論文

We explore a novel type of pairing in the repulsive Hubbard model with a confinement potential. Such an undertaking situation including the confinement potential is realized in a part of intense spatial modulations observed in High-Tc cuprate superconductors, while an atomic Fermi gas loaded on an optical lattice is described by the Hubbard model with the confinement potential. In this paper, applying the exact diagonalization method to a one-dimensional Hubbard model with the confinement potential, we find that, when U exceeds a critical value, the binding energy of two Fermi atoms becomes 'negative, indicating that an attractive interaction effectively works between two fermions. In this case, a 'Mott core' appears in the confinement center, where each site is occupied by one atom, and the Cooper-pair function strongly develops between fermions in the left and right hand sides of this core. © 2006 Elsevier B.V. All rights reserved.

In order to understand what kind of information can be extracted from the vortex-core structure in superfluid fermion-atom gases we make a systematic study for the core structure of a singly quantized vortex in the range of broad Feshbach resonance, solving numerically the generalized Bogoliubov-de Gennes equation derived from the fermion-boson model. Numerical calculations reveal that the vortex core can be well characterized by three length scales from the spatial variation of the fermionic and bosonic gap functions. We also predict that the profile of matter depletion and the quasiparticle spectrum show distinctive differences between the BCS and Bose-Einstein Condensate regimes. © 2006 The American Physical Society.

We investigate a strongly correlated Bose gas in an optical lattice. Extending the standard-basis operator method developed by Haley and Erdös to a boson Hubbard model, we calculate excitation spectra in the superfluid phase, as well as in the Mott insulating phase, at T=0. In the Mott phase, the excitation spectrum has a finite energy gap, reflecting the localized character of atoms. In the superfluid phase, the excitation spectrum is shown to have an itinerant-localized dual structure, where the gapless Bogoliubov mode (which describes the itinerant character of superfluid atoms) and a band with a finite energy gap coexist. We also show that the rf-tunneling current measurement would give useful information about the duality of a strongly correlated superfluid Bose gas near the superfluid-insulator transition. © 2006 The American Physical Society.

We theoretically propose a method to identify ±s -wave order parameter in recently discovered Fe-pnictide superconductors. Our idea uses the Riedel anomaly in ac-Josephson current through a SI (±S) (single-band s -wave superconductor/insulator/ ±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 ±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 ±s -wave pairing state in Fe-pnictide superconductors. © 2009 The American Physical Society.

We investigate the possibility of the local induction of the antiferromagnetism (AF) in high-(Formula presented) superconductors and U-based heavy fermion compounds. In the former case, assuming the d-wave superconductivity in the bulk system, we find that AF can locally appear around surfaces and impurities and can coexist with the d-wave superconductivity. The induced AF is enhanced near the surface by the presence of superconductivity. Furthermore, the zero-energy bound state near the (110) surface of (Formula presented)-wave superconductors is split by the local AF, as was observed in (Formula presented) We also show in a model that this phenomenon is mathematically equivalent to (1) the surface (Formula presented)-wave superconductivity, which has been also proposed in the high-(Formula presented) cuprates, and (2) the local AF in the unconventional spin-density wave, which has been proposed as a candidate for the magnetism in (Formula presented) In particular, the case (2) can explain the recent experiment for (Formula presented) which observes that the temperature at which the antiferromagnetic moment appears is lower than the phase-transition temperature. © 1999 The American Physical Society.

We investigate local characters of spin susceptibility around a nonmagnetic impurity in the normal state of high-Tc cuprate superconductors. In a model two-dimensional system with strong antiferromagnetic (AF) spin fluctuations and with an extended impurity potential which is finite not only at the impurity site but also around it, we find that the AF susceptibility and the uniform one are strongly enhanced around the impurity. In particular, the uniform susceptibility which is almost temperature-independent in the clean system remarkably increases with decreasing temperature. We also show that the local enhancement of the susceptibility is due to (1) an increase of the local density of states at the Fermi level near the impurity site, and (2) a mode-mode coupling effect which is caused by the impurity potential. Our results can explain the recent Knight shift measurements in YBa2(Cu1-xZnx)3O6+y and YBa2(Cu1-xLix)3O6+y showing a Curie-Weiss temperature dependence of the uniform susceptibility at (around) the impurities, and also agree with the recent experiments on the nuclear spin-lattice relaxation rate in Zn-doped YBa2Cu3O6+y and YBa2Cu4O8 which observed anomalous enhancement of the low-energy AF spin fluctuations.

