Spin Gap Phenomenon Research Articles

25aBA-3 冷却フェルミ原子ガスのBCS-BECクロスオーバーにおけるスピンギャップ現象の解析(量子エレクトロニクス(Fermi粒子系の理論),領域1(原子・分子,量子エレクトロニクス,放射線物理))

25aBA-3 冷却フェルミ原子ガスのBCS-BECクロスオーバーにおけるスピンギャップ現象の解析(量子エレクトロニクス(Fermi粒子系の理論),領域1(原子・分子,量子エレクトロニクス,放射線物理))

Spin susceptibility and effects of a harmonic trap in the BCS-BEC crossover regime of an ultracold Fermi gas

We theoretically investigate magnetic properties of a trapped ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation (ETMA), as well as effects of a harmonic trap in the local density approximation (LDA), we calculate the local spin susceptibility $\chi_{\rm t}(r,T)$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. We show that pairing fluctuations cause non-monotonic temperature dependence of $\chi_{\rm t}(r,T)$. Although this behavior looks similar to the spin-gap phenomenon associated with pairing fluctuations in a {\it uniform} Fermi gas, the trapped case is found to also be influenced by the temperature-dependent density profile, in addition to pairing fluctuations. We demonstrate how to remove this extrinsic effect from $\chi_{\rm t}(r,T)$, to study the interesting spin-gap phenomenon purely originating from pairing fluctuations. Since experiments in cold atom physics are always done in a trap, our results would be useful for the assessment of preformed pair scenario, from the viewpoint of spin-gap phenomenon.

Strong-coupling corrections to spin susceptibility in the BCS-BEC-crossover regime of a superfluid Fermi gas

We theoretically investigate the uniform spin susceptibility $\chi$ in the superfluid phase of an ultracold Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region. In our previous paper [H. Tajima, {\it et. al.}, Phys. Rev. A {\bf 89}, 033617 (2014)], including pairing fluctuations within an extended $T$-matrix approximation (ETMA), we showed that strong pairing fluctuations cause the so-called spin-gap phenomenon, where $\chi$ is anomalously suppressed even in the normal state near the superfluid phase transition temperature $T_{\rm c}$. In this paper, we extend this work to the superfluid phase below $T_{\rm c}$, to clarify how this many-body phenomenon is affected by the superfluid order. From the comparison of the ETMA $\chi$ with the Yosida function describing the spin susceptibility in a weak-coupling BCS superfluid, we identify the region where pairing fluctuations crucially affect this magnetic quantity below $T_{\rm c}$ in the phase diagram with respect to the strength of a pairing interaction and the temperature. This spin-gap regime is found to be consistent with the previous pseudogap regime determined from the pseudogapped density of states. We also compare our results with a recent experiment on a $^6$Li Fermi gas. Since the spin susceptibility is sensitive to the formation of spin-singlet preformed pairs, our results would be useful for the study of pseudogap physics in an ultracold Fermi gas on the viewpoint of the spin degrees of freedom.

Spin-gap phenomenon in a strongly interacting ultracold Fermi gas

We investigate magnetic properties of a strongly interacting ultracold Fermi gas. Within the framework of an extended T-matrix approximation, we calculate the spin susceptibility χ in the unitarity limit. We show that effects of pairing fluctuations on this magnetic quantity are quite different in between the normal state and the superfluid phase. In the normal state, pairing fluctuations cause spin-gap phenomenon near the superfluid phase transition temperature Tc, where χ is anomalously suppressed. In the superfluid phase, on the other hand, the ordinary suppression of χ by the BCS energy gap is weakened by pairing fluctuations, because they induce finite density of states inside the gap. Our results indicate that the spin susceptibility is a useful quantity for the study of pairing fluctuations in the BCS-BEC crossover regime of an ultracold Fermi gas.

Publisher's Note: Uniform spin susceptibility and spin-gap phenomenon in the BCS-BEC-crossover regime of an ultracold Fermi gas [Phys. Rev. A89, 033617 (2014)

Publisher's Note: Uniform spin susceptibility and spin-gap phenomenon in the BCS-BEC-crossover regime of an ultracold Fermi gas [Phys. Rev. A<b>89</b>, 033617 (2014)

Uniform spin susceptibility and spin-gap phenomenon in the BCS-BEC-crossover regime of an ultracold Fermi gas

We investigate the uniform spin susceptibility $\chi_{\rm s}$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Including pairing fluctuations within the framework of an extended $T$-matrix approximation, we show that $\chi_{\rm s}$ exhibits non-monotonic temperature dependence in the normal state. In particular, $\chi_{\rm s}$ is suppressed near the superfluid phase transition temperature $T_{\rm c}$ due to strong pairing fluctuations. To characterize this anomalous behavior, we introduce the spin-gap temperature $T_{\rm s}$ as the temperature at which $\chi_{\rm s}$ takes a maximum value. Determining $T_{\rm s}$ in the whole BCS-BEC crossover region, we identify the spin-gap regime in the phase diagram of a Fermi gas in terms of the temperature and the strength of a pairing interaction. We also clarify how the spin-gap phenomenon is related to the pseudogap phenomenon appearing in the single-particle density of states. Our results indicate that an ultracold Fermi gas in the BCS-BEC crossover region is a very useful system to examine the pseudogap phenomenon and the spin-gap phenomenon in a unified manner.

