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To clarify the order parameter symmetry of cuprates, the magnetic penetration depth $lambda$ was measured along the crystallographic directions $a$, $b$, and $c$ in single crystals of YBa$_2$Cu$_4$O$_8$ via muon spin rotation. This method is direct, bulk sensitive, and unambiguous. The temperature dependences of $lambda_a^{-2}$ and $lambda_b^{-2}$ exhibit an inflection point at low temperatures as is typical for two-gap superconductivity (TGS) with $s+d-$wave character in the planes. Perpendicular to the planes a pure s-wave gap is observed thereby highlighting the important role of c-axis effects. We conclude that these are generic and universal features in the bulk of cuprates.
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The temperature dependence of the in-plane magnetic penetration depth, $lambda_{ab}(T)$, has been measured in a c-axis oriented polycrystalline CaC$_{6}$ bulk sample using a high-resolution mutual inductance technique. A clear exponential behavior of $lambda_{ab}(T)$ has been observed at low temperatures, strongly suggesting isotropic s-wave pairing. Data fit using the standard BCS theory yields $lambda_{ab}(0)=(720pm 80)$ Angstroem and $Delta(0)=(1.79pm 0.08)$ meV. The ratio $2Delta(0)/k_{_B}T_{c}=(3.6pm 0.2)$ gives indication for a conventional weakly coupled superconductor.
Neutron crystal-field spectroscopy experiments in the Y- and La-type high-temperature superconductors HoBa2Cu3O6.56, HoBa2Cu4O8, and La1.81Sr0.15Ho0.04CuO4 are reviewed. By this bulk-sensitive technique, information on the gap function is obtained from the relaxation behavior of crystal-field transitions associated with the Ho3+ ions which sit as local probes close to the superconducting copper-oxide planes. The relaxation data exhibit a peculiar change from a convex to a concave shape between the superconducting transition temperature Tc and the pseudogap temperature T* which can only be modelled satisfactorily if the gap function of predominantly d-wave symmetry includes an s-wave component of the order of 20-25%, independent of the doping level. Moreover, our results are compatible with an unusual temperature dependence of the gap function in the pseudogap region (Tc<T<T*), i.e., a breakup of the Fermi surface into disconnected arcs.
We discuss a new mechanism of microwave absorption in s- and d-wave superconductors, which arises in the presence of a dc supercurrent in the system. It produces a contribution to the ac conductivity that is proportional to the inelastic quasiparticle relaxation time. This contribution also determines the supercurrent dependence of the conductivity. It may significantly exceed the conventional contribution because in typical superconductors the inelastic relaxation time is several orders of magnitude longer than the elastic one. We show that the aforementioned contribution to the conductivity may be expressed in terms of the single particle density of states in superconductors in the presence of a dc supercurrent. Our results may enable determination of the inelastic relaxation time in superconductors from microwave absorption measurements.
We explore the physical properties of a unified microscopic theory for the coexistence of superconductivity and charge density waves in two-dimensional transition metal dichalcogenides. In the case of particle-hole symmetry the elementary particles are Dirac fermions at the nodes of the charge density wave gap. When particle-hole symmetry is broken electron (hole) pockets are formed around the Fermi surface. The superconducting ground state emerges from the pairing of nodal quasi-particles mediated by acoustic phonons via a piezoelectric coupling. We calculate several properties in the s-wave superconducting phase, including specific heat, ultra-sound absorption, nuclear magnetic relaxation, thermal, and optical conductivities. In the case with particle-hole symmetry, the specific heat jump at the transition deviates strongly from ordinary superconductors. The nuclear magnetic response shows an anomalous anisotropy due to the broken time-reversal symmetry of the superconducting gap, induced by the triple charge density wave state. The loss of lattice inversion symmetry in the charge density wave phase leads to anomalous coherence factors in the optical conductivity and to the appearance of an absorption edge at the optical gap energy. Furthermore, optical and thermal conductivities display anomalous peaks in the infrared when particle-hole symmetry is broken.
It has long remained elusive whether CuCo$_{2}$S$_{4}$ thiospinel shows bulk superconductivity. Here we clarify the issue by studying on the samples of sulfur-deficient CuCo$_{2}$S$_{3.7}$ and sulfurized CuCo$_{2}$S$_{4}$. The sample CuCo$_{2}$S$_{3.7}$ has a smaller lattice constant of $a=9.454$ {AA}, and it is not superconducting down to 1.8 K. After a full sulfurization, the $a$ axis of the thiospinel phase increases to 9.475 {AA}, and the thiospinel becomes nearly stoichiometric CuCo$_{2}$S$_{4}$, although a secondary phase of slightly Cu-doped CoS$_2$ forms. Bulk superconductivity at 4.2 K and Pauli paramagnetism have been demonstrated for the sulfurized CuCo$_{2}$S$_{4}$ by the measurements of electrical resistivity, magnetic susceptibility, and specific heat.
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