Strong-coupling Superconductivity Research Articles

Superconductivity from orbital nematic fluctuations

Recent experiments suggest that, besides antiferromagnetic fluctuations, nematic fluctuations may contribute to the occurrence of superconductivity in iron pnictides. Motivated by this observation, we study superconductivity from nematic fluctuations in a minimal two-band model. The employed band parameters are appropriate for iron pnictides and lead to four pockets for the Fermi line. It is shown that low-energy, long-wavelength nematic fluctuations within the pockets give rise to strong-coupling superconductivity whereas the large momenta density fluctuations between pockets are rather irrelevant. The obtained transition temperatures are similar to those typically found in the pnictides and are rather robust against repulsive Coulomb interactions. The superconducting and nematic states coexist in a large region of the phase diagram.

Zigzag Chain Structure Transition and Orbital Fluctuations in Ni-Based Superconductors

We investigate the electronic state and structure transition of BaNi2As2, which shows a similar superconducting phase diagram as Fe-based superconductors. We construct the ten-orbital tight-binding model for BaNi2As2 by using the maximally localized Wannier function method. The Coulomb and quadrupole-quadrupole interactions are treated within the random-phase approximation. We obtain the strong developments of charge quadrupole susceptibilities driven by the in-plane and out-of-plane oscillations of Ni ions. The largest susceptibility is either O_{X^2-Y^2}-quadrupole susceptibility at q = (pi, 0, pi) or O_{XZ(YZ)}-quadrupole susceptibility at q = (pi, pi, pi), depending on the level splitting between d_{X^2-Y^2} and d_{XZ(YZ)}. These antiferro-quadrupole fluctuations would then be the origin of the strong coupling superconductivity in Ni-based superconductors. Also, we propose that the antiferro-quadrupole O_{X^2-Y^2} order with q = (pi, 0, pi) is the origin of the zigzag chain structure reported in experiments. We identify similarities and differences between Ni- and Fe-based superconductors.

Strong coupling superconductivity and prominent superconducting fluctuations in the new superconductor Bi4O4S3

Electric transport and scanning tunneling spectrum (STS) have been investigated on polycrystalline samples of the new superconductor Bi4O4S3. A weak insulating behavior in the resistive curve has been induced in the normal state when the superconductivity is suppressed by applying a magnetic field. Interestingly, a kink appears on the temperature dependence of resistivity near 4 K at all high magnetic fields above 1 T when the bulk superconductivity is completely suppressed. This kink associated with the upper critical field as well as the wide range of excess conductance at low fields and high temperatures is explained as the possible evidence of strong superconducting fluctuation. From the tunneling spectra, a superconducting gap of about 3 meV is frequently observed yielding a ratio of 2Δ/k B T C ∼ 16.6. This value is much larger than the one predicted by the BCS theory in the weak coupling regime (2Δ/k B T C ∼ 3.53), which suggests the strong coupling superconductivity in the present system. Furthermore, the gapped feature persists on the spectra until 14 K in the STS measurement, which suggests a prominent fluctuation region of superconductivity. Such a superconducting fluctuation can survive at very high magnetic fields, which are far beyond the critical fields for bulk superconductivity as inferred both from electric transport and tunneling measurements.

ON d+id DENSITY WAVE AND SUPERCONDUCTING ORDERINGS IN HOLE-DOPED CUPRATES

The d+id-density wave (chiral DDW) order, at the anti-ferromagnetic wave vector Q = (π, π), is assumed to represent the pseudo-gap (PG) state of a hole-doped cuprate superconductor. The pairing interaction U(k, k′) required for d+id ordering comprises of (Ux2-y2(k, k′), Uxy(k, k′)), where [Formula: see text] and [Formula: see text] with U1 > U2. The d-wave superconductivity (DSC), driven by an assumed attractive interaction of the form [Formula: see text] where V1 is a model parameter, is discussed within the mean-field framework together with the d+id ordering. The single-particle excitation spectrum in the CDDW + DSC state is characterized by the Bogoluibov quasi-particle bands — a characteristic feature of SC state. The coupled gap equations are solved self-consistently together with the equation to determine the chemical potential (μ). With the pinning of the van Hove-singularities close to μ, one is able to calculate the thermodynamic and transport properties of the under-doped cuprates in a consistent manner. The electron specific heat displays non-Fermi liquid feature in the CDDW state. The CDDW and DSC are found to represent two competing orders as the former brings about a depletion of the spectral weight (and Raman response function density) available for pairing in the anti-nodal region of momentum space. It is also shown that the depletion of the spectral weight below Tc at energies larger than the gap amplitude occurs. This is an indication of the strong-coupling superconductivity in cuprates. The calculation of the ratio of the quasi-particle thermal conductivity αxx and temperature in the superconducting phase is found to be constant in the limit of near-zero quasi-particle scattering rate.

