Session X11: Focus Session: MgB2-like: Properties of Exotic Superconductors

Symmetry properties and residual transport in superconducting PrOs$_4$Sb$_{12}$

We identify a three-component order parameter in the triplet channel as the most probable candidate for superconductivity in PrOs$_4 $Sb$_{12}$. Two different superconducting phases have been observed in PrOs$_4$Sb$_{12}$; the lower temperature `B phase' occupies the bulk of the phase diagram and breaks time reversal symmetry while the higher temperature `A phase' is found in a narrow region below H$_{c2} $, and possibly does not exist at all. The gap function in the A phase is unitary and has two nodes in the $[001]$ direction. In the B phase, the gap function is nonunitary and the lower branch has four cusp nodes in the $[\pm\alpha,\pm\beta,0]$ directions. The conductivity tensor, due to isotropic impurity scattering, has inequivalent diagonal components due to the off-axis nodal positions of the B phase.   

Scanning SQUID imaging of Sr$_{2}$RuO$_{4}$ and PrOs$_{4}$Sb$_{12}$

We present scanning SQUID magnetometer data on the superconducting materials strontium ruthenate (Sr$_{2}$RuO$_{4})$ and praseodymium-osmium-antimonide (PrOs$_{4}$Sb$_{12})$, both of which are believed to have spin-triplet pairing and to generate spontaneous time-reversal-symmetry-breaking fields below their superconducting transition temperatures. Our images, taken with a SQUID with a resolution of 3$\mu $m and approximately 100$\mu $G, do not show evidence for spontaneous TRSB fields, in contrast with muon spin rotation data which indicates gauss-scale fields in both materials. The fields indicated by $\mu $SR data must therefore have a short length scale and/or a short time scale. Supposing that the TRSB fields are static with the magnitudes indicated by $\mu $SR data we place upper limits on their length scales in both Sr$_{2}$RuO$_{4}$ and PrOs$_{4}$Sb$_{12}$. We also place upper limits on the strength of any distributed fields that might exist at sample edges and order parameter domain walls.   

Gauge-invariant electromagnetic response of a chiral $p_x+ip_y$ superconductor

We study electromagnetic properties of spin-triplet superconductors with chiral $p_x+ip_y$ symmetry of the pairing order parameter. As a result of spontaneously broken time-reversal symmetry, the electromagnetic response of $p_x\!+ip_y$ superconductor contains additional (anomalous) terms that are not present in conventional superconductors. Using effective action approach, we show that in $p_x\!+ip_y$ superconductors an external electric field may generate transverse Hall-like currents which depend explicitly on the chirality of the pairing order parameter. We also find an analog of the London equation in the anomalous electromagnetic response which implies complete screening of Cooper-pair intrinsic orbital momentum. The implications of our results to the experiments on $\rm Sr_2RuO_4$[1,2] are discussed. \newline [1] J. Xia \emph{et. al.} Phys. Rev. Lett. {\bf 97}, 167002 (2006) \newline [2] J. R. Kirtley \emph{et. al.} Phys. Rev. B {\bf 76}, 014526 (2007)   

Stability of Half-Quantum Vortices in px+ipy Superconductors

We have analyzed the possibility of finding half-quantum magnetic vortices in a quasi-two-dimensional $p_x+ip_y$ superconductor (such as ${\rm Sr_2 RuO_4}$ is believed to be). The predicted exotic properties of these excitations - such as containing Majorana fermion core states with non-Abelian statistics - have recently attracted much attention for their potential application to topological quantum computation. However, these excitations have not been observed yet. In fact, an isolated half-quantum vortex has a divergent energy cost in the bulk due to the associated {\it unscreened} spin current. However, we have shown in our work that tightly bound pairs of half-quantum vortices with a finite separation may be stable or metastable when the ratio of spin superfluid density to superfluid density $\rho_{{\rm sp}}/\rho_{\rm s}$ is small - something we can reasonably expect in ${\rm Sr_2 RuO_4}$. Furthermore, we find that it might be possible to isolate them with present experimental techniques in submicron-sized samples; such samples may selectively allow only single half-quantum vortices to enter. Such an experiment which would be of great fundamental and potential practical interest.   

