Wave Pairing Interaction Research Articles

Evolution of magnetic correlation in an inhomogeneous square lattice

We explore the magnetic properties of a two-dimensional Hubbard model on an inhomogeneous square lattice, which provides a platform for tuning the bandwidth of the flat band. In its limit, this inhomogeneous square lattice turns into a Lieb lattice, and it exhibits abundant properties due to the flat band structure at the Fermi level. By using the determinant quantum Monte Carlo simulation, we calculate the spin susceptibility, double occupancy, magnetization, spin structure factor, and effective pairing interaction of the system. It is found that the antiferromagnetic correlation is suppressed by the inhomogeneous strength and that the ferromagnetic correlation is enhanced. Both the antiferromagnetic correlation and ferromagnetic correlation are enhanced as the interaction increases. It is also found that the effective $d$-wave pairing interaction is suppressed by the increasing inhomogeneity. In addition, we also study the thermodynamic properties of the inhomogeneous square lattice, and the calculation of specific heat provides good support for our point. Our intensive numerical results provide a rich magnetic phase diagram over both the inhomogeneity and interaction.

Enhancing d -wave superconductivity with nearest-neighbor attraction in the extended Hubbard model

Motivated by the recent discovery of the anomalously nearest-neighbor attraction arising from the electron-phonon coupling, we quantitatively investigate the enhancing effects of this additional attractive channel on the $d$-wave SC based on dynamic cluster quantum Monte Carlo calculations of doped two-dimensional extended Hubbard model with nearest-neighbor attraction $-V$. Focusing on the range of $0<-V/t \le 2$, our simulations indicate that the dynamics of $d$-wave projected pairing interaction is attractive at all frequencies and increases with $|V|$. Moreover, turning on $-V$ attraction enhances the $(\pi,\pi)$ spin fluctuations but only enhances (suppresses) the charge fluctuations for small (large) momentum transfer. Thus, at $V/t=-1$ relevant to ``holon folding branch'', the charge fluctuations are insufficient to compete with $d$-wave pairing interaction strengthened by enhanced spin fluctuations. Our work suggest the underlying rich interplay between the spin and charge fluctuations in giving rise to the superconducting properties.

Enhanced superconductivity in quasiperiodic crystals

We study superconductivity in a family of one dimensional incommensurate system with $s$-wave pairing interaction. The incommensurate potential can alter the spatial characteristics of electrons in the normal state, leading to either extended, critical, or localized wave functions. We find that superconductivity is significantly enhanced when the electronic wave function exhibits a critical multifractal structure. This criticality also manifests itself in the power-law dependence of superconducting temperature on the pairing strength. As a consequence, an extended superconducting domain is expected to exist around the localization-delocalization transition, which can be induced by either tuning the amplitude of the incommensurate potential, or by varying the chemical potential across a mobility edge. Our results thus suggest a novel approach to enhance superconducting transition temperature through engineering of incommensurate potential.

Antiferromagnetic and d -wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group

Using the dynamical mean-field theory (DMFT) as a `booster-rocket', the functional renormalization group (fRG) can be upgraded from a weak-coupling method to a powerful computation tool for strongly interacting fermion systems. The strong local correlations are treated non-perturbatively by the DMFT, while the fRG flow can be formulated such that it is driven exclusively by non-local correlations, which are more amenable to approximations. We show that the full frequency dependence of the two-particle vertex needs to be taken into account in this approach, and demonstrate that this is actually possible -- in spite of the singular frequency dependence of the vertex at strong coupling. We are thus able to present the first results obtained from the DMFT-boosted fRG for the two-dimensional Hubbard model in the strongly interacting regime. We find strong antiferromagnetic correlations from half-filling to 18 percent hole-doping, and, at the lowest temperature we can access, a sizable $d$-wave pairing interaction driven by magnetic correlations at the edge of the antiferromagnetic regime.