A Theoretical Approach to Pseudogap and Superconducting Transitions in Hole-Doped Cuprates

We consider a two-dimensional fermion system on a square lattice described by a mean-field Hamiltonian involving the singlet id-density wave (DDW) order, assumed to correspond to the pseudo-gap (PG) state, favored by the electronic repulsion and the coexisting -wave superconductivity (DSC) driven by an assumed attractive interaction within the BCS framework. Whereas the single-particle excitation spectrum of the pure DDW state consists of the fermionic particles and holes over the reasonably conducting background, the coexisting states corresponds to Bogoliubov quasi-particles in the background of the delocalized Cooper pairs in the momentum space. We find that the two gaps in the single-particle excitation spectrum corresponding to PG and DSC, respectively, are distinct and do not merge into one “quadrature” gap if the nesting property of the normal state dispersion is absent. We show that the PG and DSC are representing two competing orders as the former brings about a depletion of the spectral weight available for pairing in the anti-nodal region of momentum space where the superconducting gap is supposed to be the largest. This indicates that the PG state perhaps could not be linked to a preformed pairing scenario. We also show the depletion of the spectral weight below at energies larger than the gap amplitude. This is an important hallmark of the strong coupling superconductivity.

Anomalous Isotope Effect in Rattling-Induced Superconductor

In order to clarify that the Cooper pair in $\beta$-pyrochlore oxides is mediated by anharmonic oscillation of guest atom, i.e., rattling, we propose an experiment to detect anomalous isotope effect. In the formula of $T_{\rm c} \propto M^{-\eta}$, where $T_{\rm c}$ is superconducting transition temperature and $M$ denotes mass of the oscillator, it is found that the exponent $\eta$ is increased with the increase of anharmonicity of a potential for the guest atom. We predict that $\eta$ becomes larger than 1/2 in rattling-induced superconductor, in sharp contrast to $\eta=1/2$ for weak-coupling superconductivity due to harmonic phonons and $\eta<1/2$ for strong-coupling superconductivity with the inclusion of the effect of Coulomb interaction.

Band Structure and Quantum Oscillations in YBa2Cu3O7: A Local Spin Density Approximation with the On-Site Coulomb Interaction Study

First-principles calculations have been performed on the Bravais lattice, the density of states (DOS), the band structure (BS) and the Fermi Surface (FS) topology for high-Tc superconductor YBa2Cu3O7. We used the method of the Full-Potential non-orthogonal Local-Orbital Minimum-Basis Band-structure Scheme (FPLO) [in the local spin density approximation with the on-site Coulomb interaction (LSDA+U) and the coherent potential approximation (CPA)] coupled with the XFSF program. Our FPLO Fermi surface consists of four large quasi-2D cylinders centered on the Brillouin zone corners with mostly CuO2 plane character and two quasi-1D sheets with mostly Cu–O apex (or apical O) chain character. The main feature of this Fermi surface is that each CuO chain-sheet shows up in its center a small tubular pocket with a funnel-like shape (Fermi pockets) with mainly Ba–O apex character which could give rise to the quantum oscillations observed by Doiron-Leyraud et al. (Nature 447: 565, 2007). Our FPLO band structure (BS) shows that three flat bands cross the Fermi level (FL) which suggests that the two Fermi pockets could be produced by the conjunction near the Fermi level of two flat bands arising from the apex oxygen (BaO layer). This is consistent with the density of states (DOS) where the Fermi level is dominated by the two O apex (BaO) peaks (∼90 %). Moreover, the strong narrow peak exhibited in the DOS just below the Fermi level (FL) corresponds to the van Hove singularity (VHS) and originates from the hybridization of Cu 3d and apex O2p (BaO) orbitals. In other hand, the calculated value of the bare band-structure Sommerfeld constant γ0band=10.60 mJ/(mol K2) corresponds to a very high Fermi level density of states N(EF)=4.72 states/(eV×cell) and the electron–phonon coupling constant λ is found to be about 1.64 which implies that YBa2Cu3O7 compound is a strong-coupling superconductor and the cyclotron effective mass m∗ is enhanced in comparison with the band mass mb [m∗=(1+λ)mb]. Also, the discrepancy between our FPLO calculated Debye temperature (274.15 K) and that obtained experimentally (437 K) may originate from a phonon anisotropy likely generated by the antiferromagnetic spin fluctuations. Our results therefore provide evidence of changes in the topology of the Fermi surface materialized by the Ba–O apex small pockets formed in the center of the Cu–O apex Fermi surface sheets.

