We have measured the complex dynamical conductivity, $σ= σ_{1} + iσ_{2}$, of superconducting Ba(Fe$_{0.9}$Co$_{0.1}$)$_{2}$As$_{2}$ ($T_{c} = 22$ K) at terahertz frequencies and temperatures 2 - 30 K. In the frequency dependence of $σ_{1}$ below $T_{c}$, we observe clear signatures of the superconducting energy gap opening. The temperature dependence of $σ_{1}$ demonstrates a pronounced coherence peak at frequencies below 15 cm$^{-1}$ (1.8 meV). The temperature dependence of the penetration depth, calculated from $σ_{2}$, shows power-law behavior at the lowest temperatures. Analysis of the conductivity data with a two-gap model, gives the smaller isotropic s-wave gap of $Δ_{A} = 3$ meV, while the larger gap is highly anisotropic with possible nodes and its rms amplitude is $Δ_{0} = 8$ meV. Overall, our results are consistent with a two-band superconductor with an $s_{\pm}$ gap symmetry.
Thermal conductivity of superconducting MgB2 was studied in both the superconducting and the normal state region. The latter is almost equally determined by the electronic - and the lattice contribution to the total thermal conductivity. In the superconducting state, however, the lattice contribution is larger. The electronic thermal conductivity below Tc was derived from the experimental data considering the Bardeen-Rickayzen-Tewordt theory together with the model of Geilikman. The analysis shows that electron scattering on static imperfections dominates.
The low temperature behaviour of the in-plane and c-axis conductivity of electron-doped cuprates like NCCO is examined; it is shown to be consistent with an isotropic quasiparticle scattering rate and an anisotropic interlayer hopping parameter which is non-zero for planar momenta along the direction of the d$_{x^2-y^2}$ order parameter nodes. Based on these hypotheses we find that both, the in-plane and the c-axis conductivity, vary linearly with temperature, in agreement with experimental data at millimiter-wave frequencies.
The superconducting state of the heavy fermion PrOs4Sb12 is studied by heat transport measure- ments on a highly homogeneous single crystal exhibiting only one transition peak in the specific heat. The field and temperature dependence of the thermal conductivity confirm multiband super- conductivity and point to fully open gaps on the whole Fermi surface.
We study the effect of thermal fluctuations on the critical dynamics of the three-dimensional disordered superconductor across the normal-superconducting transition. We employ a phenomenological hydrodynamic approach, and in particular find the thermal conductivity to be smooth and non-singular at the transition.
We analyze the behavior of the superconducting-fluctuations contribution to diamagnetism and conductivity in a model system having current-current interactions. We show that in proximity to a Mott-insulating phase one recovers an overall suppression of the fluctuating contribution to the conductivity with respect to diamagnetism, in close analogy with recent experiments on the underdoped phase of cuprate superconductors.
Opticcal conductivity spectra $σ_1(ω)$ of Nd2-xCexCuO4 thin films, measured by the reflectance-transmittance method (R-T method) which has been proposed to investigate far-infrared spectroscopy, are investigated based on the anisotropic pairing model. Precise measurements of the frequency-dependent conductivity enable us to examine quantitatively the nature of the superconducting gap through infrared properties in the electron-doped high-Tc superconductors. We show that the behavior of optical conductivity $σ_1$ is consistent with the anisotropic superconducting gap and is well explained by th…
We propose a model and derive analytical expressions for conductivity in heterogeneous fully anisotropic conductors with ellipsoid superconducting inclusions. This model and calculations are useful to analyze the observed temperature dependence of conductivity anisotropy in various anisotropic superconductors, where superconductivity onset happens inhomogeneously in the form of isolated superconducting islands. The results are applied to explain the experimental data on resistivity above the transition temperature $T_c$ in the high-temperature superconductor $\mathrm{YBa_2Cu_4O_8}$ and in the …
We have studied the Hall effect in superconducting tantalum nitride films. We find a large contribution to the Hall conductivity near the superconducting transition, which we can track to temperatures well above $T_c$ and magnetic fields well above the upper critical field, $\text{\text{H}}_{c2}(0)$. This contribution arises from Aslamazov-Larkin superconducting fluctuations, and we find quantitative agreement between our data and recent theoretical analysis based on time dependent Ginzburg-Landau theory.
