Specific heat and thermal conductivity in the mixed state of MgB2

The specific heat C and the electronic and phononic thermal conductivities kappa_e and kappa_{ph} are calculated in the mixed state for magnetic fields H near H_{c2}. The effects of supercurrent flow and Andreev scattering of the Abrikosov vortex lattice on the quasiparticles are taken into account. The resulting function C(H) is nearly linear while kappa_e(H) exhibits an upward curvature near H_{c2}. The slopes decrease with impurity scattering which improves the agreement with the data on MgB_2. The ratio of phonon relaxation times tau_n/tau_s = g(omega_0,H) for phonon energy omega_0, which is nearly a step function at omega_0 = 2Delta for the BCS state, is smeared out and tends to one for increasing H. This leads to a rapid reduction of kappa_{ph}(H) in MgB_2 for relatively small fields due to the rapid suppression of the smaller energy gap.Comment: 8 pages, 4 figures, accepted for publication in Phys. Rev. Letter

Thermal conductivity in the vortex state of the superconductor UPd_2Al_3

The magneto-thermal conductivity kappa is calculated for the vortex state of UPd_2Al_3 by assuming horizontal gap nodes. The Green's function method we employed takes into account the effects of supercurrent flow and Andreev scattering on the quasiparticles due to Abrikosov's vortex lattice order parameter. The calculated angular dependence of kappa_{yy} for field rotation theta_0 in the ac-plane depends strongly on field strength H, impurity scattering, anisotropy of the Fermi velocity, and temperature. For finite temperatures and the clean unitary scattering limit we get qualitative agreement with recent experiments for all four proposed gap functions having horizontal line nodes at ck_z = 0, pi/4, and pi/2.Comment: 12 pages, 3 figures with several part

Specific heat and thermal conductivity in the vortex state of the two-gap superconductor MgB_2

The specific heat coefficient gamma_s(H) and the electronic thermal conductivity kappa_{es}(H) are calculated for Abrikosov's vortex lattice by taking into account the effects of supercurrent flow and Andreev scattering. First we solve the gap equation for the entire range of magnetic fields. We take into account vertex corrections due to impurity scattering calculated in the Born approximation. The function gamma_s(H)/gamma_n increases from zero and becomes approximately linear above H/H_{c2} \sim 0.1. The dependence on impurity scattering is substantially reduced by the vertex corrections. The upward curvature of kappa_{es}(H)/kappa_{en}, which is caused by decreasing Andreev scattering for increasing field, is reduced for increasing impurity scattering. We also calculate the temperature dependence of the scattering rates 1/tau_{ps}(H) of a phonon and 1/tau_{es}(H) of a quasiparticle due to quasiparticle and phonon scattering, respectively. At low temperatures the ratio tau_{pn}/tau_{ps}(H) increases rapidly to one as H tends to H_{c2} which yields a rapid drop in the phononic thermal conductivity kappa_{ph}. Our results are in qualitative agreement with the experiments on the two-gap superconductor MgB_2.Comment: 12 pages, 5 figures, additions to figures 1, 2, and 3. Accepted by Phys. Rev.

Electromagnetic Response of a kx±ikyk_x\pm ik_y Superconductor: Effect of Order Parameter Collective Modes

Effects of order parameter collective modes on electromagnetic response are studied for a clean spin-triplet superconductor with $k_x\pm ik_y$ orbital symmetry, which has been proposed as a candidate pairing symmetry for Sr$_2$RuO$_4$. It is shown that the $k_x \pm ik_y$ superconductor has characteristic massive collective modes analogous to the clapping mode in the A-phase of superfluid $^3$He. We discuss the contribution from the collective modes to ultrasound attenuation and electromagnetic absorption. We show that in the electromagnetic absorption spectrum the clapping mode gives rise to a resonance peak well below the pair breaking frequency, while the ultrasound attenuation is hardly influenced by the collective excitations.Comment: 4 pages RevTex, 1 eps figur

The Gradient Expansion for the Free-Energy of a Clean Superconductor

We describe a novel method for obtaining the gradient expansion for the free energy of a clean BCS superconductor. We present explicit results up to fourth order in the gradients of the order parameter.Comment: 33 pages, Late

Ultrasonic attenuation in magnetic fields for superconducting states with line nodes in Sr2RuO4

We calculate the ultrasonic attenuation in magnetic fields for superconducting states with line nodes vertical or horizontal relative to the RuO_2 planes. This theory, which is valid for fields near Hc2 and not too low temperatures, takes into account the effects of supercurrent flow and Andreev scattering by the Abrikosov vortex lattice. For rotating in-plane field H(theta) the attenuation alpha(theta)exhibits variations of fourfold symmetry in the rotation angle theta. In the case of vertical nodes, the transverse T100 sound mode yields the weakest(linear)H and T dependence of alpha, while the longitudinal L100 mode yields a stronger (quadratic) H and T dependence. This is in strong contrast to the case of horizontal line nodes where alpha is the same for the T100 and L100 modes (apart from a shift of pi/4 in field direction) and is roughly a quadratic function of H and T. Thus we conclude that measurements of alpha in in-plane magnetic fields for different in-plane sound modes may be an important tool for probing the nodal structure of the gap in Sr_2RuO_4.Comment: 5 pages, 6 figures, replaced in non-preprint form, to appear in Phys. Rev.

Half-quantum vortex and d-soliton in Sr2_2RuO4_4

Assuming that the superconductivity in Sr$_2$RuO$_4$ is described by a planar p-wave order parameter, we consider possible topological defects in Sr$_2$RuO$_4$. In particular, it is shown that both of the ${\hat d}$-soliton and half-quantum vortex can be created in the presence of the magnetic field parallel to the $a$-$b$ plane. We discuss how one can detect the ${\hat d}$-soliton and half-quantum vortex experimentally.Comment: 8 pages, 3 figure

Correlation-function spectroscopy of inelastic lifetime in heavily doped GaAs heterostructures

Measurements of resonant tunneling through a localized impurity state are used to probe fluctuations in the local density of states of heavily doped GaAs. The measured differential conductance is analyzed in terms of correlation functions with respect to voltage. A qualitative picture based on the scaling theory of Thouless is developed to relate the observed fluctuations to the statistics of single particle wavefunctions. In a quantitative theory correlation functions are calculated. By comparing the experimental and theoretical correlation functions the effective dimensionality of the emitter is analyzed and the dependence of the inelastic lifetime on energy is extracted.Comment: 41 pages, 14 figure