A theory of the fluctuation-induced Nernst effect is developed for arbitrary magnetic fields and temperatures beyond the upper critical field line in a two-dimensional superconductor. First, we derive a simple phenomenological formula for the Nernst coefficient, which naturally explains the giant Nernst signal due to fluctuating Cooper pairs. The latter is shown to be large even far from the transition and may exceed by orders of magnitude the Fermi liquid terms. We also present a complete microscopic calculation (which includes quantum fluctuations) of the Nernst coefficient and give its asymptotic dependencies in various regions on the phase diagram. It is argued that the magnitude and the behavior of the Nernst signal observed experimentally in disordered superconducting films can be well-understood on the basis of the superconducting fluctuation theory.
A comment is made on a letter (Phys. Rev. Lett. {\bf 102}, 067001) and a paper (Phys. Rev. B {\bf 83}, 020506) regarding the correct expression of the thermal current vertex for Cooper pairs.
The observation of a large Nernst signal in cuprates above the superconducting transition temperature has attracted much attention. A potential explanation is that it originates from superconducting fluctuations. Although the Nernst signal is indeed consistent with gaussian fluctuations for overdoped cuprates, gaussian theory fails to describe the temperature dependence seen for underdoped cuprates. Here, we consider the vertex correction to gaussian theory resulting from the pseudogap. This yields a Nernst signal in good agreement with the data.
This is an extended Reply to Comment by A. Sergeev, M.Y. Reizer, and V. Mitin [arXiv:0906.2389] on our Letter [Phys. Rev. Lett. 102, 067001 (2009)]. We explicitly demonstrate that all claims by Sergeev et al. are completely unfounded, because their underlying theoretical work contains multiple errors and inconsistencies. For this reason, there is no need to revise the existing theories of thermoelectric response in superconductors.
We present a study of the Nernst effect in amorphous 2D superconductor InO$_x$, whose low carrier density implies low phase rigidity and strong superconducting phase fluctuations. Instead of presenting the abrupt jump expected at a BCS transition, the Nernst signal evolves continuously through the superconducting transition as previously observed in underdoped cuprates. This contrasts with the case of Nb$_{0.15}$Si$_{0.85}$, where the Nernst signal due to vortices below T$_{c}$ and by Gaussian fluctuations above are clearly distinct. The behavior of the ghost critical field in InO$_x$ points t…
When a superconductor is warmed above its critical temperature $T_c$, long range order is destroyed by fluctuations in the order parameter. These fluctuations can be probed by measurements of conductivity, diamagnetism, and of the Nernst effect. Here, we study a regime where superconductivity is destroyed by phase fluctuations arising from a dilute liquid of mobile vortices. We find that the Nernst effect and diamagnetic response differ significantly from Gaussian fluctuations -- in particular, a much sharper decay with temperature is obtained. We predict a rapid onset of Nernst signal at a te…
We present a new method to study the Nernst effect and diamagetism of an extreme type-II superconductor dominated by phase fluctuations. We work directly with vortex variables and our method allows us to tune vortex parameters (e.g., core energy and number of vortex species). We find that diamagnetic response and transverse thermoelectric conductivity ($α_{xy}$) persist well above the Kosterlitz-Thouless transition temperature, and become more pronounced as the vortex core energy is increased. However, they \textit{weaken} as the number of internal vortex states are increased. We find that $α_…
Long-range order is destroyed in a superconductor warmed above its critical temperature (Tc). However, amplitude fluctuations of the superconducting order parameter survive and lead to a number of well established phenomena such as paraconductivity : an excess of charge conductivity due to the presence of short-lived Cooper pairs in the normal state. According to an untested theory, these pairs generate a transverse thermoelectric (Nernst) signal. In amorphous superconducting films, the lifetime of Cooper pairs exceeds the elastic lifetime of quasi-particles in a wide temperature range above T…
In amorphous superconducting thin films of $Nb_{0.15}Si_{0.85}$ and $InO_x$, a finite Nernst coefficient can be detected in a wide range of temperature and magnetic field. Due to the negligible contribution of normal quasi-particles, superconducting fluctuations easily dominate the Nernst response in the entire range of study. In the vicinity of the critical temperature and in the zero-field limit, the magnitude of the signal is in quantitative agreement with what is theoretically expected for the Gaussian fluctuations of the superconducting order parameter. Even at higher temperatures and fin…