We report the complex optical conductivity of a superconducting thin-film of Nb$_{0.5}$Ti$_{0.5}$N in an external magnetic field. The field was applied parallel to the film surface and the conductivity extracted from far-infrared transmission and reflection measurements. The real part shows the superconducting gap, which we observe to be suppressed by the applied magnetic field. We compare our results with the pair-breaking theory of Abrikosov and Gor'kov and confirm directly the theory's validity for the optical conductivity.
We report the first study of the optical conductivity of MgB2 covering the range of its superconducting energy gap. Terahertz time-domain spectroscopy is utilized to determine the complex, frequency-dependent conductivity of thin films. The imaginary part reveals an inductive reponse due to the emergence of the superconducting condensate. The real part exhibits a strong depletion of oscillator strength near 5 meV resulting from the opening of a superconducting energy gap. The gap ratio of 2Delta/kTc = 1.9 is well below the weak-coupling value, pointing to complex behavior in this novel superco…
We study the intrinsic Hall conductivity of the ordinary and topological superconducting phases of a Rashba metal in a perpendicular Zeeman field. In this system the normal metal breaks time reversal symmetry while the superconducting order parameter does not, in contrast to the chiral p-wave superconducting state predicted in the monolayer strontium ruthenate (Sr$_2$RuO$_4$) whose Hall conductivity has been studied extensively. We study the effects of intra-band and inter-band pairing and find there is qualitatively larger change in the intrinsic Hall conductivity when there is inter-band pai…
The measurements (Phys.Rev.B {\bf 100}, 220504(R) (2019)) do not detect noticeable thermal conductivity in superconducting UTe$_2$ in the T=0 limit. At the same time the same crystals exhibit a large residual density of states comparable with its normal state value. The improvement of samples quality leads to the augmentation of critical temperature of transition to the superconducting state accompanied by the decreasing of residual specific heat ratio $C(T)/T$ at $T\to 0$. There is presented an analytic derivation of this inverse correlation property in concrete cases of triplet superconducti…
We investigate the far-infrared and submillimeter-wave conductivity of electron-doped La_(2-x)Ce_xCuO_4 tilted 1 degree off from the ab-plane. The effective conductivity measured for this tilt angle reveals an intensive peak at finite frequency (ν~ 50 cm{-1}) due to a mixing of the in-plane and out-of-plane responses. The peak disappears for the pure in-plane response and transforms to the Drude-like contribution. Comparative analysis of the mixed and the in-plane contributions allows to extract the c-axis conductivity which shows a Josephson plasma resonance at 11.7 cm{-1} in the superconduct…
The anisotropic conductivity of thin Nd$_{1.85}$Ce$_{0.15}$CuO$_{4-δ}$ films was measured in the frequency range 8 cm$^{-1}<ν<$ 40 cm$^{-1}$ and for temperatures 4 K $<T<300$ K. A tilted sample geometry allowed to extract both, in-plane and c-axis properties. The in-plane quasiparticle scattering rate remains unchanged as the sample becomes superconducting. The temperature dependence of the in-plane conductivity is reasonably well described using the Born limit for a d-wave superconductor. Below $T_{{\rm C}%}$ the c-axis dielectric constant $ε_{1c}$ changes sign at the screened c-axis plasma f…
Using the self-consistent approximation we calculate conductivity in an anisotropic heterogeneous media with superconducting inclusions and compare the results with those obtained previously using the Maxwell approximation and with available experimental data on excess conductivity above $ T_c= $~8K in FeSe. Advantages and drawbacks of these two approximations are discussed. The obtained analytical formulas can be applied to various other anisotropic heterogeneous superconductors, including high-Tc layered superconductors.