We theoretically investigate antiferromagnetic (AF) spin fluctuations in impurity-doped high-Tcsuperconductivity. We assume a dx2-y2-wave superconductor with strong AF spin fluctuations, and take into account nonmagnetic impurities within the t-matrix approximation. In the clean system, the imaginary part of the AF spin susceptibility (Imχ(Q,ω)) is suppressed far below the excitation gap Eg= 2 × Max[Δp] (Δp: superconducting order parameter), while it has a peak slightly below Eg. On the other hand, in the presence of unitarity scatterers, it is shown that Imχ(Q,ω) far below Egincreases with decreasing temperature even in the superconducting state. As a result, at low temperatures, Imχ(Q,ω) has two peaks far and slightly below Egas observed in Zn-doped YBa2Cu3O6.97. In addition, because of the enhancement of the low-energy AF spin fluctuations, the nuclear spin-lattice relaxation rate on Cu ((1/T1T)Cu) also increases at low temperatures in contrast to the case of the clean superconductivity. This result can explain the recent experiment on (1/T1T)Cuin Zn-doped YBa2Cu4O8.

©2017 The Physical Society of Japan. We theoretically investigate normal-state properties of a unitary Bose–Fermi mixture. Including strong hetero-pairing fluctuations, we evaluate the Bose and Fermi chemical potential, internal energy, pressure, entropy, as well as specific heat at constant volume C V , within the framework of a combined strong-coupling theory with exact thermodynamic identities. We show that hetero-pairing fluctuations at the unitarity cause non-monotonic temperature dependence of C V , being qualitatively different from the monotonic behavior of this quantity in the weak- and strong-coupling limit. On the other hand, such an anomalous behavior is not seen in the other quantities. Our results indicate that the specific heat C V , which has recently become observable in cold atom physics, is a useful quantity for understanding strong-coupling aspects of this quantum system.

In order to explore a universal feature of atomic Fermi gases loaded on optical lattices, we make a systematic study of the particle density profile for one- and two-dimensional attractive Hubbard models with harmonic potential wells. Using the exact diagonalization scheme and the density-matrix renormalization group technique, we show that fine inhomogeneous zigzag patterns universally emerge in the above models. Theoretical and numerical analyses suggest that these structures originate from an effective repulsive interaction between tightly bound pairs and a breakdown of translational invariance. Furthermore, it is emphasized that the pattern obtained numerically in the two-dimensional model is the checkerboard type, which is very similar to results recently observed in a vortex core of high- Tc cuprate superconductor. © 2006 The American Physical Society.

© 2015 American Physical Society. We investigate the superfluid properties of a one-component Fermi gas with a uniaxially anisotropic p-wave pairing interaction, Ux>Uy=Uz [where Ui(i=x,y,z) is a pi-wave pairing interaction]. This type of interaction is considered to be realized in a K40 Fermi gas. Including pairing fluctuations within a strong-coupling T-matrix theory, we determine the px-wave superfluid phase transition temperature Tcpx, as well as the other phase transition temperature Tcpx+ipy(

We theoretically assess the conjecture proposed by Kovtun, Son, and Starinets, stating that the ratio η/s of the shear viscosity η to the entropy density s has the lower bound as η/s ≥ ħ/(4πkB). In the normal state of a mass-imbalanced ultracold Fermi gas, consistently including strong-coupling corrections to both η and s within the self-consistent T-matrix approximation, we evaluate η/s over the entire BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, in the presence of mass imbalance. We find that η/s achieves the minimum value 4.5 × ħ/(4πkB), not at the unitarity, but slightly in the BEC regime, (kFas)-1 ≃ 0:4 > 0 (where as is the s-wave scattering length, and kF is the Fermi momentum). In contract to the previous expectation, we find that this lower bound is almost independent of mass imbalance: Our results predict that all the mass-balanced 6Li-6Li and 40K-40K mixtures and the mass-imbalanced 40K-161Dy mixture give almost the same lower bound of η/s. We also point out that the two quantum phenomena, Pauli blocking and bound-state formation, are crucial keys for the lower bound of η/s.