We study the Nernst effect in fluctuating superconductors by calculating the transport coefficient $α_{xy}$ in a phenomenological model where relative importance of phase and amplitude fluctuations of the order parameter is tuned continuously to smoothly evolve from an effective XY model to more conventional Ginzburg-Landau description. To connect with a concrete experimental realization we choose the model parameters appropriate for cuprate superconductors and calculate $α_{xy}$ and the magnetization ${\bf M}$ over the entire range of experimentally accessible values of field, temperature and…
In a recent Letter, Serbyn et al. [A] investigated thermomagnetic effects above the superconducting transition and generalized previous works for arbitrary magnetic fields and temperatures. While the results of [A] have been confirmed in [B], we have strong objections: (i) According to our results [C], the linear response calculation does not require any correction from the magnetization currents; (ii) The result of [A,B] is giant, because unlike the normal Fermi liquid, it is of zero order in the particle-hole asymmetry. Changing the interaction constant in the Cooper channel leads to ridicul…
A simple model describing the Nernst-Ettingshausen effect (NEE) in two-component electronic liquids is formulated. The examples considered include graphite, where the normal and Dirac fermions coexist, superconductor in fluctuating regime, with coexisting Cooper pairs and normal electrons, and the inter-stellar plasma of electrons and protons. We give a general expression for the Nernst constant and show that the origin of a giant NEE is in the strong dependence of the chemical potential on temperature in all cases.
Recent experiments show that the Nernst-Ettingshausen effect is orders of magnitude stronger than the thermoelectric Seebeck effect in superconductors above the critical temperature. We explain different magnitudes of the two effects accounting for the magnetization current of virtual Cooper pairs. The method allows for detailed understanding of the surprising non-monotonic dependence of the Nernst-Ettingshausen coefficient on the magnetic field.
The Nernst effect has recently proven a sensitive probe for detecting unusual normal state properties of unconventional superconductors. In particular, it may sensitively detect Fermi surface reconstructions which are connected to a charge or spin density wave (SDW) ordered state, and even fluctuating forms of such a state. Here we summarize recent results for the Nernst effect of the iron pnictide superconductor $\rm LaO_{1-x}F_xFeAs$, whose ground state evolves upon doping from an itinerant SDW to a superconducting state, and the cuprate superconductor $\rm La_{1.8-x}Eu_{0.2}Sr_xCuO_4$ which…
Fluctuating Cooper pairs formed by spatially separated electrons and holes are precursors of their equilibrium condensation. Their presence strongly impacts transport phenomena and interlayer tunneling in double-layer systems above the transition temperature. Here, we consider a hybrid graphene/quantum well double-layer system and focus on the dynamics of fluctuating Cooper pairs formed by conventional electrons and Dirac holes. We demonstrate that the chiral nature of Dirac holes is manifested in the presence of two (almost) degenerate competing pairing channels, which are intertwined by effe…
Recent scanning tunnelling microscopy experiments in NbN thin disordered superconducting films found an emergent inhomogeneity at the scale of tens of nanometers. This inhomogeneity is mirrored by an apparent dimensional crossover in the paraconductivity measured in transport above the superconducting critical temperature $T_c$. This behavior was interpreted in terms of an anomalous diffusion of fluctuating Cooper pairs, that display a {\em quasi-confinement} (i.e., a slowing down of their diffusive dynamics) on length scales shorter than the inhomogeneity identified by tunnelling experiments.…
We investigate the spin-Nernst effect in time-reversal invariant topological superconductors, and show that it provides a smoking-gun evidence for helical Cooper pairs. The spin-Nernst effect stems from asymmetric, in spin space, scattering of quasiparticles at nonmagnetic impurities, and generates a transverse spin current by the temperature gradient. Both the sign and the magnitude of the effect sensitively depend on the scattering phase shift at impurity sites. Therefore the spin-Nernst effect is uniquely suitable for identifying time-reversal invariant topological superconducting orders.