Spin Susceptibility and Strong Coupling Effects in an Ultracold Fermi Gas

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 \(T_{\rm c}\). 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.

Phase Diagram of the Electron-Doped Cuprate Superconductors

We investigate the phase diagram of the electron-doped systems in high-Tc cuprates. We calculate the superconducting transition temperature Tc, the antiferromagnetic transition temperature TN, the NMR relaxation rate 1/T1 with the antiferromagnetic fluctuations in the fluctuation-exchange (FLEX) approximation and with the superconducting fluctuations in the self-consistent t-matrix approximation. Obtained phase diagram has common features as those in the hole-doped systems, including the antiferromagnetic state, the superconducting state and the spin gap phenomenon. Doping-dependences of TN, Tc and Tsg (spin gap temperature) are, however, different with those in the hole-doped systems. These differences are due to the intrinsic nature of the ingap states which are intimately related with the Zhang-Rice singlets in the hole-doped systems and are correlated d-electrons in the electron-doped systems, respectively, which has been shown in the d-p model.

A MICROSCOPIC APPROACH TO SPIN GAP AND SINGLE CuO2 PLANE SUPERCONDUCTIVITY

We sharpen the RVB mechanism of superconductivity proposed by Anderson in 1987 and explain the spin gap phenomenon as well as superconductivity in a single CuO 2 layer. We state our mechanism in the form a theorem, and heuristic proof, in which the neutral spinon pairing in the spin gap phase frustrates the single electron kinetic energy leading to a new "singular" Landau parameter, which is a finite "tomographic" BCS interaction in an underlying tomographic Luttinger liquid.

Spin-gap phenomenon by an SO(5) model

Thermodynamic properties of the SO(5) theory for the high- T c superconductivity (SC) are explored by means of Monte Carlo simulations on a classical model hamiltonian. Temperature versus doping rate phase diagram with a bicritical point is obtained. Enhancement of antiferromagnetism (AF) correlations is observed above the SC critical temperature. Its relation with the spin-gap phenomenon is addressed.

THE STUDY ON THE SPIN GAP PHENOMENON IN OXYGEN DEFICIENT YBa2Cu3O6+δ AND Ca-DOPED Y1-xCaxBa2Cu3O6+δ SUPERCONDUCTORS

The understanding of the spin gap phenomenon in the normal state of the high temperature superconductors can provide the mechanism of the high temperature superconductivity. A specific function of thermal excitation for quasiparticles was introduced based on the experimental relationship between resistivity and temperature. This specific function describes the deviation in resistivity from the T-linear relationship w.r.t. the normal state of the high temperature superconductors. With this function, the spin gap is naturally introduced. Our experimental results indicate that the spin gap behavior is closely related not only to the oxygen deficiency but also to the structural change in the a–b plane. Furthermore, we found that the crossover from anomalous metallic state to spin gap state takes place within a temperature range T S &lt;T&lt;T*, which depends on the oxygen content and the Ca-doping level. Pressure effects on the spin gap phenomenon in bulk samples of oxygen-deficient YBa 2 Cu 3 O 6+δ and Ca-doped Y 1-x Ca x Ba 2 Cu 3 O 6+δ were also investigated. Under high hydrostatic pressure the spin gap behavior is also severely influenced by the contraction of the a–b plane due to the pressure.

Impurity-induced spin polarization and NMR line broadening in underdoped cuprates

We present a theory of magnetic (S=1) Ni and nonmagnetic Zn impurities in underdoped cuprates. Both types of impurities are shown to induce S=1/2 moments on Cu sites in the proximity of the impurity, a process which is intimately related to the spin gap phenomenon in cuprates. Below a characteristic Kondo temperature, the Ni spin is partially screened by the Cu moments, resulting in an effective impurity spin S=1/2. We further analyze the Ruderman-Kittel-Kasiya-Yosida-type response of planar Cu spins to a polarization of the effective impurity moments and derive expressions for the corresponding ^{17}O NMR line broadening. The peculiar aspects of recent experimental NMR data can be traced back to different spatial characteristics of Ni and Zn moments as well as to an inherent temperature dependence of local antiferromagnetic correlations.

Perturbation Theory on the Transition Temperature and Electronic Properties of Organic Superconductor

We study the superconducting transition temperature and the electronic properties of the metallic phase of $\kappa$-type (BEDT-TTF)$_2$X which shows unconventional properties in experiments, on the basis of the third order perturbation theory for a simple effective Hubbard model of a nearly triangular lattice. Appropriate transition temperatures and $d_{x^2-y^2}$ symmetry of the gap function are obtained in good agreement with experimental results. We also calculate the transition temperature by the fluctuation-exchange approximation(FLEX) in order to compare the two approaches; FLEX gives higher transition temperatures rather than the perturbation approach. However, it is also found that the vertex corrections, which are ignored in FLEX, have a crucial effect on $T_{\rm c}$ for strongly frustrated systems. The density of states and the normal self-energy calculated in this perturbation scheme show the nature of the conventional Fermi liquid near the Mott-insulator. Thus, our perturbation approach is applicable to the conventional metallic phase of this compound, while it cannot explain the (pseudo-)spin gap phenomenon which signals the non-Fermi liquid.

