論文

We investigate magnetic properties and strong coupling corrections in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Within the framework of an extended T-matrix theory, we calculate the spin susceptibility χ above the superfluid phase transition temperature Tc. In the crossover region, the formation of preformed Cooper pairs is shown to cause a non-monotonic temperature dependence of χ, which is similar to the so-called spin-gap phenomenon observed in the under-doped regime of high-T c cuprates. From this behavior of χ, we determine the spin-gap temperature as the temperature at which χ takes a maximum value, in the BCS-BEC crossover region. Since the spin susceptibility is sensitive to the formation of singlet Cooper pairs, our results would be useful in considering the temperature region where pairing fluctuations are important in the BCS-BEC crossover regime of an ultracold Fermi gas. © 2013 Springer Science+Business Media New York.

We theoretically propose a method to detect ±s-wave state in newly discovered Fe-pnictide superconductors, using ac Josephson current through a single-band superconductor/insulator/±s-wave superconductor (S/I/±S) junction. We show that, because of the Riedel anomaly, the ac Josephson current vanishes at some values of biased voltage across the junction. This phenomenon does not occur without the sign difference of order parameters in the two band superconductor, so that the observation of the vanishing ac Josephson current would be a clear signature of ±s-wave pairing symmetry in Fe-pnictides. © 2009 Elsevier B.V. All rights reserved.

We investigate single-particle excitations and strong-coupling effects in the BCS-BEC crossover regime of a superfluid Fermi gas. Including phase and amplitude fluctuations of the superfluid order parameter within a T-matrix theory, we calculate the superfluid density of states (DOS), as well as single-particle spectral weight, over the entire BCS-BEC crossover region below the superfluid transition temperature Tc. We clarify how the pseudogap in the normal state evolves into the superfluid gap, as one passes through Tc. While the pseudogap in DOS continuously evolves into the superfluid gap in the weak-coupling BCS regime, the superfluid gap in the crossover region is shown to appear in DOS after the pseudogap disappears below Tc. In the phase diagram with respect to the temperature and interaction strength, we determine the region where strong pairing fluctuations dominate over single-particle properties of the system. Our results would be useful for the study of strong-coupling phenomena in the BCS-BEC crossover regime of a superfluid Fermi gas. © 2010 The American Physical Society.

We study the tunneling of Bogoliubov excitations through a barrier in a Bose-Einstein condensate. We extend our previous work 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. © 2009 The American Physical Society.

In order to examine the ground state of the single-band Hubbard model from a slightly doped region to an overdoped one, we use the density renormalization group method extended directly to the ladder model and obtain hole profiles with changing the on-site repulsion and the doping ratio. The calculation results in a heavily underdoped region, in which one and two holes (up and down spins) are added, reveal that an attractive interaction works between holes which are confined inside a stripe shape pattern while strong disorders separate the two holes. When doping holes further within an underdoped range, the stripes formed by two holes merge and various stripe structures appear depending on U/t and the doping ratio. The remarkable finding in the underdoped region is a stripe formation composed of 4 holes analytically predicted by Chang and Affleck. On the other hand, in the overdoped range the stripe-like shape becomes very simple, i.e., only a small oscillating charge density profile emerges. These rich features in the underdoped range are relevant to electronic inhomogeneities experimentally observed in high-T c superconductors, while those are directly observable in atomic Fermi gases loaded on optical lattices. © 2009 Springer Science+Business Media, LLC.

In order to study the ground state of the Hubbard model from a slightly doped region to an over-doped one, we directly apply the density renormalization group method to 4-leg × 20-ladder repulsive Hubbard model and calculate hole distribution profiles with changing the on-site repulsion U / t from 0 to 15 and the doping ratio from 0.025 to 0.250. The calculation results in the underdoped range reveal that various stripe structures formed by doped holes merge or separate depending on U / t and the doping ratio. We suggest that these rich features are relevant to modulated hole distributions as experimentally observed in underdoped high-T c superconductors. © 2008.

We investigate the superfluid carrier density ρ s in the BCS-BEC crossover regime of a Fermi superfluid at finite temperatures. Including pairing fluctuations within a Gaussian approximation, we calculate the superfluid order parameter, chemical potential, and ρ s in a consistent manner in the whole BCS-BEC crossover region. In the weak-coupling BCS regime, the temperature dependence of ρ s is dominated by single-particle excitations accompanied by thermal dissociation of Cooper pairs. In the strong-coupling BEC regime, we show that single-particle excitations become less dominant and thermal excitations of collective Bogoliubov mode become important for ρ s . We clarify how the weak-coupling BCS result smoothly changes into the strong-coupling BEC result, as one increases the strength of a pairing interaction. © 2008 Elsevier B.V. All rights reserved.

