On the low temperature properties and specific anisotropy of pure anisotropically paired superconductors

Dependences of low temperature behavior and anisotropy of various physical quantities for pure unconventional superconductors upon a particular form of momentum direction dependence for the superconducting order parameter (within the framework of the same symmetry type of superconducting pairing) are considered. A special attention is drawn to the possibility of different multiplicities of the nodes of the order parameter under their fixed positions on the Fermi surface, which are governed by symmetry. The problem of an unambiguous identification of a type of superconducting pairing on the basis of corresponding experimental results is discussed. Quasiparticle density of states at low energy for both homogeneous and mixed states, the low temperature dependences of the specific heat, penetration depth and thermal conductivity, the I-V curves of SS and NS tunnel junctions at low voltages are examined. A specific anisotropy of the boundary conditions for unconventional superconducting order parameter near $T_c$ for the case of specular reflection from the boundary is also investigated.Comment: 20 page

Thermal Conductivity Anisotropy in Superconducting UPt3UPt_3

Recent thermal conductivity measurements on $UPt_3$ single crystals by Lussier et al. indicate the existence of a strong b--c anisotropy in the superconducting state. We calculate the thermal conductivity in various unconventional candidate states appropriate for the $UPt_3$ ``B phase" and compare with experiment, specifically the $E_{2u}$ and $E_{1g}$ $(1,i)$ states predicted in some Ginzburg-Landau analyses of the phase diagram. For the simplest realizations of these states over spherical or ellipsoidal Fermi surfaces, the normalized $E_{2u}$ conductivity is found, surprisingly, to be completely isotropic. We discuss the effects of inelastic scattering and realistic Fermi surface anisotropy, and deduce constraints on the symmetry class of the $UPt_3$ ground state.Comment: 4 postscript pages, UFL102

Nonmonotonous Magnetic Field Dependence and Scaling of the Thermal Conductivity for Superconductors with Nodes of the Order Parameter

We show that there is a new mechanism for nonmonotonous behavior of magnetic field dependence of the electronic thermal conductivity of clean superconductors with nodes of the order parameter on the Fermi surface. In particular, for unitary scatterers the nonmonotony of relaxation time takes place. Contribution from the intervortex space turns out to be essential for this effect even at low temperatures. Our results are in a qualitative agreement with recent experimental data for superconducting UPt_3. For E_{2u}-type of pairing we find approximately the scaling of the thermal conductivity in clean limit with a single parameter x=T/T_c\sqrt{B_{c2}/B} at low fields and low temperatures, as well as weak low-temperature dependence of the anisotropy ratio K_{zz}/K_{yy} in zero field. For E_{1g}-type of pairing deviations from the scaling are more noticeable and the anisotropy ratio is essentially temperature dependent.Comment: 37 pages, 8 Postscript figures, REVTE

Theory of Thermal Conductivity in YBa_2Cu_3O_{7-\delta}

We calculate the electronic thermal conductivity in a d-wave superconductor, including both the effect of impurity scattering and inelastic scattering by antiferromagnetic spin fluctuations. We analyze existing experiments, particularly with regard to the question of the relative importance of electronic and phononic contributions to the heat current, and to the influence of disorder on low-temperature properties. We find that phonons dominate heat transport near T_c, but that electrons are responsible for most of the peak observed in clean samples, in agreement with a recent analysis of Krishana et al. In agreement with recent data on YBa_2(Cu_1-xZn_x)_3O_7-\delta the peak position is found to vary nonmonotonically with disorder.Comment: 4 pages, 4 figures, to be published in Phys. Rev. Let

Heat Transport and the Nature of the Order Parameter in Superconducting UPt3UPt_3

Recent thermal conductivity data on the heavy fermion superconductor $UPt_3$ have been interpreted as offering support for an $E_{2u}$ model of the order parameter as opposed to an $E_{1g}$ model. In this paper, we analyze this issue from a theoretical standpoint including the detailed effects of Fermi surface and gap anisotropy. Our conclusion is that although current data put strong constraints on the gap anisotropy, they cannot definitively distinguish between these two models. Measurements on samples of varying quality could be decisive in this regard, however.Comment: 8 pages, revtex, 15 uunencoded postscript figure

Electron-Phonon Interaction and Ultrasonic Attenuation in the Ruthenate and Cuprate superconductors

This article derives an electron-phonon interaction suitable for interpreting ultrasonic attenuation measurements in the ruthenate and cuprate superconductors. The huge anisotropy found experimentally (Lupien et al., 2001) in Sr2RuO4 in the normal state is accounted for in terms of the layered square-lattice structure of Sr2RuO4, and the dominant contribution to the attenuation in Sr2RuO4 is found to be due to electrons in the gamma band. The experimental data in the superconducting state is found to be inconsistent with vertical lines nodes in the gap in either (100) or (110) planes. Also, a general method, based on the use of symmetry, is developed to allow for the analysis of ultrasonic attenuation experiments in superconductors in which the electronic band structure is complicated or not known. Our results, both for the normal-state anisotropy, and relating to the positions of the gap nodes in the superconducting state, are different from those obtained from analyses using a more traditional model for the electron-phonon interaction in terms of an isotropic electron stress tensor. Also, a brief discussion of the ultrasonic attenuation in UPt3 is given.Comment: 12 pages. Comments have been added to the original version of this article showing how, for the ultrasonic attenuation for a hexagonal crystal (which must be isotropic with respect to rotations about the c axis) our approach reproduces the results of the traditional isotropic electron stress tensor mode

d-Wave Model for Microwave Response of High-Tc Superconductors

We develop a simple theory of the electromagnetic response of a d- wave superconductor in the presence of potential scatterers of arbitrary s-wave scattering strength and inelastic scattering by antiferromagnetic spin fluctuations. In the clean London limit, the conductivity of such a system may be expressed in "Drude" form, in terms of a frequency-averaged relaxation time. We compare predictions of the theory with recent data on YBCO and BSSCO crystals and on YBCO films. While fits to penetration depth measurements are promising, the low temperature behavior of the measured microwave conductivity appears to be in disagreement with our results. We discuss implications for d-wave pairing scenarios in the cuprate superconductors.Comment: 33 pages, plain TeX including all macros. 16 uuencoded, compressed postscript figures are appended at the en

Deep Theorizing in International Relations

This paper starts from the observation that, at a time when the popularity of grand theory is in decline among IR scholars, they do not agree on what they mean by theory. In fact, the celebration of theoretical pluralism is accompanied by the relative absence of a serious conversation about what ‘theory’ is, could, or should be. Taking the view that we need such a conversation, this puts forward the notion of ‘deep theorizing’. Countering both the shallow theorizing of modern scholarship that conflates theory with scientific method, and the postmodern view that abstract narratives must be deconstructed and rejected, it offers a reading of the parameters along which substantial theorizing proceeds. Specifically, it suggests that ‘deep theorizing’ is the conceptual effort of explaining (inter)action by developing a reading of drives/basic motivations and the ontology of its carrier through an account of the human condition, that is, a particular account of how the subject (the political actor) is positioned in social space and time. The paper illustrates the plausibility of this meta-theoretical angle in a discussion of realist, liberal and postcolonial schools of thought