Appropriate conditions to realize a p -wave superfluid state starting from a spin-orbit-coupled s -wave superfluid Fermi gas

We theoretically investigate a spin-orbit coupled $s$-wave superfluid Fermi gas, to examine the time evolution of the system, after an $s$-wave pairing interaction is replaced by a $p$-wave one at $t=0$. In our recent paper, we proposed that this manipulation may realize a $p$-wave superfluid Fermi gas, because the $p$-wave pair amplitude that is induced in the $s$-wave superfluid state by a parity-broken antisymmetric spin-orbit interaction gives a non-vanishing $p$-wave superfluid order parameter, immediately after the $p$-wave interaction is turned on. In this paper, using a time-dependent Bogoliubov-de Gennes theory, we assess this idea under various conditions with respect to the $s$-wave and $p$-wave interaction strengths, as well as the spin-orbit coupling strength. From these, we clarify that the momentum distribution of Fermi atoms in the initial $s$-wave state ($t<0$) is a key to produce a large $p$-wave superfluid order parameter. Since the realization of a $p$-wave superfluid state is one of the most exciting and difficult challenges in cold Fermi gas physics, our results may provide a possible way to accomplish this.

Specific Heat and Effects of Uniaxial Anisotropy of ap-Wave Pairing Interaction in a Strongly Interacting Ultracold Fermi Gas

We investigate the specific heat $C_V$ at constant volume and effects of uniaxial anisotropy of a $p$-wave attractive interaction in the normal state of an ultracold Fermi gas. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we evaluate this thermodynamic quantity as a function of temperature, in the whole interaction regime. While the uniaxial anisotropy is not crucial for $C_V$ in the weak-coupling regime, $C_V$ is found to be sensitive to the uniaxial anisotropy in the strong-coupling regime. This originates from the population imbalance among $p_i$-wave molecules ($i=x,y,z$), indicating that the specific heat is a useful observable to see which kinds of $p$-wave molecules dominantly exist in the strong-coupling regime when the $p$-wave interaction has uniaxial anisotropy. Using this strong point, we classify the strong-coupling regime into some characteristic regions. Since a $p$-wave pairing interaction with uniaxial anisotropy has been discovered in a $^{40}$K Fermi gas, our results would be useful in considering strong-coupling properties of a $p$-wave interacting Fermi gas, when the interaction is uniaxially anisotropic.

Dip-Hump Temperature Dependence of Specific Heat and Effects of Pairing Fluctuations in the Weak-Coupling Side of a P-Wave Interacting Fermi Gas

We investigate the specific heat $C_V$ at constant volume in the normal state of a $p$-wave interacting Fermi gas. Including $p$-wave pairing fluctuations within the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that, in the weak-coupling side, $C_V$ exhibits a dip-hump behavior as a function of the temperature. While the dip is associated with the pseudogap phenomenon near $T_{\rm c}$, the hump structure is found to come from the suppression of Fermi quasiparticle scattering into a $p$-wave molecular state in the Fermi degenerate regime. Since the latter phenomenon does not occur in the ordinary $s$-wave interacting Fermi gas, it may be viewed as a characteristic phenomenon associated with a $p$-wave pairing interaction.

A Novel Route to Reach a p-Wave Superfluid Fermi Gas

We theoretically propose an idea to realize a $p$-wave superfluid Fermi gas. To overcome the experimental difficulty that a $p$-wave pairing interaction to form $p$-wave Cooper pairs damages the system before the condensation growth, we first prepare a $p$-wave pair amplitude ($\Phi_{p}$) in a spin-orbit coupled $s$-wave superfluid Fermi gas, without any $p$-wave interaction. Then, by suddenly changing the $s$-wave interaction with a $p$-wave one ($U_{p}$) by using a Feshbach resonance, we reach the $p$-wave superfluid phase with the $p$-wave order parameter being symbolically written as $\Delta_{p}\sim U_{p}\Phi_{p}$. In this letter, we assess this scenario within the framework of a time-dependent Bogoliubov-de Gennes theory. Our results would contribute to the study toward the realization of unconventional pairing states in an ultracold Fermi gas.

