Cooper-pair Size Research Articles

Coherence length versus transition temperature of hydride-based and room temperature superconductors

Recent discoveries of carbon-sulfur-hydrogen (C-S-H) room temperature superconductor (287.7 K) and near room temperature in hydride-based materials under high pressure have opened up an interesting and new avenue in the field of superconductivity. One of the important parameters of a superconductor is the coherence length, ξ which is the variation in the density of superconducting phase. ξ can also be related to the characteristic Cooper pair size. In this paper we report on the relation between ξ and the transition temperature, Tc of heavy fermions, conventional, iron arsenide-, cuprate- and hydride-based superconductors. This work showed that the coherence length was large for low Tc but for high Tc, ξ is short and tends to reach saturation value between 15 and 30 Å. ξ of the newly discovered hydride superconductors was found to be in the range of the cuprates. In this work, the coherence length of a 300 K superconductor extrapolated from the hydride-based data was found to be around 15 Å. This coherence length is sufficiently large to allow an effective Coulombic attraction between electrons in a Cooper pair.

Inhomogeneous superconductivity in LuxZr1−xB12 dodecaborides with dynamic charge stripes

We have studied the normal and superconductive state characteristics (resistivity, Hall coefficient, heat capacity and magnetization) of model strongly correlated electronic systems LuxZr1-xB12 with cooperative Jahn-Teller instability of the boron rigid cage and with dynamic charge stripes. It was found that these metals are s-wave dirty limit superconductors with a small mean free path of charge carriers l = 5 - 140 A and with a Cooper pair size changing non-monotonously in the range 450 - 4000 A. The parent ZrB12 and LuB12 borides are type-I superconductors, and Zr to Lu substitution induces a type-I - type-II phase transition providing a variation of the Ginzburg-Landau-Maki parameter in the limits 0.65 < kappa1,2 < 6. We argue in favor of the two-band scenario of superconductivity in LuxZr1-xB12 with gap values Delta_1 ~ 14 K and Delta_2 ~ 6 - 8 K, with pairing corresponding to strong coupling limit (lambda_e-ph ~ 1) in the upper band, and to weak coupling (lambda_e-ph ~ 0.1 - 0.4) in the lower one. A pseudogap Delta_ps-gap ~ 60 - 110 K is observed in LuxZr1-xB12 above Tc. We discuss also the possibility of anisotropic single-band superconductivity with stripe-induced both pair-breaking and anisotropy, and analyze the origin of unique enhanced surface superconductivity detected in these model compounds.

Cooper-pair size and binding energy for unconventional superconducting systems

The main proposal of this paper is to analyze the size of the Cooper pairs composed by unbalanced mass fermions from different electronic bands along the BCS–BEC crossover and study the binding energy of the pairs. We are considering an interaction between fermions with different masses leading to an inter-band pairing. In addiction to the attractive interaction we have an hybridization term to couple both bands, which in general acts unfavorable for the pairing between the electrons. We get first order phase transitions as the hybridization breaks the Cooper pairs for the s-wave symmetry of the gap amplitude. The results show the dependence of the Cooper-pair size as a function of the hybridization for T=0. We also propose the structure of the binding energy of the inter-band system as a function of the two-bands quasi-particle energies.

Coherence lengths in attractively interacting Fermi gases with spin-orbit coupling

Extensive research has been lavished on effects of spin-orbit couplings (SOC) in attractively interacting Fermi systems in both neutral cold atom systems and condensed matter systems. Recently, it was suggested that a SOC drives a new class of BCS to BEC crossover which is different than the conventional one without a SOC. Here, we explore what are the most relevant physical quantities to describe such a new BCS to BEC crossover and their experimental detections. We extend the concepts of the pairing length and "Cooper-pair size" in the absence of SOC to Fermi systems with SOC. We investigate the dependence of chemical potential, pairing length, "Cooper-pair size" on the SOC strength and the scattering length at $ 3d $ (the bound state energy at $ 2d $) for three attractively interacting Fermi gases with 3 dimensional (3d) Rashba, 3d Weyl and 2d Rashba SOC respectively. We show that only the pairing length can be used to characterize this new BCS to BEC crossover. Furthermore, it is the only length which can be directly measured by radio-frequency dissociation spectra type of experiments. We stress crucial differences among the pairing length, "Cooper-pair size " and the two-body bound state size. Our results provide the fundamental and global picture of the new BCS to BEC crossover and its experimental detections in various cold atom and condensed matter systems.