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We theoretically investigate the isothermal compressibility κT in the normal state of an ultracold Fermi gas with a tunable attractive interaction. We calculate this thermodynamic quantity by considering fluctuations in the Cooper channel, within the framework of the self-consistent T-matrix approximation (SCTMA). For comparison, we also evaluate this quantity in a “non”-self-consistent T-matrix approximation (TMA). We show that the calculated κT diverges at Tc in the BCS–BEC crossover region. On the other hand, such a singular behavior is absent when we deal with this quantity in SCTMA. We point out that the origin of this difference is the neglect of an effective inter-pair interaction in the former approximation. We also explicitly show how such an interaction is involved in the theory when one deals with pairing fluctuations in SCTMA. Our results indicate that the isothermal compressibility is a useful quantity in considering how preformed Cooper pairs interact with one another in the BCS–BEC crossover regime of an ultracold Fermi gas.

We present a theoretical review of the recent progress in non-equilibrium BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover physics. As a paradigmatic example, we consider a strongly interacting driven-dissipative two-component Fermi gas where the non-equilibrium steady state is tuned by adjusting the chemical potential difference between two reservoirs that are coupled with the system. As a powerful theoretical tool to deal with this system, we employ the Schwinger-Keldysh Green’s function technique. We systematically evaluate the superfluid transition, as well as the single-particle properties, in the non-equilibrium BCS-BEC crossover region, by adjusting the chemical potential difference between the reservoirs and the strength of an s-wave pairing interaction associated with a Feshbach resonance. In the weak-coupling BCS side, the chemical potential difference is shown to imprint a two-step structure on the particle momentum distribution, leading to an anomalous enhancement of pseudogap, as well as the emergence of exotic Fulde-Ferrell-Larkin-Ovchinnikov-type superfluid instability. Since various non-equilibrium situations have recently been realized in ultracold Fermi gases, the theoretical understanding of non-equilibrium BCS-BEC crossover physics would become increasingly important in this research field.

We theoretically investigate the temperature dependence of nuclear spin–lattice relaxation rate T1-1 in bulk odd-frequency superconductivity. For a model odd-frequency pairing interaction, we first evaluate the superconducting order parameter, within the framework of the combined path-integral formalism with the saddle-point approximation. We then calculate T1-1 below the superconducting phase transition temperature Tc, to see how the odd-frequency pairing affects this physical quantity. In the odd-frequency p-wave state, while the so-called coherence peak is suppressed as in the even-frequency p-wave case, T1-1 is found to exhibit the Korringa-law-like behavior (T1-1 / T) except just below Tc, even without impurity scatterings. In the odd-frequency s-wave case, the behavior of T1-1 is found to be sensitive to the detailed spin structure of the superconducting order parameter: In a case, T1-1 is enhanced far below Tc, being in contrast to the conventional (even-frequency) s-wave BCS case, where the coherence peak appears just below Tc. We also show that the calculated T1-1 in the odd-frequency p-wave case well explains the recent experiment on CeRh0.5Ir0.5In5, where the possibility of odd-frequency p-wave superconductivity was recently suggested experimentally.

We investigate the electronic state around a magnetic impurity in the superconductivity in order to clarify how the anisotropy of the s-d interaction works in the presence of the superconducting energy gap. Using the numerical renormalization group method, we obtain regions induced by the anisotropy where two localized excited states with different energies appear at the same time; they cannot obtain as far as the isotropic interaction is considered. This means that the anisotropy of the s-d interaction works relevantly in some cases in the superconducting state. We also examine whether or not the bound state energy for the anisotropic and antiferromagnetic s-d interaction is scaled by TK/Δ (TK: Kondo temperature. Δ: superconducting order parameter), and find that it does not hold in the regions with two bound states.