We present a study of the Nernst effect in amorphous superconducting thin films of Nb$_{0.15}$Si$_{0.85}$. The field dependence of the Nernst coefficient above T$_{c}$ displays two distinct regimes separated by a field scale set by the Ginzburg-Landau correlation length. A single function $F(ξ)$, with the correlation length as its unique argument set either by the zero-field correlation length (in the low magnetic field limit) or by the magnetic length (in the opposite limit), describes the Nernst coefficient. We conclude that the Nernst signal observed on a wide temperature ($30 \times T_c$) …
We propose the magnetoplasmon resonance technique to investigate two-dimensional superconductors (taking MoS$_2$ as an example) in the fluctuating regime, where the temperature is slightly above the critical temperature of the superconducting transition. Thus, unpaired electrons and fluctuating Cooper pairs coexist in the system and interact with each other via long-range Coulomb forces, forming a Bose-Fermi mixture. We expose the sample to external time-dependent electromagnetic field with a frequency in sub-terahertz range and a permanent magnetic field, and show that the magnetoplasmon resp…
The Nernst effect in metals is highly sensitive to two kinds of phase transition: superconductivity and density-wave order. The large positive Nernst signal observed in hole-doped high-Tc superconductors above their transition temperature Tc has so far been attributed to fluctuating superconductivity. Here we show that in some of these materials the large Nernst signal is in fact caused by stripe order, a form of spin / charge modulation which causes a reconstruction of the Fermi surface. In LSCO doped with Nd or Eu, the onset of stripe order causes the Nernst signal to go from small and negat…
We derive exact expressions for the fluctuation conductivity in two dimensional superconductors as a function of temperature and magnetic field in the whole fluctuation region above the upper critical field H_{c2}(T). Focusing on the vicinity of the quantum phase transition near zero temperature, we propose that as the magnetic field approaches the line near H_{c2}(0) from above, a peculiar dynamic state consisting of clusters of coherently rotating fluctuation Cooper-pairs forms and estimate the characteristic size and lifetime of such clusters. We find the zero temperature magnetic field dep…
Following the observation of an anomalous Nernst signal in cuprates, the Nernst effect was explored in a variety of metals and superconductors during the past few years. This paper reviews the results obtained during this exploration, focusing on the Nernst response of normal quasi-particles as opposed to the one generated by superconducting vortices or by short-lived Cooper pairs. Contrary to what has been often assumed, the so-called Sondheimer cancelation does not imply a negligible Nernst response in a Fermi liquid. In fact, the amplitude of the Nernst response measured in various metals i…
We theoretically investigate the vortex spin Hall effect, i.e., a novel spin Hall effect driven by the motion of superconducting vortices, by focusing on the role of superconducting fluctuations. Within the BCS-Gor'kov microscopic approach combined with the Kubo formula, we find a strong similarity between the vortex spin Hall effect and the vortex Nernst/Ettingshausen effect. Calculated temperature dependence of the voltage signal due to the inverse vortex spin Hall effect exhibits a strong enhancement by vortex fluctuations. This result not only provides a possible explanation for a prominen…
The Nernst effect is the transverse electric field produced by a longitudinal thermal gradient in presence of magnetic field. In the beginning of this century, Nernst experiments on cuprates were analyzed assuming that: i) The contribution of quasi-particles to the Nernst signal is negligible; and ii) Gaussian superconducting fluctuations cannot produce a Nernst signal well above the critical temperature. Both these assumptions were contradicted by subsequent experiments. This paper reviews experiments documenting multiple sources of a Nernst signal, which, according to the Brigman relation, m…
A liquid of superconducting vortices generates a transverse thermoelectric response. This Nernst signal has a tail deep in the normal state due to superconducting fluctuations. Here, we present a study of the Nernst effect in two-dimensional hetero-structures of Nb-doped strontium titanate (STO) and in amorphous MoGe. The Nernst signal generated by ephemeral Cooper pairs above the critical temperature has the magnitude expected by theory in STO. On the other hand, the peak amplitude of the vortex Nernst signal below $T_c$ is comparable in both and in numerous other superconductors despite the …