Triplet pair amplitude in a trapped s-wave superfluid Fermi gas with broken spin rotation symmetry. II. Three-dimensional continuum case

We extend our recent work [Y. Endo et. al., Phys. Rev. 92, 023610 (2015)] for a parity-mixing effect in a model two-dimensional lattice fermions to a realistic three-dimensional ultracold Fermi gas. Including effects of broken local spatial inversion symmetry by a trap potential within the framework of the real-space Bogoliubov-de Gennes theory at $T=0$, we point out that an odd-parity $p$-wave Cooper-pair amplitude is expected to have already been realized in previous experiments on an (even-parity) $s$-wave superfluid Fermi gas with spin imbalance. This indicates that, when one suddenly changes the $s$-wave pairing interaction to an appropriate $p$-wave one by using a Feshbach technique in this case, a non-vanishing $p$-wave superfluid order parameter is immediately obtained, which is given by the product of the $p$-wave interaction and the $p$-wave pair amplitude that has already been induced in the spin-imbalanced $s$-wave superfluid Fermi gas. Thus, by definition, the system is in the $p$-wave superfluid state, at least just after this manipulation. Since the achievement of a $p$-wave superfluid state is one of the most exciting challenges in cold Fermi gas physics, our results may provide an alternative approach to this unconventional pairing state. In addition, since the parity-mixing effect cannot be explained as far as one deals with a trap potential in the local density approximation (LDA), it is considered as a crucial example which requires us to go beyond LDA.

Pairing fluctuations and an anisotropic pseudogap phenomenon in an ultracold superfluid Fermi gas with pluralp-wave superfluid phases

We investigate superfluid properties of a one-component Fermi gas with a uniaxially anisotropic $p$-wave pairing interaction, $U_x>U_y=U_z$ (where $U_i$ ($i=x,y,z)$ is a $p_i$-wave pairing interaction). This type of interaction is considered to be realized in a $^{40}$K Fermi gas. Including pairing fluctuations within a strong-coupling $T$-matrix theory, we determine the $p_x$-wave superfluid phase transition temperature $T^{p_x}_{\rm c}$, as well as the other phase transition temperature $T_{\rm c}^{p_x+ip_y}$ ($<T_{\rm c}^{p_x}$), below which the superfluid order parameter has the $p_x+ip_y$-wave symmetry. In the normal state near $T^{p_x}_{\rm c}$, $p_x$-wave pairing fluctuations are shown to induce an anisotropic pseudogap phenomenon, where a dip structure in the angle-resolved density of states around $\omega=0$ is the most remarkable in the $p_x$ direction. In the $p_x$-wave superfluid phase ($T_{\rm c}^{p_x+ip_y}<T\le T_{\rm c}^{p_x}$), while the pseudogap in the $p_x$ direction continuously changes to the superfluid gap, the pseudogap in the perpendicular direction to the $p_x$ axis is found to continue developing, because of enhanced $p_y$-wave and $p_z$-wave pairing fluctuations around the node of the $p_x$-wave superfluid order parameter. Since pairing fluctuations are always suppressed in the isotropic $s$-wave superfluid state, this phenomenon is peculiar to an unconventional Fermi superfluid with a nodal superfluid order parameter. Since the $p$-wave Fermi superfluid is the most promising non $s$-wave pairing state in an ultracold Fermi gas, our results would contribute to understanding how the anisotropic pairing fluctuations, as well as the existence of plural superfluid phases, affect many-body properties of this unconventional Fermi superfluid.

Triplet pair amplitude in a trappeds-wave superfluid Fermi gas with broken spin rotation symmetry

We investigate the possibility that the broken spatial inversion symmetry by a trap potential induces a spin-triplet Cooper-pair amplitude in an $s$-wave superfluid Fermi gas. Being based on symmetry considerations, we clarify that this phenomenon may occur, when a spin rotation symmetry of the system is also broken. We also numerically confirm that a triplet pair amplitude is really induced under this condition, using a simple model. Our results imply that this phenomenon is already present in a trapped $s$-wave superfluid Fermi gas with spin imbalance. As an interesting application of this phenomenon, we point out that one may produce a $p$-wave superfluid Fermi gas, by suddenly changing the $s$-wave pairing interaction to a $p$-wave one by using the Feshbach resonance technique. Since a Cooper pair is usually classified into the spin-singlet (and even-parity) state and the spin-triplet (and odd-parity) state, our results would be useful in considering how to mix them with each other in a superfluid Fermi gas. Such admixture has recently attracted much attention in the field of non-centrosymmetric superconductivity, so that our results would also contribute to the further development of this research field, on the viewpoint of cold Fermi gas physics.