We study the effect of superconducting fluctuations on the longitudinal and the transverse (Hall) conductivity in homogeneously disordered films. Our calculation is based on the Usadel equation in the real-time formulation. We adjust this approach to derive analytic expressions for the fluctuation corrections in the entire metallic part of the temperature-magnetic field phase diagram, including the effects of both classical and quantum fluctuations. This method allows us to obtain fluctuation corrections in a compact and effective way, establishing a direct connection between phenomenological …
Frequency-dependent terahertz conductivities of La$_{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.…
Driving superconductors out of equilibrium is a promising avenue to study their equilibrium properties as well as to control the superconducting state. Non-equilibrium superconductors are often studied using time resolved optical conductivity measurements. Thus, the characterization of a superconducting state in a pump driven non-equilibrium state requires careful attention in the time domain. We calculate time-resolved optical conductivity of a pumped superconducting state using a non-equilibrium Keldysh approach. Through functional derivation, the optical conductivity is obtained with full v…
The superconductivity precursor phenomena in high temperature cuprate superconductors was studied by direct measurements of superconducting condensate with the use of the $c$-axis optical conductivity of YBa$_{2}$(Cu$_{1-x}$Zn$_{x}$)$_{3}$O$_{y}$ for several doping levels ($p$) as well as for several Zn-concentrations. Both of the real and imaginary part of the optical conductivity clearly showed that the superconducting carriers persist up to the high temperatures $T$$_{p}$ that is higher than the critical temperature $T$$_{c}$ but lower than the pseudogap temperature $T$$^{\ast}$. $T$$_{p}$ …
We discuss the excess conductivity at nonzero frequencies in a superconductor above T_c within the gaussian approximation. We focus the attention on the temperature range not too close to T_c: within a time-dependent Ginzburg-Landau formulation, we phenomenologically introduce a short wavelength cutoff (of the order of the inverse coherence length) in the fluctuational spectrum to suppress high momentum modes. We treat the general cases of thin wires, anisotropic thin films and anisotropic bulk samples. We obtain in all cases explicit expressions for the finite frequency fluctuational conducti…
To clarify the superconducting gap structure of the spin-triplet superconductor Sr_2RuO_4, the in-plane thermal conductivity has been measured as a function of relative orientations of the thermal flow, the crystal axes, and a magnetic field rotating within the 2D RuO_2 planes. The in-plane variation of the thermal conductivity is incompatible with any model with line nodes vertical to the 2D planes and indicates the existence of horizontal nodes. These results place strong constraints on models that attempt to explain the mechanism of the triplet superconductivity.
In this paper, we discuss the c axis optical conductivity Re [sigma_c(omega)] in the high T_c superconductors, in the superconducting state. The basic premise of this work is that electrons travelling along the c axis between adjacent CuO_2 layers must pass through several intervening layers. In earlier work we found that, for weak inter-layer coupling, it is preferable for electrons to travel along the c axis by making a series of interband transitions rather than to stay within a single (and very narrow) band. Moreover, we found that many of the properties of the normal state optical conduct…
We measured the in-plane optical conductivity of a nearly optimally doped (Ba,K)Fe2As2 single crystal with Tc = 39.1 K. Upon entering the superconducting state the optical conductivity below ~20 meV vanishes, strongly suggesting a fully gapped system. A BCS-like fit requires two different isotropic gaps to describe the optical response of this material. The temperature dependence of the gaps and the penetration depth suggest a strong interband coupling, but no impurity scattering induced pair breaking is present. This contrasts to the large residual conductivity observed in optimally doped Ba(…
The temperature-dependent optical reflectivity and complex transmissivity of an epitaxially grown Ba(Fe$_{0.9}$Co$_{0.1}$)$_2$As$_2$ thin film were measured and the optical conductivity and permittivity evaluated over a wide frequency range. The opening of the superconducting gap $2Δ_0 = 3.7$ meV below $T_c\approx 20$ K is {\em directly} observed by a completely vanishing optical conductivity. The temperature and frequency dependent electrodynamic properties of Ba(Fe$_{0.9}$Co$_{0.1}$)$_2$As$_2$ in the superconducting state agree well with the BCS predictions with no nodes in the order paramet…
The ab initio anisotropic Migdal-Eliashberg formalism has been used to examine the pairing mechanism and the nature of the superconducting gap in the recently discovered lithium-decorated monolayer graphene superconductor. Our results provide evidence that the superconducting transition in Li-decorated monolayer graphene can be explained within a standard phonon-mediated mechanism. We predict a single anisotropic superconducting gap and a critical temperature Tc = 5.1-7.6 K, in very good agreement with the experimental results.