Dynamics of a quantum quench in an ultracold atomic BCS superfluid

We study dynamics of an ultracold atomic BCS superfluid driven toward the BCS superfluid--Fermi-liquid quantum critical point by a gradual decrease of the pairing interaction. We analyze how the BCS superfluid falls out of equilibrium and show that the nonequilibrium gap and Cooper pair size reflect critical properties of the transition. We observe three stages of evolution: adiabatic where the Cooper pair size is inversely proportional to the equilibrium gap, weakly nonequilibrium where it is inversely proportional to the nonequilibrium gap, and strongly nonequilibrium where it decouples from both equilibrium and nonequilibrium gap. These phenomena should stimulate future experimental characterization of nonequilibrium ultracold atomic BCS superfluids.

Properties of a two-orbital model for oxypnictide superconductors: Magnetic order,B2gspin-singlet pairing channel, and its nodal structure

A recently proposed two-orbital model for the Fe-based superconductors is studied using the Lanczos method on small clusters as well as pairing mean-field approximations. Our main goals are (i) to provide a comprehensive analysis of this model using numerical techniques with focus on the magnetic state at half-filling and the quantum numbers of the state with two more electrons than half-filling and (ii) to investigate the nodal structure of the mean-field superconducting state and compare the results with angle-resolved photoemission data. In particular, we provide evidence that the dominant magnetic state at half-filling contains spin ``stripes,'' as observed experimentally using neutron scattering techniques. Competing spin states are also investigated. The symmetry properties of the state with two more electrons added to half-filling are also studied: depending on parameters, either a spin-singlet or spin triplet state is obtained. Since experiments suggest spin-singlet pairs, our focus is on this state. Under rotations, the spin-singlet state transforms as the ${B}_{2\text{g}}$ representation of the ${D}_{4\text{h}}$ group. We also show that the $s\ifmmode\pm\else\textpm\fi{}$ pairing operator transforms according to the ${A}_{1\text{g}}$ representation of ${D}_{4\text{h}}$ and becomes dominant only in an unphysical regime of the model where the undoped state is an insulator. We obtain qualitatively very similar results both with hopping amplitudes derived from a Slater-Koster approximation and with hoppings selected to fit band-structure calculations, the main difference between the two being the size of the Fermi surface pockets. For robust values of the effective electronic attraction producing the Cooper pairs, assumption compatible with recent angle-resolved photoemission spectroscopy (ARPES) results that suggest a small Cooper-pair size, the nodes of the two-orbital model are found to be located only at the electron pockets. Note that recent ARPES efforts have searched for nodes at the hole pockets or only in a few directions at the electron pockets. Thus, our results for the nodal distribution will help us to guide future ARPES experiments in their search for the existence of nodes in the Fe-based superconductors. More in general, the investigations reported here aim to establish several of the properties of the two-orbital model. Only a detailed comparison with experiments will clarify whether this simple model is or not a good approximation to describe the Fe pnictides.

Cooper pair wavefunction approach to the Josephson effect

We introduce an approach to the Josephson effect in the superconductor-insulator-superconductor (SIS) tunnel junctions. The Josephson coupling energy is calculated from the overlap of real space Cooper pair wavefunctions in two superconductors through an insulating barrier. It is shown that the Josephson tunneling is limited by the size of the Cooper pair and its shrinking during the tunneling. Therefore, the Josephson coupling energy and the critical current become extremely small in high Tc superconductors, including MgB2. This shrinking also causes the observed direct current (dc) supercurrent in low Tc superconductors, such as Nb, Pb, and Sn, to fall off much faster than 1∕Rn for tunneling resistance Rn above a few ohms. Consequently, there is a material-dependent threshold resistance, above which the supercurrent decreases much faster with increasing resistance. Spectacular confirmation is provided by the MgB2 break and tunnel junctions, where only small gap shows the supercurrents, while the big gap does not. The impurity-induced shrinking is also shown to limit the critical current. Furthermore, the (weak) temperature dependence of the Cooper pair size is found to contribute to the temperature dependence of the dc supercurrent. This understanding may lead to the discovery of better materials for SIS junctions other than Nb and the optimum miniaturization of the SIS junctions for the petaflops superconducting supercomputers.

Nonzero orbital angular momentum superfluidity in ultracold Fermi gases

We analyze the evolution of superfluidity for nonzero orbital angular momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit in three dimensions. First, we analyze the low energy scattering properties of finite range interactions for all possible angular momentum channels. Second, we discuss ground state ($T = 0$) superfluid properties including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, atomic compressibility, ground state energy and low energy collective excitations. We show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the s-wave case where the BCS to BEC evolution is just a crossover. Third, we present a gaussian fluctuation theory near the critical temperature ($T = T_{\rm c}$), and we analyze the number of bound, scattering and unbound fermions as well as the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau functional near $T_{\rm c}$, and compare the Ginzburg-Landau coherence length with the zero temperature average Cooper pair size.