Angle-resolved Photoemission Study of Ca$_{1.8}$Sr$_{0.2}$RuO$_{4}$

We report angle-resolved photoemission spectroscopy results of the Fermi surface of Ca$_{1.8}$Sr$_{0.2}$RuO$_{4}$ which is at the boundary between a magnetic metal and an antiferromagnetic insulator in the phase diagram of the Ca-substituted strontium ruthenates. We did observe an orbital-selective Mott transition, which is, however, different with what has been predicted theoretically [1] for this material. Our ARPES results are consistent with both magnetic and transport properties observed in this material. \newline [1] V. I. Anisimov et al., Eur. Phys. J. B \textbf{25}, 191(2002)   

Superconducting pairing symmetries in the 3-K and bulk phases of Sr$_2$RuO$_4$

We report recent progress on our single-particle tunneling and phase-sensitive measurements on 3-K and bulk phases of Sr$_2$RuO$_4$. The latter refers to an eutectic phase of Sr$_2$RuO$_4$ that features Ru microdomains embedded in a single crystal of Sr$_2$RuO$_4$. These Ru microdomains are of a mesoscopic size and varying shape. Therefore their pairing symmetries are not subject to the same set of constraints as those in the bulk. We have performed tunneling measurements on the 3-K phase to identify $all$ possible pairing states in this unique superconducting system. The junctions used earlier were prepared by pressing In wire onto a cleaved $ab$ face of a Ru-containing Sr$_2$RuO$_4$ single crystal containing multiple Ru microdomains. More recently we focused on tunnel junctions prepared on pre-selected single Ru microdomains. Possible existence of an intrinsic mixed pairing state in the interior of a Ru microdomain featuring simultaneous presence of both the $s$- and $p$-wave superconducting condensates. We will also discuss briefly our current effort in the phase-sensitive measurements on bulk Sr$_2$RuO$_4$, focusing on detecting possible $/k_z$ dependence of the order parameter and the existence of domains.   

Hall Conductivity in a Spin-Triplet Superconductor

We calculate the Hall conductivity for a spin-triplet superconductor, using a generalized pairing symmetry dependent on an arbitrary phase, $\phi$. A promising candidate for such an order parameter is Sr$_{2}$RuO$_{4}$, whose superconducting order parameter symmetry is still subject to investigation. The value of this phase can be determined through Kerr rotation and DC Hall conductivity measurements. Our calculations impose significant constraints on $\phi$.   

Upper Critical Field and SdH Quantum Oscillation Studies in Organic Superconductor $\beta''$-(BEDT-TTF)$_2$SF$_5$CH$_2$CF$_2$SO$_3$

Upper critical fields and SdH quantum oscillations in the organic superconductor $ \beta''$-(BEDT-TTF )$_2$SF$_5$CH$_2$CF$_2$SO$_3$ have been studied by measuring the in-plane rf penetration depth with a tunnel diode oscillator technique. Previous measurements from other groups, with the applied field parallel to the conducting layers, were inconsistent. We report here that for the applied field parallel to the conducting layers the low temperature upper critical fields exceed the Pauli paramagnetic limit calculated by using a semi-empirical method. We will also discuss SdH quantum oscillation with the applied field perpendicular to the conducting layers, which has been found to have a frequency of 181 T and an effective mass of 1.84 $m_e$. The effective mass is consistent with those of other groups, but the oscillation frequency smaller than theirs ($\sim$196 T).   

Absolute penetration depth measurements in deuterated organic superconductor $\kappa $-(ET)$_{2}$Cu[N(CN)$_{2}$]Br

Penetration depth measurements were performed on fully deuterated $\kappa $-(ET)$_{2}$Cu[N(CN)$_{2}$]Br, an organic superconductor. A novel aluminum plating technique was used to determine the absolute penetration depth $\lambda $(T). As the cooling rate is varied from 30 mK/min to 180 K/min we observe systematic changes in T$_{C}$, superconducting fraction and $\lambda $(T). The data is analyzed using a model of superconducting domains embedded in an antiferromagnetic background.   

Determination of the Pauli Paramagnetic Limit in Quasi 2D Superconductors

We have calculated the Pauli paramagnetic limit ($H_p$) for different quasi 2D superconductors using a semi-empirical method. We then compared the calculated Pauli paramagnetic limits to penetration depth data obtained using a tunnel diode oscillator technique at low temperatures in a swept applied magnetic field. The organic superconductors examined are layered such that their behavior is dependent on their orientation to the applied magnetic field. In order to eliminate the effect of vortex dynamics, we examined data taken with the conducting layers oriented parallel to the applied magnetic field. For one of these materials, $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$, we find that eliminating vortex effects leaves us with one remaining feature in the data that may correspond to $H_p$. We also find that the material $\beta''$-(BEDT-TTF)$_2$SF$_5$CH$_2$CF$_2$SO$_3$ exhibits a change in slope for temperature versus upper critical field when the upper critical field exceeds the calculated $H_p$. In addition, many of the examined quasi 2D superconductors, including the above organic superconductors and CeCoIn$_5$, exhibit upper critical fields that exceed their calculated $H_p$ suggesting some type of non-conventional superconductivity.   