Electronic structure of new multiple band Pt-pnictide superconductors APt3P

We report LDA calculated band structure, densities of states and Fermi surfaces for recently discovered Pt-pnictide superconductors APt3P (A = Ca, Sr, La), confirming their multiple band nature. Electronic structure is essentially three dimensional, in contrast to Fe pnictides and chalcogenides. LDA calculated Sommerfeld coefficient agrees rather well with experimental data, leaving little space for very strong coupling super-conductivity, suggested by experimental data on specific heat of SrPt3P. Elementary estimates show, that the values of critical temperature can be explained by rather weak or moderately strong coupling, while the decrease in superconducting transition temperature T c from Sr to La compound can be explained by corresponding decrease in total density of states at the Fermi level N(E F). The shape of the density of states near the Fermi level suggests that in SrPt3P electron doping (such as replacement Sr by La) decreases N(E F) and T c , while hole doping (e.g., partial replacement of Sr with K, Rb or Cs, if possible) would increase N(E F) and possibly T c .

Fully-gapped superconductivity in Ba0.55K0.45Fe1.95Co0.05As2: A low-temperature specific heat study

We have studied the Fe-based superconductor Ba${}_{0.55}$K${}_{0.45}$Fe${}_{1.95}$Co${}_{0.05}$As${}_{2}$ in order to identify the structure of the order parameter in this system by performing extensive low-temperature specific heat measurements in zero and in applied magnetic field. The pronounced superconducting jump at ${T}_{c}=32.5$ K and ${\ensuremath{\Delta}}_{0}/({k}_{B}{T}_{c})=2.57$ indicate strong-coupling superconductivity in this material. Here we provide evidence for fully gapped superconductivity in Ba${}_{0.55}$K${}_{0.45}$Fe${}_{1.95}$Co${}_{0.05}$As${}_{2}$. A linear magnetic field dependence of the low-temperature specific heat points to $s$-wave symmetry of the order parameter. Below ${T}_{c}$ the superconducting electronic part of the specific heat can be described by the BCS $\ensuremath{\alpha}$ model with ${\ensuremath{\Delta}}_{0}=7.2$ meV.

Strong-coupling superconductivity with mixed even- and odd-frequency pairing

We investigate general structure of Landau free energy for stabilizing a novel superconducting state with both even-frequency and odd-frequency components in gap function. On the basis of the Luttinger-Ward functional, we elucidate an emergent mixing between different "parities" in time. The simplest case of the conventional s-wave singlet mixed with the odd-frequency triplet state under broken time-reversal symmetry is examined to demonstrate the anomalous structure of the free-energy functional. The induced odd-frequency component alters behaviors of physical quantities from those obtained by neglecting the odd-frequency component. The novel mixed state may also be relevant to strong-coupling superconductivity coexisting with ferromagnetism.

Strong Coupling Superconductivity, Pseudogap, and Mott Transition

An intricate interplay between superconductivity, pseudogap, and Mott transition, either bandwidth driven or doping driven, occurs in materials. Layered organic conductors and cuprates offer two prime examples. We provide a unified perspective of this interplay in the two-dimensional Hubbard model within cellular dynamical mean-field theory on a 2×2 plaquette and using the continuous-time quantum Monte Carlo method as impurity solver. Both at half filling and at finite doping, the metallic normal state close to the Mott insulator is unstable to d-wave superconductivity. Superconductivity can destroy the first-order transition that separates the pseudogap phase from the overdoped metal, yet that normal state transition leaves its marks on the dynamic properties of the superconducting phase. For example, as a function of doping one finds a rapid change in the particle-hole asymmetry of the superconducting density of states. In the doped Mott insulator, the dynamical mean-field superconducting transition temperature T(c)(d) does not scale with the order parameter when there is a normal-state pseudogap. T(c)(d) corresponds to the local pair formation temperature observed in tunneling experiments and is distinct from the pseudogap temperature.