We investigate the collective phase oscillations in superconductivity, i.e., the Carlson-Goldman mode in the charged system and the phason in the neutral, focusing on their velocities and how they appear in the structure function of the phase fluctuation of the order parameter. Our microscopic theory can cover from the clean to the dirty system, and furthermore it can treat the Landau damping correctly. Based on our formulation, we obtain following results: (1) The velocity of the phason is proportional to (TC- T)1/6(T ≲ TC) in the clean system, though it has been believed as (TC- T)1/4(TC: superconducting transition temperature). (2) The structure function has a central peak which grows as T → TC. This phenomenon is related to the central peak problem in the field of the structural phase transition. (3) The Carlson-Goldman mode can be observed by a tunneling experiment in case of the dirty system, while not in the clean. It is in contrast to the previous prediction. All of these results are found to be deeply related to the presence of the Landau damping as well as the screening effect, both of which are caused by the quasi-particles excited thermally.

We investigate the effective interaction between Cooper-pair molecules in the strong-coupling BEC regime of a superfluid Fermi gas with a Feshbach resonance. Our work uses a path integral formulation and a renormalization group (RG) analysis of fluctuations in a single-channel model. We show that a physical cutoff energy ωc originating from the finite molecular binding energy is the key to understanding the interaction between molecules in the BEC regime. Our work thus clari.es recent results by showing that a M = 2aF is a bare molecular scattering length while a M = (0.6-0.75)aF is the low-energy molecular scattering length renormalized to include high-energy scattering up to ωc (here, aF is the scattering length between Fermi atoms). We also include many-body effects at finite temperatures. We find that aM is strongly dependent on temperature, vanishing at Tc, consistent with the earlier Bose gas results of Bijlsma and Stoof. ©2005 The Physical Society of Japan.

We investigate interband impurity scattering effects on a double gap structure in the superconducting density of states (SDOS) in a two-band superconductor. Using the self-consistent t-matrix theory, we show how the double gap structure gradually disappears/revives when impurity concentration and the magnitude of impurity potential are varied. The increase of impurity concentration leads to an averaged single gap SDOS due to the mixing of two bands by interband scattering. However, this mixing effect is shown to disappear in the strong interband scattering limit. We also show that the intraband impurity scattering suppresses the interband scattering effect because it tends to exclude electrons away from impurity sites. © 2004 Elsevier B.V. All rights reserved.

We present a theoretical study of the BCS-BEC (Bose-Einstein condensation) crossover in a trapped gas of Fermi atoms including the effect of a Feshbach resonance. Going past the simple mean field approximation, we include the effect of fluctuations in the strong coupling limit involving two kinds of Bose molecules, i.e., Feshbach molecules associated with the resonance and preformed Cooper-pairs in which the pairing interaction is mediated by Feshbach quasi-molecules. The superfluid phase transition is shown to change continuously from the BCS-type to a BEC of these two kinds of Bosons, as the threshold energy of the Feshbach resonance is lowered. © 2003 Elsevier Science B.V. All rights reserved.

We theoretically investigate the Carlson-Goldman (CG) mode in two-dimensional dx2-y2-wave superconductivity. In conventional s-wave superconductors, it is known that the CG mode is observed as a peak in the structure function of the pair field susceptibility S(q,ω) only just below the transition temperature Tc and only in dirty systems. On the other hand, in the d-wave state, we show that the peak structure can be observed down to T≁0.2Tc in clean systems. Furthermore, we also show that the peak splits into two when the direction of the momentum q deviates from the qx or qy axes, or nodal directions of the order parameter. These features originate from a singularity in the charge-density fluctuation due to the presence of the nodes of the d-wave order parameter: It enhances the screening of the long-range Coulomb interaction so that the CG mode can exist far below Tc. We also investigate a quasi-two-dimensional system, and show that the Josephson plasma can be observed in S(q,ω) when q is parallel to the c direction.