We present thermal conductivity measurements on very pure and dense bulk samples, as indicated by residual resistivity values as low as 0.5 mW cm and thermal conductivity values higher than 200 W/mK. In the normal state we found that the Wiedemann Franz law, in its generalized form, works well suggesting that phonons do not contribute to the heat transport. The thermal conductivity in the superconducting state has been analysed by using a two-gap model. Thank to the large gap anisotropy we were able to evaluate quantitatively intraband scattering relaxation times of $π$ and $σ$ bands, which de…
We present a theoretical investigation of anisotropic superconducting spin transport at a magnetic interface between a p-wave superconductor and a ferromagnetic insulator. Our formulation describes the ferromagnetic resonance modulations due to spin current generation depending on spin-triplet Cooper pair, including the frequency shift and enhanced Gilbert damping, in a unified manner. We find that the Cooper pair symmetry is detectable from the qualitative behavior of the ferromagnetic resonance modulation. Our theory paves the way toward anisotropic superconducting spintronics.
We study dynamics of a two-dimensional s-wave superconductor in the presence of a moving single vortex. Our analysis is based on the quasiclassical theory including the Hall term, generalized by Kita[T. Kita, PRB, 64, 054503 (2001)]. We numerically calculate the linear response of a moving single vortex driven by a dc external current in a self-consistent way, in the sense that Dyson equation, gap equation, Maxwell equations and generalized quasiclassical equation are solved simultaneously. We obtain Hall conductivity induced by vortex motion using the generalized quasiclassical equation, whil…
We investigated the complex conductivity spectrum of a Co-doped BaFe$_2$As$_2$ epitaxial thin film in the THz region. In the normal state, the complex conductivity shows a Drude-type frequency dependence, while in the superconducting state, the frequency dependence of the complex conductivity changes to that of a typical superconducting materials. We estimated the magnetic penetration depth at absolute zero to be 710 nm and the superconducting gap energy to be 2.8 meV, which is considered to be the superconducting gap opened at the electron-type Fermi surface near the M point. We succeeded in …
We derive the fluctuational magnetization and the paraconductivity of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductors in their normal state. The FFLO superconducting fluctuations induce oscillations of the magnetization between diamagnetism and unusual paramagnetism which originates from the competition between paramagnetic and orbital effects. We also predict a strong anisotropy of the paraconductivity when the FFLO transition is approached in contrast with the case of a uniform BCS state. Finally building a Ginzburg-Levanyuk argument, we demonstrate that these fluctuation effects can…
We report investigations of molybdenum nitride (MoN) thin films with different thickness and disorder and with superconducting transition temperature 9.89 K $\ge{T_c}\ge$ 2.78 K. Using terahertz frequency-domain spectroscopy we explore the normal and superconducting charge carrier dynamics for frequencies covering the range from 3 to 38 cm$^{-1}$ (0.1 to 1.1 THz). The superconducting energy scales, i.e. the critical temperature $T_c$, the pairing energy $Δ$, and the superfluid stiffness $J$, and the superfluid density $n_s$ can be well described within the Bardeen-Cooper-Schrieffer theory for …
Our measurements of the low frequency ac conductivity in strongly disordered two-dimensional films near the magnetic field-tuned superconductor-to-insulator transition show a sudden drop in the phase stiffness of superconducting order with either increased temperature or magnetic field. Surprisingly, for two different material systems, the abrupt drop in the superfluid density in a magnetic field has the same universal value as that expected for a Berezinskii-Kosterlitz-Thouless transition in zero magnetic field. The characteristic temperature at which phase stiffness is suddenly lost can be t…
The optical response of the two-band superconductor MgB$_2$ has been studied in the 0.7-4 THz range on films with very low impurity level. The effect of the high-energy $σ$-gap is observed in the ratio $R_S/R_N$ between the normal and superconducting state reflectance, while in a neutron irradiated film with a slightly higher impurity level mainly the effect of the $π$-gap is evident as reported in previous experiments. At terahertz frequencies, the electrodynamic of MgB$_2$ can be well described by the two-band parallel conductivity model and is dominated by the $π$-bands when the impurity le…
Superconducting properties of hypothetical simple hexagonal CaB2 are studied using the fully anisotropic Eliashberg formalism based on electronic and phononic structures and electron-phonon interactions which are obtained from ab initio pseudopotential density functional calculations. The superconducting transition temperature Tc, the superconducting energy gap Delta(k) on the Fermi surface, and the specific heat are obtained and compared with corresponding properties of MgB2. Our results suggest that CaB2 will have a higher Tc and a stronger two-gap nature, with a larger Delta(k) in the sigma…
The magnetic field of vortices in anisotropic superconducting films is considered in the framework of anisotropic London approach. It is found that at distances large relative to the core size, the magnetic field normal to the film surface may change sign. We find that the magnetic field attenuates at large distances as $1/r^3$ as it does in isotropic films, but the anisotropy induces an angular dependence to the supercurrents which causes the sign of the field to change for anisotropy parameters $γ=λ_2/λ_1>\sqrt{2}$ in some parts of the $(x,y)$ plane.