Upper Critical Magnetic Field far above the Paramagnetic Pair-Breaking Limit of Superconducting One-DimensionalLi0.9Mo6O17Single Crystals

The upper critical field H(c2) of purple bronze Li0:9Mo6O17 is found to exhibit a large anisotropy, in quantitative agreement with that expected from the observed electrical resistivity anisotropy. With the field aligned along the most conducting axis, H(c2) increases monotonically with decreasing temperature to a value 5 times larger than the estimated paramagnetic pair-breaking field. Theories for the enhancement of H(c2) invoking spin-orbit scattering or strong-coupling superconductivity are shown to be inadequate in explaining the observed behavior, suggesting that the pairing state in Li0:9Mo6O17 is unconventional and possibly spin triplet.

Specific heat and upper critical fields in KFe2As2single crystals

We report low-temperature specific heat measurements for high-quality single crystalline KFe2As2 (T_c about 3.5 K). The investigated zero-field specific heat data yields an unusually large nominal Sommerfeld coefficient gamma_n of 94(3) mJ/mol K^2 which is however significantly affected by extrinsic contributions as evidenced by a sizable residual linear specific heat and various theoretical considerations including also an analysis of Kadowaki-Woods relations. Then KFe2As2 should be classified as a weak to intermediately strong coupling superconductor with a total electron-boson coupling constant lambda_tot near 1 (including a calculated weak electron-phonon coupling constant of lambda_el-ph =0.17. From specific heat and ac susceptibility studies in external magnetic fields the magnetic phase diagram has been constructed. We confirm the high anisotropy of the upper critical fields B_c2(T) ranging from a factor of 5 near T_c to a slightly reduced value approaching T=0 for fields B || ab$ and || c and show that their ratio Gamma slightly exceeds the mass anisotropy of 4.35 derived from our full-relativistic LDA-band structure calculations. Its slight reduction when approaching T=0 is not a consequence of Pauli-limiting as in less perfect samples but point likely to a multiband effect. We also report irreversibility field data obtained from ac susceptibility measurements. The double-maximum in the T-dependence of its imaginary part for fields B || c indicates a peak-effect in the T-dependence of critical currents.

Comparative study of the centrosymmetric and noncentrosymmetric superconducting phases of Re3W using muon spin spectroscopy and heat capacity measurements

We compare the low-temperature electronic properties of the centrosymmetric (CS) and noncentrosymmetric (NCS) phases of Re${}_{3}$W using muon-spin spectroscopy and heat capacity measurements. The zero-field $\ensuremath{\mu}$SR results indicate that time-reversal symmetry is preserved for both structures of Re${}_{3}$W. Transverse-field muon-spin rotation has been used to study the temperature dependence of the penetration depth $\ensuremath{\lambda}(T)$ in the mixed state. For both phases of Re${}_{3}$W, $\ensuremath{\lambda}(T)$ can be explained using a single-gap $s$-wave BCS model. The magnetic penetration depth at zero temperature $\ensuremath{\lambda}(0)$ is $164(7)$ and $418(6)$ nm for the centrosymmetric and noncentrosymmetric phases of Re${}_{3}$W, respectively. Low-temperature-specific heat data also provide evidence for an $s$-wave gap symmetry for the two phases of Re${}_{3}$W. Both the $\ensuremath{\mu}$SR and heat capacity data show that the CS material has a higher ${T}_{c}$ and a larger superconducting gap $\ensuremath{\Delta}(0)$ at 0 K than the NCS compound. The ratio $\ensuremath{\Delta}(0)/{k}_{B}{T}_{c}$ indicates that both phases of Re${}_{3}$W should be considered as strong-coupling superconductors.