Temperature dependencies of excess conductivity, Sigma', have been studied in detail for three FeSe_{0.94} textured polycrystalline samples prepared by partial melting and solid state reaction. It was revealed that both Sigma' and its temperature dependence are extremely sensitive to the method of sample preparation. Then, it was shown that in the range from the superconducting transition temperature Tc ~ 9 K up to the characteristic temperature T_01 ~ 19 K, Sigma'(T) obeys the classical fluctuation theories of Aslamazov-Larkin (AL) and Hikami-Larkin (Maki-Thompson (MT) term) pointing to the e…
In a two-dimensional noncentrosymmetric Ising superconductor in the fluctuating regime under the action of a uniform external electromagnetic field there emerge two contributions to the photogalvanic effect due to the trigonal warping of the valleys. The first contribution stems from the current of the electron gas in its normal state, while the second contribution is of Aslamazov-Larkin nature: it originates from the presence of fluctuating Cooper pairs when the ambient temperature approaches (from above) the temperature of superconducting transition in the sample. The way to lift the valley …
In the cuprate superconductors, Nernst and torque magnetization experiments have provided evidence that the disappearance of the Meissner effect at $T_c$ is caused by the loss of long-range phase coherence, rather than the vanishing of the pair condensate. Here we report a series of torque magnetization measurements on single crystals of $\mathrm{La_{2-x}Sr_xCuO_4}$ (LSCO), $\mathrm{Bi_2Sr_{2-y}La_yCuO_6}$ (Bi 2201), $\mathrm{Bi_2Sr_2CaCu_2O_{8+δ}}$ (Bi 2212) and optimal $\mathrm{YBa_2Cu_3O_7}$. Some of the measurements were taken to fields as high as 45 T. Focusing on the magnetization above …
When a superconductor is heated above its critical temperature $T_c$, macroscopic coherence vanishes, leaving behind droplets of thermally fluctuating Cooper pair. This superconducting fluctuation effect above $T_c$ has been investigated for many decades and its influence on the transport, thermoelectric and thermodynamic quantities in most superconductors is well understood by the standard Gaussian fluctuation theories. The transverse thermoelectric (Nernst) effect is particularly sensitive to the fluctuations, and the large Nernst signal found in the pseudogap regime of the underdoped high-$…
Various superconductors, including cuprate superconductors, exhibit peculiar features above the transition temperature T_c. In particular the observation of a large diamagnetism and Nernst signal in a wide temperature window above T_c attracted considerable attention. Noting that this temperature window exceeds the fluctuation dominated regime drastically and that in these materials the spatial extent of homogeneity is limited, we explore the relevance of the zero dimensional (0D)-model, neglecting thermal fluctuations. It is shown that both, the full 0D-model as well as its Gaussian approxima…
We develop a theory of the coherent photogalvanic effect (CPGE) in low-dimensional superconductors in the fluctuating regime. It manifests itself in the appearance of a stationary electric current of Cooper pairs under the action of two coherent electromagnetic fields of light with frequencies lying in the sub-terahertz range. We derive the general formula for the electric current density, study the particular cases of linear and circular polarizations of the external light fields, and show that the current might have a non-monotonous spectrum at certain polarization angles and turns out very …
In conventional superconductors, very narrow superconducting fluctuation regions are observed above $T_c$ because of the strong overlapping of Cooper pairs in a coherence volume. In the bulk form of iron chalcogenide superconductor FeSe, it is argued that the system may locate in the crossover region of BCS to BEC, indicating a strong superconducting fluctuation. In this respect, we have carried out measurements of magnetization, specific heat and Nernst effect on FeSe single crystals in order to investigate the superconducting fluctuation effect near $T_c$. The region of diamagnetization indu…
