Session V38: Superconductivity-Thermodynamics and Structure

Specific heat studies of heavy ion irradiated YBCO.

We present a systematic study of the effect of heavy ion irradiation induced columnar defects on the vortex phase diagram in single-crystal YB$_{2}$Cu$_{3}$O$_{7 }$using ac - specific heat measurements. In pristine, naturally untwinned crystals the transition between the vortex liquid and vortex lattice states in intermediate fields is of first order as evidenced by a sharp peak in the specific heat. On our sample we observed the first order transition between the lower critical point near 0.35T and the upper critical point near 6T. The pristine sample was cleaved into several pieces of typical size 70x100x9 $\mu $m, which were irradiated along the c axis with 1.1 GeV Pb ions at different dose matching fields ranging from 0.1 T to 0.35 T. Specific heat measurements pertaining to the transformation of the first order transition to higher order with increasing disorder as exemplified by the shift in the lower critical point will be addressed.   

Low temperature specific heat study on Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta}$

By annealing the electron-doped Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-\delta}$ (PLCCO) in vacuum at different temperatures, we have successfully obtained several superconducting PLCCO samples with different T$_{c}$. The specific heat of all the samples show a 1/T$^2$ behavior below 1K. Above 1K, the low field specific heat can be fitted by $\gamma(H) T + \beta T^3$, where the $\gamma(H)$ is the Sommerfeld coefficient. We present magnetic field dependent data of $\gamma(H)$ for several samples of PLCCO and discuss the evolution of $\gamma(H)$ as PLCCO is tuned from an antiferromagnetically ordered insulator to a Tc=25 K superconductor.   

Anisotropic properties of unconventional superconductors in a magnetic field: testing the nodal stucture

We present a calculation of electronic specific heat and heat conductivity in a vortex state of quasi-two dimensional d-wave superconductors. We employ quasiclassical theory and use the Brand-Pesch-Tewordt approximation to model the superconducting state at moderate to high magnetic fields. Within this framework we investigate the dependence of heat capacity and heat conductivity on the angle of rotation of magnetic field with respect to the nodal directions. We find that the fourfold anisotropy due to nodal structure in both quantities changes sign in the temperature-field plane. This result helps resolve the apparent disagreement about the gap symmetry reached from the specific heat and the thermal conductivity measurements in CeCoIn5. We comment on the physics behind the difference between our results and those obtained in the Doppler shift approximation.   

Comparative analysis of specific heat of YNi$_{2}$B$_{2}$C using nodal and two-gap models

The magnetic field dependence of low temperature specific heat in YNi$_{2}$B$_{2}$C was measured and analyzed using various pairing order parameters. At zero magnetic field, the two-gap model which has been successfully applied to MgB$_{2 }$and the point-node model, appear to describe the superconducting gap function$_{ }$of YNi$_{2}$B$_{2}$C better than other models based on the isotropic $s$-wave, the $d$-wave line nodes, or the $s+g$ wave. The two energy gaps, \textit{$\Delta $}$_{L}$=2.67 meV and \textit{$\Delta $}$_{S}$=1.19 meV are obtained. The observed nonlinear field dependence of electronic specific heat coefficient, \textit{$\gamma $}($H)\sim H^{0.47},$ is quantitatively close to\textit{ $\gamma $}($H)\sim H^{0.5}_{ }$expected for nodal superconductivity or can be qualitatively explained using two-gap scenario. Furthermore, the positive curvature in $H_{c2}(T)$ near $T_{c}$ is qualitatively similar to that in the other two-gap superconductor MgB$_{2}$.   

Probing the anisotropic phonon attenuation in superconducting lead.

Phonon imaging of single crystals of superconducting Pb have uncovered a strong attenuation of phonons in (111) planes. Early data by Wolfe and Short$^{2}$ raised the possibility of a spin-density-wave ground state as proposed by Overhauser and Daemen.$^{3}$ This interpretation depends on the frequencies of the ballistic phonons, which previously were determined by a Planckian heater source and isotope scattering. We have designed and fabricated a low-pass filter in an attempt to select phonon energies below a characteristic activation energy, in order to clarify the source of the attenuation lines. We present new phonon-imaging data under various conditions and discuss the possible interpretations. $^{2}$ Physica B 316-317 (2002) 107-109 $^{3 }$ Phys. Rev. B 39, 6431 (1989)   