Coexistence of Even- and Odd-Frequency Superconductivities Under Broken Time-Reversal Symmetry

A novel superconducting state under the broken time-reversal symmetry is studied in conventional phonon-mediated superconductors. By solving the Eliashberg equation self-consistently with the mass renormalization effect, it is found that the even- and odd-frequency components of the order parameter coexist in the bulk system as a consequence of the broken time-reversal symmetry. This finding would direct more attention to the odd-frequency pairing that affects physical quantities, especially in strong coupling superconductors.

Shallow pockets and very strong coupling superconductivity in FeSexTe1−x

We measured the electronic-structure of FeSe_xTe_1-x above and below Tc. In the normal state we find multiple bands with remarkably small values for the Fermi energy, E_F. Yet,below Tc we find a superconducting gap, Delta, that is comparable in size to E_F, leading to a ratio Delta/E_F~0.5 that is much larger than found in any previously studied superconductor. We also observe an anomalous dispersion of the coherence peak which is very similar to the dispersion found in cold Fermi-gas experiments and which is consistent with the predictions of the BCS-BEC crossover theory.

Pressure-Induced Change of the Antiferromagnetic Structure in CeRhIn5Studied by In-NQR Measurements

We report a pressure-induced evolution of magnetism and superconductivity in a helical magnet CeRhIn 5 with an incommensurate wave vector Q i =(1/2,1/2,0.297) through the 115 In nuclear quadrupole resonance (NQR) measurements under P . From systematic measurements of the 115 In-NQR spectrum, it is suggested that the commensurate antiferromagnetic order with Q c =(1/2,1/2,1/2) is realized near an antiferromagentic quantum critical point. The homogeneous coexistence of superconductivity and the commensurate antiferromagnetism is observed from the measurements of a nuclear spin–lattice relaxation rates (1/ T 1 ) at 1.82 GPa. The analysis for 1/ T 1 data below T c indicates that the strong coupling superconductivity is realized above an antiferromagnetic quantum critical point.

Superconducting Gap Structure of the Cage Compound Sc5Rh6Sn18

We report on the superconducting properties of the cage compound Sc 5 Rh 6 Sn 18 with T c = 5 K determined by magnetic susceptibility, electrical resistivity, and specific heat measurements. Measurements in magnetic fields indicate type-II superconductivity with the upper critical field µ 0 H c2 (0) = 7.24 T. H c2 ( T ) shows a clear enhancement over the Werthamer–Helfand–Hohenberg prediction, suggesting a strong electron–phonon coupling. Specific heat data reveal that Sc 5 Rh 6 Sn 18 is indeed a strong-coupling BCS superconductor having an isotropic superconducting gap.

Strong-coupling d-wave superconductivity in PuCoGa5 probed by point-contact spectroscopy

Superconductivity is due to an attractive interaction between electrons that, below a critical temperature, drives them to form Cooper pairs and to condense into a ground state separated by an energy gap from the unpaired states. In the simplest cases, the pairing is mediated by lattice vibrations and the wavefunction of the pairs is isotropic. Less conventional pairing mechanisms can favour more exotic symmetries of the Cooper pairs. Here, we report on point-contact spectroscopy measurements in PuCoGa5, a moderate heavy-fermion superconductor with a record high critical temperature Tc=18.5 K. The results prove that the wavefunction of the paired electrons has a d-wave symmetry, with four lobes and nodes, and show that the pairing is likely to be mediated by spin fluctuations. Electronic structure calculations, which take into account the full structure of the f-orbital multiplets of Pu, provide a hint of the possible origin of these fluctuations.

Quantitative reliability study of the Migdal-Eliashberg theory for strong electron-phonon coupling in superconductors

We reassess the validity of the Migdal-Eliashberg (ME) theory for coupled electron-phonon systems for large couplings $\ensuremath{\lambda}$. Although model calculations have found that the ME theory breaks down for $\ensuremath{\lambda}\ensuremath{\sim}0.5$, it is routinely applied for $\ensuremath{\lambda}&gt;1$ to strong-coupling superconductors. To resolve this discrepancy, it is important to distinguish between bare parameters, used as input in models, and effective parameters, derived from experiments. We show explicitly that ME gives accurate results for the critical temperature and the spectral gap for large effective $\ensuremath{\lambda}$. This provides quantitative theoretical support for the applicability of the ME theory to strong-coupling conventional superconductors.