Abstract:
We investigate nonmagnetic impurity effects in two-band superconductors, focusing on the effects of interband scatterings. Within the Born approximation, it is known that interband scatterings mix order parameters in the two bands. In particular, only one averaged energy gap appears in the excitation spectrum in the dirty limit. [G. Gusman: J. Phys. Chem. Solids {\bf 28} (1967) 2327.] In this paper, we take into account the interband scattering within the $t$-matrix approximation beyond the Born approximation in the previous work. We show that, although the interband scattering is responsible for the mixing effect, this effect becomes weak when the interband scattering becomes very strong. In the strong interband scattering limit, a two-gap structure corresponding to two order parameters recovers in the superconducting density of states. We also show that a bound state appears around a nonmagnetic impurity depending on the phase of interband scattering potential.

Abstract:
We investigate unconventional superfluidity in a gas of Fermi atoms with an anisotropic p-wave Feshbach resonance. Including the p-wave Feshbach resonance as well as the associated three kinds of quasi-molecules with finite orbital angular momenta $L_z=\pm1,0$, we calculate the transition temperature of the superfluid phase. As one passes through the p-wave Feshbach resonance, we find the usual BCS-BEC crossover phenomenon. The p-wave BCS state continuously changes into the BEC of bound molecules with L=1. Our calculation includes the effect of fluctuations associated with Cooper-pairs and molecules which are not Bose-condensed.

Abstract:
Effects of superconducting fluctuations on the Fulde-Ferrell (FF) state are discussed in a spatially isotropic three-dimensional superconductor under a magnetic field. For this system, Shimahara recently showed that within the phenomenological Ginzburg-Landau theory, the long-range order of the FF state is suppressed by the phase fluctuation of the superconducting order parameter. [H. Shimahara: J. Phys. Soc. Jpn. {\bf 67} (1998) 1872, Physica B {\bf 259-261} (1999) 492] In this letter, we investigate this instability of the FF state against superconducting fluctuations from the microscopic viewpoint, employing the theory developed by Nozi\'eres and Schmitt-Rink in the BCS-BEC crossover field. Besides the absence of the second-order phase transition associated with the FF state, we show that even if the pairing interaction is weak, the shift of the chemical potential from the Fermi energy due to the fluctuations is crucial near the critical magnetic field of the FF state obtained within the mean-field theory.

Abstract:
We investigate tunneling properties of a bound pair of Fermi atoms in an optical lattice, comparing with results obtained in an attractive Hubbard model. In the strong coupling regime of the Hubbard model, it has been predicted that the motion of a bound pair between lattice sites is accompanied by virtual dissociation. To explore the possibility of this interesting phenomenon in optical lattice, we calculate molecular wavefunction in a cosine-shape periodic potential. We show that the molecular tunneling accompanied by dissociation occurs in the intermediate coupling regime of the optical lattice system. In the strong coupling regime, in contrast to the prediction in the Hubbard model, the bound pair is shown to tunnel through lattice potential without dissociation. As a result, the magnitude of molecular band mass M remains finite even in the strong coupling limit, which is in contrast to the diverging molecular mass in the case of the Hubbard model. Including this finite value of molecular band mass, we evaluate the superfluid phase transition temperature Tc in the BEC limit of the optical lattice system, where the Hubbard model gives Tc=0 due to the diverging molecular mass.

Abstract:
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.

Abstract:
We theoretically investigate a possible idea to introduce magnetic impurities to a superfluid Fermi gas. In the presence of population imbalance ($N_\uparrow>N_\downarrow$, where $N_\sigma$ is the number of Fermi atoms with pseudospin $\sigma=\uparrow,\downarrow$), we show that nonmagnetic potential scatterers embedded in the system are magnetized in the sense that some of excess $\uparrow$-spin atoms are localized around them. They destroy the superfluid order parameter around them, as in the case of magnetic impurity effect discussed in the superconductivity literature. This pair-breaking effect naturally leads to localized excited states below the superfluid excitation gap. To confirm our idea in a simply manner, we treat an attractive Fermi Hubbard model within the mean-field theory at T=0. We self-consistently determine superfluid properties around a nonmagnetic impurity, such as the superfluid order parameter, local population imbalance, as well as single-particle density of states, in the presence of population imbalance. Since the competition between superconductivity and magnetism is one of the most fundamental problems in condensed matter physics, our results would be useful for the study of this important issue in cold Fermi gases.

Abstract:
We study the Bloch theorem which states absence of the spontaneous current in interacting electron systems. This theorem is shown to be still applicable to the system with the magnetic field induced by the electric current. Application to the spontaneous surface current is also examined in detail. Our result excludes the possibility of the recently proposed $d$-wave superconductivity having the surface flow and finite total current.

Abstract:
We study the tunneling of Bogoliubov excitations through a barrier in a Bose-Einstein condensate. We extend our previous work [Phys. Rev. A \textbf{78}, 013628 (2008)] to the case when condensate densities are different between the left and right of the barrier potential. In the framework of the Bogoliubov mean-field theory, we calculate the transmission probability and phase shift, as well as the energy flux and quasiparticle current carried by Bogoliubov excitations. We find that Bogoliubov phonons twist the condensate phase due to a back-reaction effect, which induces the Josephson supercurrent. While the total current given by the sum of quasiparticle current and induced supercurrent is conserved, the quasiparticle current flowing through the barrier potential is shown to be remarkably enhanced in the low energy region. When the condensate densities are different between the left and right of the barrier, the excess quasiparticle current, as well as the induced supercurrent, remains finite far away from the barrier. We also consider the tunneling of excitations and atoms through the boundary between the normal and superfluid regions. We show that supercurrent can be generated inside the condensate by injecting free atoms from outside. On the other hand, atoms are emitted when the Bogoliubov phonons propagate toward the phase boundary from the superfluid region.

Abstract:
We investigate tunneling properties of Bogoliubov mode in a Bose-Einstein condensate. Using an exactly solvable model with a delta-functional barrier, we show that each component in the two-component wavefunction (u,v) of low-energy Bogoliubov phonon has the same form as the condensate wavefunction in the supercurrent state. As a result, the currents J_u and J_v associated with u and v, respectively, have the same tunneling properties as those of supercurrent carried by condensate. Thus, the tunneling of low-energy Bogoliubov phonon described by the tunneling of these two currents shows perfect transmission. We also show that the supercurrent behaviors of Bogoliubov phonon still exist in the presence of supercurrent carried by condensate, except in the critical supercurrent state. In the critical current state, the perfect transmission is absent, because J_u or J_v exceeds their upper limit given by the critical value of the supercurrent associated with the condensate. Our results consistently explain the recently proposed two tunneling phenomena associated with Bogoliubov phonon, namely, the anomalous tunneling effect (perfect transmission in the low-energy limit) and the breakdown of the perfect transmission in the critical supercurrent state.

Abstract:
We theoretically propose a method to identify $\pm s$-wave order parameter in recently discovered Fe-pnictide superconductors. Our idea uses the Riedel anomaly in ac-Josephson current through an SI($\pm$ S) (single-band s-wave superconductor/insulator/$\pm$s-wave two-band superconductor) junction. We show that the Riedel peak effect leads to vanishing ac-Josephson current at some values of biased voltage. This phenomenon does not occur in the case when the $\pm s$-wave superconductor is replaced by a conventional s-wave one, so that the observation of this vanishing Josephson current would be a clear signature of $\pm s$-wave pairing state in Fe-pnictide superconductors.