We investigate the superfluid carrier density ρ s in the BCS-BEC crossover regime of a superfluid Fermi gas at finite temperatures. Including pairing fluctuations within the gaussian fluctuation approximation, we determine the superfluid order parameter Δ, Fermi chemical potential μ, as well as ρ s , in a consistent manner. In the weak-coupling regime, the normal fluid density ρ n ρ-ρ s is dominated by quasi-particle excitations associated with the dissociation of Cooper pairs. As one approaches the BCS-BEC crossover regime, effects of pairing fluctuations on ρ n become strong. In the strong-coupling BEC regime, ρ n is shown to be dominated by Bogoliubov phonon in a molecular Bose superfluid. © 2007 Springer Science+Business Media, LLC.

In the strong-coupling Bose-Einstein condensation (BEC) region where a Feshbach resonance gives rise to tightly bound dimer molecules, we show that a spin-polarized Fermi superfluid reduces to a simple Bose-Fermi mixture of Bose-condensed dimers and the leftover unpaired fermions. Using a many-body functional integral formalism, the Gaussian fluctuations give rise to an induced dimer-dimer interaction mediated by the unpaired fermions, with the dimer-fermion vertex being given by the (mean-field) Born approximation. Treating the pairing fluctuations to quartic order, we show how the action for a spin-polarized Fermi superfluid reduces to one for a Bose-Fermi mixture. This Bose-Fermi action includes an expression for the effective dimer-unpaired fermion interaction in a spin-polarized Fermi superfluid beyond the Born approximation, in the BEC limit. In the low-density limit, we show how this dimer-fermion interaction gives the s -wave scattering length aBF =1.18 aF (aF is the s -wave fermion scattering length), a result first derived by Skorniakov and Ter-Martirosian in 1957 for three interacting fermions. © 2007 The American Physical Society.

The superfluid density is a fundamental quantity describing the response to a rotation as well as in two-fluid collisional hydrodynamics. We present extensive calculations of the superfluid density Ïs in the BCS-BEC crossover regime of a uniform superfluid Fermi gas at finite temperatures. We include strong-coupling or fluctuation effects on these quantities within a Gaussian approximation. We also incorporate the same fluctuation effects into the BCS single-particle excitations described by the superfluid order parameter Î" and Fermi chemical potential Î, using the NoziÃresâ€"Schmitt-Rink approximation. This treatment is shown to be necessary for consistent treatment of Ïs over the entire BCS-BEC crossover. We also calculate the condensate fraction Nc as a function of the temperature, a quantity which is quite different from the superfluid density Ïs. We show that the mean-field expression for the condensate fraction Nc is a good approximation even in the strong-coupling BEC regime. Our numerical results show how Ïs and Nc depend on temperature, from the weak-coupling BCS region to the BEC region of tightly bound Cooper pair molecules. In a companion paper, we derive an equivalent expression for Ïs from the thermodynamic potential, which exhibits the role of the pairing fluctuations in a more explicit manner. © 2007 The American Physical Society.

© Published under licence by IOP Publishing Ltd. We investigate an asymmetric nuclear matter consisting of protons and neutrons with spin degrees of freedom (σ = ↑, ↓). By generalizing the Nozières and Schmitt-Rink theory for two-component Fermi gases to the four-component case, we analyze the critical temperature T c of the superfluid phase transition. Although the pure neutron matter exhibits the dineutron condensation in the low-density region, the superfluid instability toward the deuteron condensation is found to take place as the proton fraction increases. We clarify the mechanism of the competition between the deuteron condensation and dineutron condensation. Our results would serve for understanding the properties of asymmetric nuclear matter realized in the interior of neutron stars.

© 2017, Springer Science+Business Media New York. We theoretically investigate the shear viscosity η, as well as the entropy density s, in the normal state of an ultracold Fermi gas. Including pairing fluctuations within the framework of a T-matrix approximation, we calculate these quantities in the Bardeen–Cooper–Schrieffer (BCS)–Bose–Einstein condensation (BEC) crossover region. We also evaluate η/ s, to compare it with the lower bound of this ratio, conjectured by Kovtun, Son, and Starinets (KSS bound). In the weak-coupling BCS side, we show that the shear viscosity η is remarkably suppressed near the superfluid phase transition temperature T c , due to the so-called pseudogap phenomenon. In the strong-coupling BEC side, we find that, within the neglect of the vertex corrections, one cannot correctly describe η. We also show that η/ s decreases with increasing the interaction strength, to become very close to the KSS bound, ħ/ 4 πk B , on the BEC side.

©2017 The Physical Society of Japan. We theoretically investigate the specific heat CV at constant volume in the normal state of a p-wave interacting Fermi gas. Including fluctuations in the p-wave Cooper channel within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we clarify how CV as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime, CV is shown to be enhanced by p-wave pairing fluctuations, near the superfluid phase transition temperature Tc. Similar enhancement of CV(T ≃ Tc) is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of p-wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the p-wave molecular Bose gas regime, and (3) the region between the two, where p-wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a p-wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above Tc.