Second{\_}harmonic thermal conductivity of LSCO in magnetic fields

We describe a second harmonic technique to probe the thermal conductivity of LSCO with superconductivity suppressed by high magnetic fields. The technique is suitable for the high noise environment of pulsed magnets. By subtracting the thermal conductivity in field and at zero field, we obtain information about the temperature dependence of the order parameter. Work performed under the auspices of the National High Magnetic Field Laboratory   

Disorder induced weak and strong localization and their influence on superconductivity in underdoped Bi2+xSr2-xCuO6

In-plane resistivity and magnetoresistance(MR) measurements were carried out on high-quality underdoped Bi$_{2+x}$Sr$_{2-x}$CuO$_{6+\delta}$ (0.1$\leq$x$\leq$0.4) single crystals. The results show that the superconductivity and the normal state MR behaviors strongly rely on the doping level of samples. In the slightly doping level of Bi, a metallic normal state and a finite superconducting transition temperature are observed, and there is always a positive MR in the normal state which is explained by the fluctuating superconductivity mixed with the transport of quasiparticles. With further doping, the low temperature resistivity shows an up turn together with a negative MR. Detailed analysis on the negative MR in this region may suggest that weak localization effect is dominant. As the superconductivity is depressed by more doping and thus more disorders, the delocalization gets much harder and the spin-order contribution may be involved in MR. Moreover, in the heavily underdoped doping, the superconductivity is suppressed completely and resistivity evolves into a strong localization behavior with a Coulomb gap opening at the Fermi energy. After summarizing the doping dependence of MR, we construct a new phase diagram to illustrate how does the disorder give the influence both on the superconductivity and magnetoresistance.   

Unusual diamagnetic response in p-wave superconductors $\rm Sr_2RuO_4$

The magnetization $\bf M$ of the $p$-wave superconductor $\rm Sr_2RuO_4$ has not been measured previously in the geometry with magnetic field $\bf H\| c$ because of the small upper critical field ($H_{c2}\sim$ 660 Oe) and low $T_c$ (1.4 K). We have used high-resolution torque magnetometry to study in detail the magnetization curves in this geometry. We find that, in the superconducting state, the $M$-$H$ curves display highly unusual hysteretic behavior. In the critical state, whenever $\rm H$ crosses zero, we observe a break in the slope $\partial M/\partial H$. In a broad field interval $[-H_0, H_0]$ bracketing zero field, $\rm M$ is reversible (to our resolution) under reversal of sweep direction. This anomalous behavior is not encountered in conventional type-II superconductors, where the critical-state behavior is always non-reversible. A possible interpretation of these unusual features is the existence of reversible edge currents. We also discuss the magnetization curves with $\bf H \| ab$, where $\rm M$ jumps sharply at $\rm H = H_{c2}$. Research supported by NSF grant DMR 0213706.   

Emergence of dissipative structures in current-carrying stabilized superconducting wires.

We discuss the emergence of a dissipative structure in current-carrying superconducting wire. This is a phenomenon similar to the emergence of thermal convection cells, oscillatory chemical reactions, etc. In response to the initial localized temperature perturbation that leads to current exchange between the superconductor and the stabilizer the temperature and critical current density of the wire acquire spontaneous spatial modulation that forces the transport current to crisscross the interface between the superconducting film and metal stabilizer. This generates additional heat that makes such a structure self-sustainable. The central role in this phenomenon is played by the interfacial resistance between the stabilizer and superconducting film. The spatial scale of the modulation is of the order of the thermal diffusion length. This resistance also determines the speed of propagation of the conventional normal zone. We will present the results of numerical and analytical analysis of a model which describes current sharing between the superconducting and normal metal layers - a configuration typical of the state of the art YBCO-coated conductors.   

Thermoelectric effects and band-dependent scattering of normal-state quasiparticles in spin-triplet superconductor Sr$_2$RuO$_4$

We present the $first$ measurement on Nernst effects in the normal state of odd-parity, spin-triplet superconductor Sr$_2$RuO$_4$. Below 100 K, the negative Nernst signal was found to be large and nonlinear as a function of magnetic field with its absolute value increasing rapidly as the temperature was lowered. After reaching a maximum around $T$ = $T^*$ = 20 - 25 K, however, the Nernst signal drops linearly with the decreasing temperature. No corresponding feature was found around this temperature in the specific heat. We argue that the large value of the Nernst signal is related to the presence of multibands and the nonlinearity to band-dependent magnetic fluctuation in Sr$_2$RuO$_4$. Furthermore, the quasiparticle scattering from the magnetic fluctuation is suppressed below $T^*$ due to the emergence of coherence among quasiparticles in the $\gamma$ band, an active band for superconductivity in Sr$_2$RuO$_4$. Results on temperature dependence of the thermopower, which was seen to exhibit a sharp kink around $T^*$, provided further support to this picture of band-dependent normal-state properties. Our thermoelectric measurements appear to suggest that the suppression of the magnetic fluctuation makes it possible for the spin-triplet superconductivity to emerge in Sr$_2$RuO$_4$.