We calculate superconducting gaps and quasiparticle density of states of YNi$_2$B$_2$C in the framework of the density functional theory for superconductors to investigate the origin of a highly anisotropic superconducting gaps in this material. Calculated phonon frequencies, the quasiparticle density of states, and the transition temperature show good agreement with experimental results. From our calculation of superconducting gaps and orbital character analysis, we establish that the orbital character variation of the Fermi surface is the key factor of the anisotropic gap. Since the electron…
The thermopower and thermal conductivity of superconducting perovskite $MgCNi_3$ ($T_c \approx$ 8 K) have been studied. The thermopower is negative from room temperature to 10 K. Combining with the negative Hall coefficient reported previously, the negative thermopower definetly indicates that the carrier in $MgCNi_3$ is electron-type. The nonlinear temperature dependence of thermopower below 150 K is explained by the electron-phonon interaction renormalization effects. The thermal conductivity is of the order for intermetallics, larger than that of borocarbides and smaller than $MgB_2$. In th…
We report a systematic study of the dynamic microwave conductivity near $T_c$ for La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) thin films with $x$=0.07 to 0.16. The strong frequency dependence of the phase stiffness together with scaling analysis of the ac fluctuating conductivity of superconductivity provide direct evidence for the 2D-XY behavior of nearly decoupled CuO$_2$ planes in underdoped LSCO ($x$=0.07 and 0.12). On the other hand, the critical exponents for slightly overdoped LSCO ($x$=0.16) were found to agree with those for the relaxational 3D-XY model, indicating that the universality class in L…
We measured the optical conductivity of superconducting LiFeAs. In the superconducting state, the formation of the condensate leads to a spectral-weight loss and yields a penetration depth of 225 nm. No sharp signature of the superconducting gap is observed. This suggests that the system is likely in the clean limit. A Drude-Lorentz parametrization of the data in the normal state reveals a quasiparticle scattering rate supportive of spin fluctuations and proximity to a quantum critical point.
Transmission of terahertz waves through a thin layer of the superconductor NbN deposited on an anisotropic R-cut sapphire substrate is studied as a function of temperature in a magnetic field oriented parallel with the sample. A significant difference is found between transmitted intensities of beams linearly polarized parallel with and perpendicular to the direction of applied magnetic field.
We report on the first measurements of thermal conductivity in the superconducting state of (TMTSF)_2ClO_4. The electronic contribution to heat transport is found to decrease rapidly below T_c, indicating the absence of low-energy electronic excitations. We argue that this result provides strong evidence for a nodeless superconducting gap function but does not exclude a possible unconventional order parameter.