Atomic-scale superconductor/ferromagnet (S/F) and superconductor/antiferromagnet (S/AF) multilayered systems are investigated in order to clarify the stability of the π-phase where the phase difference of the superconducting (SC) order parameter between neighboring SC layers is π. We clarify the stable region of this phase in the phase diagram with respect to temperature and exchange field (B) in magnetic layers. In the phase diagram, we show that the π-phase appears in both the S/F and S/AF cases. In particular, although a previous work reported that the π-phase is not obtained for any reasonable value of B in the S/AF case where the band structure in the normal state of SC and magnetic layers are metallic and identical with each other, we find in this case that the stable region of the π-phase is as wide as that in the S/F case under a certain condition. We also investigate how the π-phase is affected by detailed band structures and the symmetry of SC order parameter, and discuss the possibility of this phase in the layered magnetic superconductor, RuSr2GdCu2O8.

In order to study an interplay between electronic inhomogeneity and superconductivity as seen in high-Tc cuprates, we numerically examine attractive Hubbard model in the absence of the translation symmetry. We systematically calculate the particle density profile for both 1-D and 2-D attractive Hubbard models with harmonic potential wells using the exact diagonalization and the density-matrix renormalization group methods. The numerical results reveal that fine inhomogeneous zig-zag patterns universally emerge in the 1-D model case and the zig-zag structure becomes checkerboard type in the 2-D one. Moreover, it is numerically and theoretically found that such inhomogeneities are caused by double occupation component, i.e., pairs tightly bound on a site. © 2007 Elsevier B.V. All rights reserved.

We investigate tunneling properties of Bogoliubov mode in a Bose-Einstein condensate. Using an exactly solvable model with a δ -functional barrier, we show that each component in the two-component wave function (u,v) of low-energy Bogoliubov phonon has the same form as the condensate wave function in the supercurrent state. As a result, the currents Ju and Jv 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 Ju or Jv 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. © 2008 The American Physical Society.

We investigate the possibility of a superfluid-ferromagnet-superfluid (SFS) junction in a superfluid Fermi gas. To examine this possibility in a simple manner, we consider an attractive Hubbard model at T=0 within the mean-field theory. When a potential barrier is embedded in a superfluid Fermi gas with population imbalance (N↑>N↓, where Nσ is the number of atoms with pseudospin σ= ↑, ↓), this barrier is shown to be magnetized in the sense that excess ↑-spin atoms are localized around it. The resulting superfluid Fermi gas is spatially divided into two by this ferromagnet, so that one obtains a junction similar to the superconductor- ferromagnet-superconductor junction discussed in superconductivity. Indeed, we show that the so-called π phase, which is a typical phenomenon in the SFS junction, is realized, where the superfluid order parameter changes its sign across the junction. Our results would be useful for the study of magnetic effects on fermion superfluidity using an ultracold Fermi gas. © 2010 The American Physical Society.

We present a microscopic theory for the c-axis transverse Josephson plasma oscillation in quasi-two-dimensional d-wave superconductors. In our model, the incoherent motion of electrons along the c axis are introduced by potential scattering with arbitrary scattering strength, and their depairing effect on superconductivity is determined self-consistently. We show that the plasma frequency decreases with increasing temperature in the presence of the scattering. In particular, when the scattering strength exceeds a critical value, it vanishes at the transition temperature (Formula presented) as is observed in (Formula presented) In this case, when the scattering is in the Born limit, the V-shaped superconducting density of states (DOS) can be obtained in spite of the impure system. This result can explain why the V-shaped DOS is observed in this material by tunneling experiment although the temperature-dependent plasma indicates the presence of a scattering. Our model also produces a good fit to experimental data on (Formula presented) From the fit, we find that both the superfluid and the normal electrons contribute to the plasma oscillation in this material. This feature is different from the ordinary Josephson plasma, which is the oscillation of only the superfluid component. © 2000 The American Physical Society.

A new experimental method to judge the symmetry of the order parameter in high-Tc superconductivity is proposed. The interference of reflected holes from different directions due to the Andreev reflection causes quite different phenomena among s-,dx2-y2- and dxy-wave superconductivity. It is shown that this interference effect may be observed as a change of the conductance below Tc, which enables us to identify the symmetry of the pairing state in high-Tc superconductivity. Various cases in which the experimental setup deviates from the ideal situation are also studied and experimental condition for this method is clarified.

We present a theoretical explanation for the correlation between the c-axis penetration depth and the c-axis conductivity (σc) in high-Tccuprates which was experimentally discovered by Basov et al. [Phys. Rev. B 50 (1994) 3511]. Our model is based on the BCS theory for the quasi-two-dimensional d-wave superconductivity in which the strength of the incoherency in the c-axis charge dynamics is controlled by potential scatterings. We show that the Basov correlation is realized when the difference in the magnitude of σcamong various high-Tc cuprate materials is dominated not by the damping of electrons but by the carrier density and/or the band mass along the c-axis. It is also shown that there exists a correlation between the c-axis Josephson plasma frequency and σcin high-Tccuprates.