We study the two-dimensional spin-charge separated Ginzburg-Landau theory containing U(1) gauge interactions as a semi-phenomenological model describing fluctuating condensates in high temperature superconductivity. Transforming the original GL action, we abstract the effective action of Cooper pair. Especially, we clarify how Cooper pair correlation evolves in the normal state from the point of view of spin-charge separation. Furthermore, we point out how Cooper pair couples to gauge field in a gauge-invariant way, stressing the insensitivity of Cooper pair to infrared gauge field fluctuation…
Herewith, we review the available experimental data of thermoelectric transport properties of iron-based superconductors and parent compounds. We discuss possible physical mechanisms into play in determining the Seebeck effect, from whence one can extract information about Fermi surface reconstruction and Lifshitz transitions, multiband character, coupling of charge carriers with spin excitations and its relevance in the unconventional superconducting pairing mechanism, nematicity, quantum critical fluctuations close to the optimal doping for superconductivity, correlation. Additional informat…
The interplay between fluctuating Cooper pairs and magnetic impurities in conventional BCS low-Tc superconductors has been studied through measurements of the magnetic field dependence of the fluctuation diamagnetism (FD) above Tc in lanthanum with praseodymium impurities. These measurements provide a crucial confirmation of our previous observation [Europhys. Lett. 73, 587 (2006)] that in the dilute impurity regime the FD increases almost linearly with the concentration of magnetic impurities. This striking effect is attributed to a variation due to the presence of the fluctuating Cooper pair…
We study theoretically the contribution of fluctuating Cooper pairs to the persistent current in superconducting rings threaded by a magnetic flux. For sufficiently small rings, in which the coherence length $ξ$ exceeds the radius $R$, mean field theory predicts a full reduction of the transition temperature to zero near half-integer flux. We find that nevertheless a very large current is expected to persist in the ring as a consequence of Cooper pair fluctuations that do not condense. For larger rings with $R\gg ξ$ we calculate analytically the susceptibility in the critical region of strong …
We extend previous theoretical studies of the contribution of fluctuating Cooper pairs to the persistent current in superconducting rings subjected to a magnetic field. For sufficiently small rings, in which the coherence length $ξ$ exceeds the radius $R$, mean field theory predicts the emergence of a flux-tuned quantum critical point separating metallic and superconducting phases near half-integer flux through the ring. For larger rings with $R\gtrsim ξ$, the transition temperature is periodically reduced, but superconductivity prevails at very low temperatures. We calculate the fluctuation p…
Superconductivity arises from two distinct quantum phenomena: electron pairing and long-range phase coherence. In conventional superconductors, the two quantum phenomena generally take place simultaneously, while the electron pairing occurs at higher temperature than the long-range phase coherence in the underdoped high-Tc cuprate superconductors. Recently, whether electron pairing is also prior to long-range phase coherence in single-layer FeSe film on SrTiO3 substrate is under debate. Here, by measuring Knight shift and nuclear spin-lattice relaxation rate, we unambiguously reveal a pseudoga…
The origin of the pseudogap (PG) phase and superconducting behaviors in high-Tc superconductors is proposed, based on the picture of Euclidean Q-balls formation, that carry Cooper/local-pair condensates inside their volumes. Unlike the baryonic Q-balls in supersymmetric standard model, the Euclidean Q-balls describe spin-/charge densities, that oscillate in Matsubara time, and are found in the 'nested' repulsive Hubbard model of high-Tc superconductors. Euclidean Q-balls arise due to global invariance of the effective theory under the phase rotation of the Fourier amplitudes of spin-/charge fl…
The fluctuation-induced diamagnetism (FD), associated with the presence of precursor Cooper pairs in the normal state, has been measured in lanthanum with dilute magnetic (Pr) and nonmagnetic (Lu) impurities. It is found that while for pure La and La-Lu alloys the FD agrees, as expected, with the theoretical predictions, it is much larger for La-Pr alloys (around a factor 5 for La-2at.%Pr). These results suggest the existence of an indirect contribution to the FD arising from the interaction between fluctuating Cooper pairs and magnetic impurities.