Hard X-ray Structural Studies of HgBa$_2$CuO$_{4+\delta}$

Recent high-energy x-ray diffuse scattering work on the compounds YBCO and BSCCO shows that these high-$T_c$ superconductors are typically intrinsically inhomogeneous [1-3]. These inhomogeneities are short-range-ordered lattice modulations driven by oxygen dopants, and they appear to have an important role in the electronic, transport, and spectroscopic properties of these systems. HgBa$_2$CuO$_{4+\delta}$ (Hg1201) has a simple structure and the highest $T_c$ (at optimal doping) among all single-layer compounds. It is thus a perfect candidate system to address the issue of charge modulations. Here we present evidence for short-range incommensurate displacement modulations and discus our results in the context of similar findings in other compounds. \begin{enumerate} \item Z. Islam et al. PRL 93, 157008 (2004) \item J. Strempfer et al. PRL 93, 157007 (2004) \item J. P. Castellan et al. http://arXiv.org/abs/cond-mat/0507505 \end{enumerate}   

Structure at low temperature of oxygen isotope exchanged La$_{1.8875}$Sr$_{0.1125}$CuO$_{4}$

The crystal structures at low temperatures of oxygen isotope-exchanged pairs of La$_{1.8875}$Sr$_{0.1125}$CuO$_{4}$ were examined using high resolution synchrotron powder x-ray diffraction at NSLS X7A. This study was designed to examine the possibility that small structural differences might contribute to the observed superconducting isotope effects. The x-ray diffraction regions about the orthorhombic (200),(020) peaks of $^{16}$O and $^{18}$O isotope-exchanged pairs were studied in detail. There is no significant difference in orthorhombic lattice parameters at any temperature. A minority ($\sim $10{\%}) tetragonal (LTT) phase is also necessary to adequately account for the observed intensities at low temperatures. The fraction of LTT phase does not differ perceptibly with oxygen isotope exchange. We conclude, based on direct measurement of crystal structure at low temperatures, that the observed differences in superconductivity of oxygen isotope exchanged pairs are likely intrinsic effects.   

Preliminary Inelastic Neutron Scattering Results for the Magnetic Excitations in the Model Superconductor HgBa$_{2}$CuO$_{4+\delta }$

HgBa$_{2}$CuO$_{4+\delta }$ has a simple crystal structure and possess the highest T$_{c}$ (97 K at optimal doping) among all the single-layer cuprates. In a significant breakthrough, we were able to grow large HgBa$_{2}$CuO$_{4+\delta }$ single crystals, enabling us to perform the first inelastic magnetic neutron scattering experiments on this model superconductor. We performed energy scans at ($\pi $,$\pi )$ and momentum scans at fixed energy at 10 K and above Tc. Our preliminary results include the observation of a 52 meV feature at ($\pi $, $\pi )$ that resembles the ``resonance'' found in other cuprates.   

Stability Constraints and Local Criteria for the Bounds on $T_c$ of Conventional Superconductors

In the regime of weak electron-phonon coupling, the scale of and bounds on $T_c$ are set by the real phonon frequencies of a material. In the strong coupling limit of Eliashberg theory, the phonon frequencies no longer limit the transition temperature because $T_c$ can grow without bound as $\sim \sqrt {\lambda}\omega_{ph}$, where $\lambda$ is the electron-phonon coupling parameter. However, structural stability of the system puts bounds on $T_c$ even in the strongly coupled regime due to the softening of phonons. In this case, $T_c$ is also bounded by an averaged un-renormalized phonon frequency defined for a non-metallic precursor material. Additional features of this model will also be discussed.   

Anisotropic Superconducting Phase Diagram of C$_{6}$Ca

We present a study of the anisotropic superconducting phase diagram of the new carbon intercalation superconductor C$_{6}$Ca employing magnetization and specific heat measurements. The intercalation of Ca into flakes of natural graphite takes place through vapor transport at temperatures near 500 $^{0}$C. The resulting crystals display an onset of superconductivity at 11.3 K and a transition width of about 1 K as seen in heat capacity and low-field magnetization measurements. A clear step in the heat capacity confirms the bulk nature of the superconducting state. Roughly 1/3 to 1/2 of the sample volume is superconducting as evidenced by the reduced step height of the heat capacity. From measurements of the upper critical field, H$_{c2}$, we determined an in-plane coherence length of $\xi _{ab}$ $\approx $ 36 nm. The angular dependence of H$_{c2}$ is well described within the model of effective mass anisotropy yielding an anisotropy parameter of $\Gamma \quad \approx $ 3.5 to 4.   