Proposed method to realize thep-wave superfluid state using ans-wave superfluid Fermi gas with a synthetic spin-orbit interaction

We theoretically propose an idea to reach the $p$-wave superfluid phase in an ultracold Fermi gas. The key of our idea is that the pairing symmetry of a Fermi superfluid is fully dominated by the symmetry of the superfluid order parameter, which is essentially given by the product of a pair amplitude and a pairing interaction. Noting this, in our proposal, we first prepare a $p$-wave pair amplitude by, not using a $p$-wave interaction, but using the phenomenon that a $p$-wave pair amplitude is induced in an $s$-wave superfluid Fermi gas with antisymmetric spin-orbit interaction. In this case, although the system is still in the $s$-wave superfluid state with the $s$-wave superfluid order parameter, when one suddenly replaces the $s$-wave interaction by an appropriate $p$-wave one (which is possible in cold Fermi gases by using a Feshbach resonance technique), the product of the $p$-wave interaction and the $p$-wave pair amplitude that has already been prepared in the spin-orbit coupled $s$-wave superfluid state immediately gives a finite $p$-wave superfluid order parameter. Thus, at least just after this manipulation, the system is in the $p$-wave superfluid state, being characterized by the artificially produced $p$-wave superfluid parameter. In this paper, to assess our idea, we evaluate the $p$-wave pair amplitude in a spin-orbit coupled $s$-wave superfluid Fermi gas at $T=0$. We determine the region where a large $p$-wave pair amplitude is obtained in the phase diagram with respect to the strengths of the $s$-wave pairing interaction and the spin-orbit coupling. We also discuss the accessibility of this optimal region on the viewpoint of the superfluid phase transition temperature. Since the achievement of a $p$-wave superfluid Fermi gas is one of the most crucial issues in cold atom physics, our proposal would be useful for this exciting challenge.

Proximity of the Superconducting Dome and the Quantum Critical Point in the Two-Dimensional Hubbard Model

We use the dynamical cluster approximation to understand the proximity of the superconducting dome to the quantum critical point in the two-dimensional Hubbard model. In a BCS formalism, T(c) may be enhanced through an increase in the d-wave pairing interaction (V(d)) or the bare pairing susceptibility (χ(0d)). At optimal doping, where V(d) is revealed to be featureless, we find a power-law behavior of χ(0d)(ω=0), replacing the BCS log, and strongly enhanced T(c). We suggest experiments to verify our predictions.

Magnetic correlations on the full chains of ortho-IIYBa2Cu3O6.5

We propose that the NMR line shape on the chain Cu in the stoichiometric high-${T}_{c}$ superconductor ortho-II ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{6.5}$ is determined by the magnetization induced on Cu near O vacancies due to strong magnetic correlations in the chains. An unrestricted Hartree-Fock calculation of a coupled chain-plane Hubbard model with nearest-neighbor $d$-wave pairing interaction shows that the broadening of NMR lines is consistent with disorder-induced magnetization at low temperatures. In addition, we give a possible explanation of the anomalous bimodal line shape observed at high temperatures in terms of nonuniform Cu valence in the chains. The proximity between chains and CuO plane induces anisotropic magnetization on the planar Cu and broadens the plane NMR lines in accordance with that of the chain lines, in agreement with experiment. We discuss implications of the model for other experiments on underdoped ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{7\ensuremath{-}\ensuremath{\delta}}$.

Suppression ofd-wave superconductivity in the checkerboard Hubbard model

Using a dynamical cluster quantum Monte Carlo approximation, we investigate the $d$-wave superconducting transition temperature ${T}_{c}$ in the doped two-dimensional repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings ${t}^{\ensuremath{'}}$ and $t$ in the form of a checkerboard pattern where $t$ is the hopping within a $2\ifmmode\times\else\texttimes\fi{}2$ plaquette, and ${t}^{\ensuremath{'}}$ is the hopping between the plaquettes. We find inhomogeneity suppresses ${T}_{c}$. The characteristic spin excitation energy and the strength of $d$-wave pairing interaction decrease with decreasing ${T}_{c}$, suggesting a strong correlation between these quantities.

Possible vortex splitting in high-temperature cuprate superconductors

We propose that the observed splitting of the vortices in the cuprates into fractional vortices (partons) may be of static rather than of dynamic origin. This interpretation is backed by a study of a model with a dominant $d$-wave and subdominant $s$-wave pairing interaction. We find that the vortex may split into two partons, both of which carry one-half of the magnetic flux quantum. The partons are held together by a confining string along which the phase jumps approximately by $\ensuremath{\pi}$ and their equilibrium distance increases with lowering the energy difference $\ensuremath{\epsilon}$ between the pairing states. The partons become deconfined at the critical point where $\ensuremath{\epsilon}$ vanishes.