We introduce a critical-state model incorporating the anisotropy of flux-line pinning to analyze the critical states developing in an anisotropic biaxial superconducting slab exposed to a uniform perpendicular magnetic field and to two crossed in-plane magnetic fields which are applied successively. The theory is an extension of the anisotropic collective pinning theory developed by Mikitik and Brandt. The anisotropic flux-line pinning enters into the critical states by generating the angular dependence of the critical current density and by deviating the direction of the electric field from t…
We have performed magnetic susceptibility measurements in Mo$_{(1-x)}$Ge$_x$ amorphous thin films biased with an electrical current using anisotropic coils. We tested the symmetry of the vortex response changing the relative orientation between the bias current and the susceptibility coils. We found a region in the DC current - temperature phase diagram where the dynamical vortex structures behave anisotropically. In this region the shielding capability of the superconducting currents measured by the susceptibility coils is less effective along the direction of vortex motion compared to the tr…
Imaginary part of the microwave conductivity σ''(T<T_c) and the resistivity ρ(T)=1/σ(T>T_c) along (σ_{ab}'' and ρ_{ab}) and perpendicular to (σ_c'' and ρ_c) cuprate ab-planes of YBa_2Cu_3O_{7-x} crystal were measured in the temperature range 5\leq T \leq 200 K, having varied the oxygen doping level x in the crystal from 0.07 to 0.47. The superconducting state was found to have the dependences σ_{ab}''(T)/σ_{ab}''(0) and σ_c''(T)/σ_c''(0) coincide in the optimally doped (x=0.07) crystal. With the increase of x the dependences σ_c''(T)/σ_c''(0) have smaller slope at T<T_c/3 with σ_{ab}''(T)/σ_{a…
High resolution magnetization measurements performed in a high quality Ba_(1-x)K_xFe2As2 single crystal allowed to determine the diamagnetism induced above the superconducting transition by thermally activated Cooper pairs. These data, obtained with magnetic fields applied along and transverse to the crystal ab layers, demonstrate experimentally that the superconducting transition of iron pnictides may be explained at a phenomenological level in terms of the Gaussian Ginzburg-Landau approach for three-dimensional anisotropic superconductors.
Nonlinear conductivity of point contacts (PCs) on the base of FeSe single crystals has been investigated. Measured dV/dI dependencies demonstrate the prevailing contribution to the PC conductivity caused by the degraded surface. Superconducting (SC) feature in dV/dI like a sharp zero-bias minimum develops for relatively low ohmic PCs, where the deep areas of FeSe are involved. Analysis of dV/dI has shown that the origin of the zero-bias minimum is connected with the Maxwell part of the PC resistance, what masks energy dependent spectral peculiarities. Even so, we have found the specific featur…
An anisotropic lattice anomaly near the superconducting transition temperature, Tc, was observed in MgB2 by high-resolution neutron powder diffraction. The a-axis thermal expansion becomes negative near Tc, while the c-axis thermal expansion is unaffected. This is qualitatively consistent with a depletion of the boron-boron s-band as the superconducting gap opens, resulting in weaker bonding. However, the observed anomaly is much larger than predicted by the Ehrenfest relation, strongly suggesting that the phonon thermal expansion also changes sign, as commonly observed in hexagonal layered cr…
There exists significant in-plane anisotropy between $a$ and $b$ axis for various properties in YBCO. However recent thermal conductivity measurement by Chiao et al. which confirms previous microwave conductivity measurement by Zhang et al., shows no obvious anisotropy in the context of universal transport. We give a possible explanation of why the anisotropy is seen in most properties but not seen in the universal transport.
We have recently proposed the s+g wave model for superconducting borocarbides. In spite of a substantial s-wave component, this order parameter exhibits the H^1/2 dependent specific heat and a thermal conductivity linear in H in the vortex state. This is characteristic for nodal superconductors when T, Γ<< Δwhere Γis the quasiparticle scattering rate and Δthe maximum superconducting gap. Here we investigate the thermal conductivity parallel to the c- and a- axis in a magnetic field tilted by θfrom the c- axis and rotating within the a-b plane.
We report a complete analytical expression for the one-loop correction to the ac conductivity $σ(ω)$ of a disordered two-dimensional electron system in the diffusive regime. The obtained expression includes the weak localization and Altshuler-Aronov corrections as well as the corrections due to superconducting fluctuations above superconducting transition temperature. The derived expression has no $1/(iω)$ divergency in the static limit, $ω\to 0$, in agreement with general expectations for the normal state conductivity of a disordered electron system.
We evaluate the superconducting fluctuation corrections to thermal conductivity in the normal state which diverge as T approaches T_c. We find zero total contribution for one, two and three-dimensional superconductors for arbitrary impurity concentration. The method used is diagrammatic many-body theory, and all contributions -- Aslamazov-Larkin (AL), Maki-Thompson (MT), and density-of-states (DOS) -- are considered. The AL contribution is convergent, whilst the divergences of the DOS and MT diagrams exactly cancel.