In many unconventional superconductors, the presence of a pseudogap - a suppression in the electronic density of states extending above the critical temperature - has been a long-standing mystery. Here, we employ combined \textit{in situ} electrical transport and angle-resolved photoemission spectroscopy (ARPES) measurements to reveal an unprecedentedly large pseudogap regime in single-layer FeSe/SrTiO$_3$, an interfacial superconductor where incoherent Cooper pairs are initially formed above $T_Δ$ $\approx$ 60 K, but where a zero resistance state is only achieved below $T_{0}$ $<$ 30 K. We sh…
A superconducting phase with an extremely low carrier density of the order of 10^13 cm^-2 is present at LaAlO3-SrTiO3 interfaces. If depleted from charge carriers by means of a gate field, this superconducting phase undergoes a transition into a metallic/insulating state that is still characterized by a gap in the spectral density of states. Measuring and analyzing the critical field of this gap, we provide evidence that macroscopically phase-coherent Cooper pairs are present in the metallic/insulating state. This is characterized by fluctuating vortex-antivortex pairs, and not by individual, …
We show that an array of Josephson coupled Cooper paired planes can never have long range phase coherence at any finite temperature due to an infrared divergence of phase fluctuations. The phase correlations decay in a slow enough manner providing enough local phase coherence as to make possible the nucleation of vortices. The planes then acquire Kosterlitz-Thouless topological order with its intrinsic rigidity and concomitant superfluidity. We thus conclude that the high temperature superconducting cuprates are topologically ordered superconductors rather than phase ordered superconductors. F…
The mutual interaction between Cooper pairs is proposed as a mechanism for the superconducting state. Above $T_c$, pre-existing but fluctuating Cooper pairs give rise to the unconventional {\it pseudogap} (PG) state, well-characterized by experiment. At the critical temperature, the pair-pair interaction induces a Bose-like condensation of these preformed pairs leading to the superconducting (SC) state. Below $T_c$, both the condensation energy and the pair-pair interaction $β$ are proportional to the condensate density $N_{oc}(T)$, whereas the usual Fermi-level spectral gap $Δ_p$ is independe…
We present a systematic photoemission study of the newly discovered high Tc superconductor class (Sr/Ba)1-xKxFe2As2. By utilizing a unique photon energy range and scattering geometry we resolve the details of the single particle dynamics of interacting electrons on the central Fermi surfaces of this series which shows overall strong coupling behavior (2D/kBTc = 6). Quasiparticle dispersion kinks are observed in a binding energy range of 15 to 50 meV which matches the magnetic excitation energy scales (parameterized by J1,J2). The size of the Cooper pair wavefunction is found to be less than 20…
We study anomalous mesoscopic transport effects at the onset of the superconducting transition focusing on the observed large Nernst-Ettinghausen signal in disordered thin films. In the vicinity of the transition, as the Ginzburg-Landau coherence length of preformed Cooper pairs diverges, short-range mesoscopic fluctuations are equivalent to local fluctuations of the critical temperature. As a result, the dynamical susceptibility function of pair propagation acquires a singular mesoscopic component, and consequently, superconducting correlations give rise to enhanced mesoscopic fluctuations of…
Frequency-dependent terahertz conductivities of La$_{2-x}$Sr$_x$CuO$_4$ thin films with various carrier concentrations were investigated. The imaginary part of the complex conductivity considerably increased from far above a zero-resistance superconducting transition temperature, $T_\text{c}^\text{zero}$, because of the existence of the fluctuating superfluid density with a short lifetime. The onset temperature of the superconducting fluctuation is at most $\sim 2T_\text{c}^\text{zero}$ for underdoped samples, which is consistent with the previously reported analysis of microwave conductivity.…
We propose to employ an optical spectroscopy technique to monitor the superconductivity and properties of superconductors in the fluctuating regime. This technique is operational close to the plasmon resonance frequency of the material, and it intimately connects with the superconducting fluctuations slightly above the critical temperature $T_c$. We find the Aslamazov-Larkin corrections to AC linear and DC nonlinear electric currents in a generic two-dimensional system exposed to an external longitudinal electromagnetic field. First, we study the plasmon resonance of normal electrons near $T_c…
In Hund's metals, the local ferromagnetic interaction between orbitals leads to an emergence of complex electronic states with large and slowly fluctuating magnetic moments. Introducing the Hund's coupled mixed valence quantum impurity, we gain analytic insight into recent numerical renormalization group studies. We show that valence fluctuations drastically impede the development of a large fluctuating moment over a wide range of temperatures and energy, characterized by quenched orbital degrees of freedom and a singular logarithmic behavior of the spin susceptibility $χ_{\rm sp}''(ω) \propto…
We study effects of strong fluctuations on the transport properties of superconductors near the classical critical point. In this regime conductivity is set by the delicate interplay of two competing effects. The first is that strong electron-electron interactions in the Cooper channel increase the life-time of fluctuation Cooper pairs and thus enhance conductivity. On the other hand, quantum pair-breaking effects tend to suppress superconductivity. An interplay between these processes defines new regime where fluctuation induced transport becomes more singular. The most singular contributions…
We investigate the specific heat at constant volume $C_V$ in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature $T_{\rm c}$. Within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while $C_V(T\gesim T_{\rm c})$ in the unitary regime is remarkably enhanced by {\it metastable} preformed Cooper pairs or pairing fluctuations, it is well described b…