Systematic analysis of a spin-susceptibility representation of the pairing interaction in the two-dimensional Hubbard model

A dynamic cluster quantum Monte Carlo algorithm is used to study a spin-susceptibility representation of the pairing interaction for the two-dimensional Hubbard model with an on-site Coulomb interaction equal to the bandwidth for various doping levels. We find that the pairing interaction is well approximated by $\frac{3}{2}\overline{U}{(T)}^{2}\ensuremath{\chi}(K\ensuremath{-}{K}^{\ensuremath{'}})$, with an effective temperature and doping dependent coupling $\overline{U}(T)$ and the numerically calculated spin susceptibility $\ensuremath{\chi}(K\ensuremath{-}{K}^{\ensuremath{'}})$. We show that at low temperatures, $\overline{U}$ may be accurately determined from a corresponding spin-susceptibility based calculation of the single-particle self-energy. We conclude that the strength of the $d$-wave pairing interaction, characterized by the mean-field transition temperature, can be determined from a knowledge of the dressed spin susceptibility and the nodal quasiparticle spectral weight. This has important implications with respect to the questions of whether spin fluctuations are responsible for pairing in the high-${T}_{c}$ cuprates.

Spin susceptibility representation of the pairing interaction for the two-dimensional Hubbard model

Using numerical dynamic cluster quantum Monte Carlo results, we study a simple approximation for the pairing interaction of a two-dimensional Hubbard model with an on-site Coulomb interaction $U$ equal to the bandwidth. We find that with an effective temperature-dependent coupling $\overline{U}(T)$ and the numerically calculated spin susceptibility $\ensuremath{\chi}(K\ensuremath{-}{K}^{\ensuremath{'}})$, the $d$-wave pairing interaction is well approximated by $\frac{3}{2}{\overline{U}}^{2}\ensuremath{\chi}(K\ensuremath{-}{K}^{\ensuremath{'}})$.

Pairing correlation functions in the triangulart−Jmodel:d-wave andf-wave superconductivity

Equal-time pairing correlation functions of the two-dimensional $t\text{\ensuremath{-}}J$ model on the triangular lattice are studied using high-temperature expansions method. We calculate the pairing correlation lengths and the effective pairing interactions down to $T\ensuremath{\sim}0.2t$, and find the growth of pairing correlations. When $tg0$ with hole doping, a rapid growth of effective $d$-wave pairing interaction is found that indicates the resonating-valence-bond superconductivity. In contrast, when $tl0$, where the ferromagnetic correlation and antiferromagnetic correlation compete, correlation lengths of triplet pairings as well as $d$-wave pairing grow at low temperatures, although they do not diverge for $T\ensuremath{\rightarrow}0$ in the competing region, i.e., near half-filling. On the other hand, around $n=0.4$, $f$-wave pairing correlation tends to diverge, although its effective interaction is small. Relation of the present study to the recently discovered superconductor, ${\mathrm{Na}}_{x}\mathrm{Co}{\mathrm{O}}_{2}∙y{\mathrm{H}}_{2}\mathrm{O}$, is discussed.

Proximity effect in normal metal–high-Tcsuperconductor contacts

We study the proximity effect in good contacts between normal metals and high-${T}_{c}$ (${d}_{{x}^{2}\ensuremath{-}{y}^{2\ensuremath{-}}}$-wave) superconductors. We present theoretical results for the spatially dependent order parameter and local density of states, including effects of impurity scattering in the two sides, $s$-wave pairing interaction in the normal metal side (attractive or repulsive) and subdominant $s$-wave paring in the superconductor side. For the [100] orientation, a real combination $d+s$ of the order parameters is always found. The spectral signatures of the proximity effect in the normal metal include a suppression of the low-energy density of states and a finite-energy peak structure. These features are mainly due to the impurity self-energies, which dominate over the effects of induced pair potentials. For the [110] orientation, for moderate transparencies, induction of a $d+is$ order parameter on the superconductor side leads to a proximity induced $is$ order parameter also in the normal metal. The spectral signatures of this type of proximity effect are potentially useful for probing time-reversal symmetry breaking at a [110] interface.