Motivated by a previous "$sd^2$-graphene" study, the pairing symmetry in the superconducting state and the thermal Hall conductivity are investigated by a self-consistent Bogoliubov--de Gennes approach on the kagome lattice with intrinsic spin-orbit coupling near van Hove fillings. While the topologically trivial state with broken time-reversal symmetry appears in the absence of spin-orbit coupling, the highest flat band becomes dispersive with a hexagonal symmetry due to spin-orbit coupling, which leads to a topological superconducting state. Since the thermal Hall conductivity in the low-tem…
The anisotropy in the temperature dependence of the in-plane and c-axis conductivities of high-T_c cuprates in the superconducting state is shown to be consistent with a strong in-plane momentum dependence of both the quasiparticle scattering rate and the interlayer hopping integral. Applying the cold spot scattering model recently proposed by Ioffe and Millis (Phys. Rev. B {\bf 58}, 11631 (1998)) to the superconducting state, we find that the c-axis conductivity varies approximately as T^3 in an intermediate temperature regime, in good agreement with the experimental result for optimally dope…
The thermal conductivity of organic superconductor kappa-(BEDT-TTF)2Cu(NCS)2 (Tc =10.4 K) has been studied in a magnetic field rotating within the 2D superconducting planes with high alignment precision. At low temperatures (T < 0.5 K), a clear fourfold symmetry in the angular variation, which is characteristic of a d-wave superconducting gap with nodes along the directions rotated 45 degrees relative to the b and c axes of the crystal, was resolved. The determined nodal structure is inconsistent with recent theoretical predictions of superconductivity induced by the antiferromagnetic spin flu…
We present new measurements of the thermal conductivity of UPt3 down to very low temperatures (16mK) and under magnetic fields (up to 4 T) which cover all the superconducting phases of UPt3. The measurements in zero field are compared with recent theoretical predictions for the thermal conductivity, which is dominated by impurity states at the lowest temperatures studied. The measurements under magnetic field at low temperatures are surprising since they don't show the expected low field square root dependence. The discontinuity of d kappa/dT at Tc changes drastically when passing from the hig…
We present anisotropic thermal expansion measurements on single crystalline ErNi2B2C. All three, superconducting, antiferromagnetic and weak ferromagnetic phase transitions are unambiguously distinguished in the data. Anisotropic uniaxial pressure dependencies of the transitions are estimated based on the Ehrenfest relation, leading to a conclusion, in particular, that weak ferromagnetic state will be suppressed by small, order of several kbar, hydrostatic pressure.
We compute the optical conductivity of 2D f-wave superconductors and also of the multigap model proposed recently by Zhitomirsky and Rice at T=0K in the Born limit. The presence of interband impurity scattering was found to play an important role: the contributions from the two bands mix up, and new structures are seen in the tunneling density of states and in the optical spectrum as well, corresponding to interband transitions. This will provide a sensitive test in selecting the competing models for the triplet superconductivity in Sr_2RuO_4.
We calculate the fluctuation correction to the normal state conductivity in the vicinity of a quantum phase transition from a superconducting to normal state, induced by applying a magnetic field parallel to a dirty thin film or a nanowire with thickness smaller than the superconducting coherence length. We find that at zero temperature, where the correction comes purely from quantum fluctuations, the positive Aslamazov-Larkin contribution, the negative density of states contribution, and the Maki-Thompson interference contribution, are all of the same order and the total correction is negativ…
The anisotropy in the microwave conductivity of the ortho-II YBa$_2$Cu$_3$O$_{6.50}$ is studied within the kinetic energy driven superconducting mechanism. The ortho-II YBa$_2$Cu$_3$O$_{6.50}$ is characterized by a periodic alternative of filled and empty $\hat{b}$-axis CuO chains. By considering the CuO chain induced extended anisotropy impurity scattering, the main features of the anisotropy in the microwave conductivity of the ortho-II YBa$_2$Cu$_3$O$_{6.50}$ are reproduced based on the nodal approximation of the quasiparticle excitations and scattering processes, including the intensity an…
