are localized around extended impurities (and result from scattering between pair-potential lobes that differ in sign) is identified. Its (divergent) contribution to the total density of states is determined by taking advantage of connections with certain one-dimensional random tight-binding models. The states under discussion should be distinguished from those associated with nodes in the pair potential.Comment: 5 pages, 1 figur