Antiferromagnetism and superconductivity transitions with SO (5) symmetry

Using Monte Carlo simulation we have computed the phase diagram of a superspin model of the SO(5) symmetry between antiferromagnetism (AF) and d-wave superconductivity (SC). A bicritical point is observed at a finite temperature where the second-order AF and SC transition lines merge tangentially into a first-order line in the temperature vs. doping rate phase diagram. In the regime of the doping rate where the SC is achieved at low temperatures, maximal AF correlation length is observed at a temperature above the SC transition point T c when AF coupling is much stronger than SC coupling. The relationship between this behavior and the spin-gap phenomenon is addressed.

High Tc copper oxides: A theoretical view from Mott insulators

The conducting state of high T c cuprates is realized in proximity to the Mott insulators (to be precise the insulating state of charge-transfer type), i.e. in the doped Mott insulators, and their transport and magnetic properties show various anomalies and the conducting state is then called the anomalous metallic state (AMS). Key experimental factors of this AMS are summarized briefly with special emphasis on the spin-gap phenomena. These features are theoretically analyzed based on the slave-boson mean-field approximation to the t-J model and then the effects of fluctuations around these mean-field solutions, treated as gauge fields, are discussed. It is seen that the present theoretical approach will be a first step towards the coherent understanding of the mysterious properties of AMS of doped Mott insulators.

On the spin excitations of high- T c cuprates

The results of theoretical analysis of the spin excitation of high- T c cuprates based on the slave-boson mean-field approximation of the t-J model are summarized with special emphasis on the spin gap phenomenon typically seen in NMR rate and neutron scattering. Possible consequences of the spin gap on the anomalous frequency shifts of some particular oxygen phonon modes and important roles played by disorder are indicated.

Auxiliary boson approach for electronic states in the two-dimensional Hubbard model

Electronic states in the two-dimensional Hubbard model are studied in the doped paramagnetic states by use of the auxiliary boson approach. Four auxiliary bosons are introduced by means of the Hubbard-Stratonovich transformation within the functional integral treatment. These bosons correspond to one charge and three spin fluctuations. An effective model is formulated. Going beyond the boson fluctuations around the saddle point, the single-electron Green's function including one-loop self-energy effects of fermion-boson interaction is derived. The behavior of the fermion self-energy, spectral functions, and density of states are investigated for several values of the Coulomb interaction $U$ within the limit imposed by the Stoner criterion and also for small and moderate doping concentrations $\ensuremath{\delta}$. For small doping $(\ensuremath{\delta}=0.2)$, as $U$ approaches a value determined by the Stoner criterion, the spin-boson spectrum has a striking low-energy enhancement around $\mathbf{q}\ensuremath{\sim}2{\mathbf{k}}_{F}.$ This enhancement of the spin fluctuation causes a non-Fermi-liquid-like low-energy $\ensuremath{\omega}$ linear dependence in the imaginary part of the self-energy. Due to the self-energy effects, band splittings and a band narrowing are produced in the spectral functions. As a consequence of this, the density of states has pseudogap structures around the quasiparticle band with a narrow bandwidth on the Fermi energy. These features seem to be precursors of the metal-insulator (Mott-Hubbard) transition and they might be related to the spin-gap phenomena observed in high-${T}_{c}$ materials. Our results for the density of states, the spectral function, and the band dispersions show qualitative agreement with the data of finite-size cluster simulations.

The spin gap and extended t- J model

Key experimental facts of high T c cuprates have been summarized and theoretical understanding of these systems viewed as doped Mott insulators is given based on the slave-boson mean-field theory of the extended t- J model. A special emphasis is placed on the spin-gap phenomena. Effects of fluctuations around this mean field theory treated as a gauge field are also briefly discussed.

Cuprate superconductors from the viewpoint of strong correlation

There is now a growing consensus that the physics of cuprate superconductors is dominated by strong correlation and that the fundamental challenge to the theorist is to achieve an understanding of the doped Mott-Hubbard insulator. From this viewpoint, the Hubbard and the t-J models are reasonable Hamiltonians to study. I shall review the gauge theory description of the t-J model. I shall discuss two recent advances: 1) the study of bosons in a strongly fluctuating gauge field in collaboration with Derek Lee and Don Kim, and 2) the descripton of the underdoped regime, focusing on the photoemission spectra and the relation to the spin gap phenomenon, in collaboration with Xiao-Gang Wen.

Theory of highT c cuprates: Extendedt-J model

Key experimental facts of highT c cuprates have been summarized briefly and the present status of theoretical understanding of these systems viewed as doped Mott insulators is given based on the slave-boson mean-field theory of the extendedt-J model with special emphasis on the spin-gap phenomena. It has been indicated that this spin gap is sensitive to disorder. Various questions including effects of fluctuations around this mean field theory treated as a gauge field are discussed.