Superfluidity and excitations at unitarity

We present lattice results for spin-1/2 fermions at unitarity, where the effective range of the interaction is zero and the scattering length is infinite. We measure the spatial coherence of difermion pairs for a system of 6, 10, 14, 18, 22, 26 particles with equal numbers of up and down spins in a periodic cube. Using Euclidean time projection, we analyze ground state properties and transient behavior due to low-energy excitations. At asymptotically large values of t we see long-range order consistent with spontaneously broken U(1) fermion-number symmetry and a superfluid ground state. At intermediate times we see exponential decay in the t-dependent signal due to an unknown low-energy excitation. We probe this low-energy excitation further by calculating two-particle correlation functions. We find that the excitation has the properties of a chain of particles extending across the periodic lattice.Comment: 40 pages, 19 figures, revised version includes new data on two-particle density correlation

Triplet superconducting pairing and density-wave instabilities in organic conductors

Using a renormalization group approach, we determine the phase diagram of an extended quasi-one-dimensional electron gas model that includes interchain hopping, nesting deviations and both intrachain and interchain repulsive interactions. We find a close proximity of spin-density- and charge-density-wave phases, singlet d-wave and triplet f-wave superconducting phases. There is a striking correspondence between our results and recent puzzling experimental findings in the Bechgaard salts, including the coexistence of spin-density-wave and charge-density-wave phases and the possibility of a triplet pairing in the superconducting phase.Comment: 4 pages, 5 eps figure

Singlet and triplet BCS pairs in a gas of two-species fermionic polar molecules

We investigate the BCS pairing in a mixture of fermionic polar molecules with two different hyperfine states. We derive a set of coupled gap equations and find that this system supports both spin-singlet and -triplet BCS pairs. We also calculate the critical temperatures and the angular dependence of order parameters. In addition, by tuning short-range interaction between inter-species molecules, the transition between singlet and triplet paired states may be realized.Comment: 5 pages, 4 figure

Nature of superconducting state in the new phase in (TMTSF)2_{2}PF6_{6} under pressure

The unusual phase has been recently observed in the organic material (TMTSF)$_{2}$PF$_{6}$, where superconductivity (SC) coexists with spin-density wave (SDW) in the pressure interval $p_{c1}<p<p_{c}$ below the first order transition into SC or normal metal phase. Assuming that the coexistence takes place on the microscopic scale, we consider the properties of the intermediate phase. We show that the new superconducting state inside SDW phase just above $p_{c1}$ must bear a triplet pairing.Comment: 4 pages, 1 figur

Asymptotic exchange coupling of quasi-1D excitons in carbon nanotubes

An analytical expression is obtained for the biexciton binding energy as a function of the inter-exciton distance and binding energy of constituent quasi-one-dimensional excitons in carbon nanotubes. This allows one to trace biexciton energy variation and relevant non-linear absorption under external conditions whereby the exciton binding energy varies. The non-linear absorption lineshapes calculated exhibit characteristic asymmetric (Rabi) splitting as the exciton energy is tuned to the nearest interband plasmon resonance. These results are useful for tunable optoelectronic device applications of optically excited semiconducting carbon nanotubes, including the strong excitation regime with optical non-linearities.Comment: 4 pages, 3 figures. Text and figures updated. References adde

Topological p_x+ip_y Superfluid Phase of Fermionic Polar Molecules

We discuss the topological p_x+ip_y superfluid phase in a 2D gas of single-component fermionic polar molecules dressed by a circularly polarized microwave field. This phase emerges because the molecules may interact with each other via a potential V_0(r) that has an attractive dipole-dipole 1/r^3 tail, which provides p-wave superfluid pairing at fairly high temperatures. We calculate the amplitude of elastic p-wave scattering in the potential V_0(r) taking into account both the anomalous scattering due to the dipole-dipole tail and the short-range contribution. This amplitude is then used for the analytical and numerical solution of the renormalized BCS gap equation which includes the second order Gor'kov-Melik-Barkhudarov corrections and the correction related to the effective mass of the quasiparticles. We find that the critical temperature T_c can be varied within a few orders of magnitude by modifying the short-range part of the potential V_0(r). The decay of the system via collisional relaxation of molecules to dressed states with lower energies is rather slow due to the necessity of a large momentum transfer. The presence of a constant transverse electric field reduces the inelastic rate, and the lifetime of the system can be of the order of seconds even at 2D densities ~ 10^9 cm^{-2}. This leads to T_c of up to a few tens of nanokelvins and makes it realistic to obtain the topological p_x+ip_y phase in experiments with ultracold polar molecules.Comment: 15 pages, 9 figures, published versio

Interplay of paramagnetic, orbital and impurity effects on the phase transition of a normal metal to superconducting state

We derive the generalized Ginzburg-Landau free energy functional for conventional and unconventional singlet superconductors in the presence of paramagnetic, orbital and impurity effects. Within the mean field theory, we determine the criterion for appearence of the non uniform (Fulde-Ferrell-Larkin-Ovchinnikov) superconducting state, with vortex lattice structure and additional modulation along the magnetic field. We also discuss the possible change of the order of transition from normal to superconducting state. We find that the superconducting phase diagram is very sensitive to geometrical effects such as the nature of the order parameter and the shape of the Fermi surface. In particular, we obtain the qualitative phase diagrams for three-dimensional isotropic s-wave superconductors and in quasi two-dimensional d-wave superconductors under magnetic field perpendicular to the conducting layers. In addition, we determine the criterion for instability toward non uniform superconducting state in s-wave superconductors in the dirty limit.Comment: 15 pages, 4 figure

Spin-orbit mediated anisotropic spin interaction in interacting electron systems

We investigate interactions between spins of strongly correlated electrons subject to the spin-orbit interaction. Our main finding is that of a novel, spin-orbit mediated anisotropic spin-spin coupling of the van der Waals type. Unlike the standard exchange, this interaction does not require the wave functions to overlap. We argue that this ferromagnetic interaction is important in the Wigner crystal state where the exchange processes are severely suppressed. We also comment on the anisotropy of the exchange between spins mediated by the spin-orbital coupling.Comment: 4.1 pages, 1 figure; (v2) minor changes, published versio

The motion of superconducting vortices in thin films of varying thickness

The interaction of superconducting vortices with superconductor/vacuum interfaces is considered. A vortex is first shown to intersect such an interface normally. Various thin-film models are then formulated, corresponding to different parameter regimes. A local analysis of a vortex is performed, and a law of motion for each vortex deduced. This law of motion implies that the vortex will move to the locally thinnest part of the film, and is consistent with the vortex moving under the curvature induced by being forced to intersect the boundaries of the film normall

Magnetic properties of superconductors with strong spin-orbit coupling

We study the response of a superconductor with a strong spin-orbit coupling on an external magnetic field. The Ginzburg-Landau free energy functional is derived microscopically for a general crystal structure, both with and without an inversion center, and for an arbitrary symmetry of the superconducting order parameter. As a by-product, we obtain the general expressions for the intrinsic magnetic moment of the Cooper pairs. It is shown that the Ginzburg-Landau gradient energy in a superconductor lacking inversion symmetry has unusual structure. The general formalism is illustrated using as an example CePt$_3$Si, which is the first known heavy-fermion superconductor without an inversion center.Comment: Published version, 14 pages, minor correction