Upper critical field H$_{c2}$ in PrOs$_{4}$Sb$_{12}$

We study the upper critical field of the A and B phases in the triplet superconductor PrOs$_{4}$Sb$_{12}$ within the p+h-wave superconductivity proposed recently for this material. The present result is compared with H$_{c2}$(t) and H*(t), the boundary between the A and B phase in PrOs$_{4}$Sb$_{12}$, reported earlier and with more recent data of H$_{c2}(t)$ for the single phase crystal. We find H$_{c2}$(t)'s for both the two phase crystal and the single phase crystal are described by the model for the A phase. From this fitting one can deduce the Fermi velocity as $v=2.5 \times 10^6$ cm/s. On the other hand H$_{c2}$(t)for the B phase is found to be somewhat smaller than H*(t), which is rather puzzling.   

Superconductivity and magnetism in small attractive and repulsive Hubbard clusters

The existing mapping between the ground state properties of $U>0$ and $U<0$ Hubbard models are extended to finite temperatures, arbitrary magnetic field and electron doping or chemical potential for small two and four sites clusters. The microscopic origin of charge-spin separation effect and pseudogap formation are studied in response thermodynamics for spin and charge susceptibilities, using exact analytical diagonalization technique and grand canonical ensemble method. In the limiting case of non- interacting particles there are no temperature or magnetically driven driven spin-charge separation. The obtained knowledge we use to compare the thermodynamic phase diagrams of $U>0$ and $U<0$ clusters in a multidimensional parameter space of temperature, magnetic field and chemical potential. Magnetism and superconductivity are often thought to be incomparable with one another, however, we found many identical features for $U>0$ and $U<0$ at various range of doping level in the specific heat, spin and charge pseudogaps, Mott-Hubbard and antiferromagnetic crossovers, when these physical characteristics are monitored as a function of chemical potential or doping level. The developed bottom up approach for small clusters displays important intrinsic characteristics of high$T_c$ superconductors.   

Spin-triplet pairing in noncentrosymmetric superconductors: Li$_2$Pd$_3$B and Li$_2$Pt$_3$B

Superconductors lacking inversion symmetry exhibit qualitatively distinct properties from those with an inversion center. In this presentation, we report strong evidence for triplet superconductivity caused solely by the absence of parity symmetry in two closely related cubic compounds Li$_2 $Pd$_3$B and Li$_2$Pt$_3$B. Broken inversion symmetry admits antisymmetric spin-orbit coupling, admixing spin-singlet and spin-triplet pairing even with s-wave orbital symmetry. The triplet contribution is weak in Li$_2$Pd$_3$B, a BCS-like superconductor with an anisotropic gap. With increased spin- orbit coupling the spin-triplet component dominates in Li$_2 $Pt$_3$B, producing line nodes in the energy gap. Results are supported by the quantitative agreement between experimental penetration depth data and theory. Our findings demonstrate that unconventional superconducting properties can originate from a conventional phonon pairing mechanism rather than requiring purely electronic coupling mechanisms as usually considered.   

Low Temperature Normal State Specific Heat properties of La$_{2-x}$Sr$_x$CuO$_4$ using High Magnetic Fields

A number of models for high Tc cuprates suggest that the anomalous electronic properties of HTS are governed by the existence of a quantum critical point (QCP). According to this scenario, the superconductivity arises from the competition between two states and the resulting fluctuation-mediated pairing. In heavy fermions, non-Fermi liquid behavior has often been observed near a QCP: eg near-linear power-law resistivity and a divergence in the Sommerfeld coefficient in the zero temperature limit. By using extremely high magnetic fields we suppress superconductivity and reveal the normal state in the zero temperature limit. The specific heat is measured using the relaxation technique on several different dopings of LSCO. The electronic specific heat is isolated by subtracting the phonon specific heat measured on LCO, the parent insulating compound. One overdoped single crystal studied (LSCO with a nominal Srx=0.22) was cut from the same crystal that displays a linear electrical resistivity between room temperature and $\sim $5K, when the superconductivity is suppressed with a 45T magnetic field applied along the $c$-axis.