Evolution from BCS to BEC Superfluidity inp-Wave Fermi Gases

We consider the evolution of superfluid properties of a three-dimensional p-wave Fermi gas from a weak coupling Bardeen-Cooper-Schrieffer (BCS) to strong coupling Bose-Einstein condensation (BEC) limit as a function of scattering volume. At zero temperature, we show that a quantum phase transition occurs for p-wave systems, unlike the s-wave case where the BCS to BEC evolution is just a crossover. Near the critical temperature, we derive a time-dependent Ginzburg-Landau (GL) theory and show that the GL coherence length is generally anisotropic due to the p-wave nature of the order parameter, and becomes isotropic only in the BEC limit.

Superfluidity ofp-wave ands-wave atomic Fermi gases in optical lattices

We consider p-wave pairing of single hyperfine state and s-wave pairing of two hyperfine states ultracold atomic gases trapped in quasi-two-dimensional optical lattices. First, we analyse superfluid properties of p-wave and s-wave symmetries in the strictly weak coupling BCS regime where we discuss the order parameter, chemical potential, critical temperature, atomic compressibility and superfluid density as a function of filling factor for tetragonal and orthorhombic optical lattices. Second, we analyse superfluid properties of p-wave and s-wave superfluids in the evolution from BCS to BEC regime at low temperatures ($T \approx 0$), where we discuss the changes in the quasiparticle excitation spectrum, chemical potential, atomic compressibility, Cooper pair size and momentum distribution as a function of filling factor and interaction strength for tetragonal and orthorhombic optical lattices.

Determination of the Coherence Length and the Cooper-Pair Size in Unconventional Superconductors by Tunneling Spectroscopy

The main purpose of the paper is to discuss a possibility of the determination of the values of the coherence length and the Cooper-pair size in unconventional superconductors by using tunnelling spectroscopy. In the mixed state of type-II superconductors, an applied magnetic field penetrates the superconductor in the form of vortices which form a regular lattice. In unconventional superconductors, the inner structure of a vortex core has a complex structure which is determined by the order parameter of the superconducting state and by the pairing wavefunction of the Cooper pairs. In clean superconductors, the spatial variations of the order parameter and the pairing wavefunction occur over the distances of the order of the coherence length and the Cooper-pair size, respectively. Therefore, by performing tunnelling spectroscopy along a line passing through a vortex core, one is able, in principle, to estimate the values of the coherent length and the Cooper-pair size.

Coherence length in superconductors from weak to strong coupling

We investigate the evolution of the superconducting coherence length ${\ensuremath{\xi}}_{0}$ from weak to strong coupling, within both an s-wave and a d-wave lattice model. We show that the identification of ${\ensuremath{\xi}}_{0}$ with the Cooper-pair size ${\ensuremath{\xi}}_{\mathrm{pair}}$ in the weak-coupling regime is meaningful only for a fully gapped (e.g., s-wave) superconductor. Instead in a d-wave superconductor, where ${\ensuremath{\xi}}_{\mathrm{pair}}$ diverges, we show that ${\ensuremath{\xi}}_{0}$ is finite (and of the expected order of magnitude) when properly defined as the characteristic length scale for the correlation function of the amplitude of the superconducting order parameter. The strong-coupling regime is quite intriguing, since the interplay between the particle-particle and the particle-hole channel is no more negligible. In the case of s-wave pairing, which allows for an analytical treatment, we show that ${\ensuremath{\xi}}_{0}$ is of the order of the lattice spacing at finite densities. In the diluted regime ${\ensuremath{\xi}}_{0}$ diverges, recovering the behavior of the coherence length of an effective bosonic system. Similar results are expected to hold for d-wave superconductors. We also comment on the consequences of our results with respect to the physics of high-${T}_{c}$ superconducting cuprates.

Phonon-Exchange Attraction. Optical Phonons and Type II Superconductivity, and d-Wave Cooper Pairs

The electron-pair density matrix \gr(k 1, k 2; k 3, k 4, t) =: \gr(1, 2; 3, 4, t) changes in time, following a quantum Liouville equation with in the presence of a Coulomb interaction {itv}{in{itc}}, where \gW is the volume. If the virtual phonon exchange is in action, the density matrix \gr is shown to change similarly with an effective interaction {itv}{in{ite}}, by using a time-dependent perturbation theory and a Markoffian approximation. The dominant longitudinal-acoustic-(optical)-phonon-exchange attraction at 0K is shown to be q-independent (-dependent). The results are used to discuss the Cooper pair size, the origin of type II superconductivity and the formation of d-wave Cooper pairs in the cuprates.