Perspectives on Nodal Superconductors

Searching for topological insulators/superconductors is a central subject in recent condensed matter physics. As a theoretical aspect, various classification methods of symmetry-protected topological phases have been developed, where the topology of a gapped Hamiltonian is investigated from the viewpoint of its onsite/crystal symmetry. On the other hand, topological physics also appears in semimetals, whose gapless points can be characterized by topological invariants. Stimul...

We present preliminary measurements of the thermal conductivity of the heavy fermion superconductor UPd$_2$Al$_3$ for the normal and superconducting states at low temperatures. As T$\to$0, the superconducting state is characterized by a finite linear term, about 10% of the normal state value, which suggests a residual density of low energy quasiparticle states. This agrees qualitatively with resonant impurity scattering theories applied to exotic superconductors with nodes in...

This course has a dual purpose. First we review the successes of the weak-coupling BCS theory in describing new classes of superconductors discovered since 1979. They include the heavy-fermion superconductors, high-Tc cuprate superconductors, organic superconductors, Sr2RuO4, etc. Second, we present the quasiclassical approximation introduced by Volovik, which we extend to describe the thermodynamics and the thermal conductivity of the vortex state in nodal superconductors. T...

Determination of the symmetry property of superconducting gaps has been a central issue in studies to understand the mechanisms of unconventional superconductivity. Although it is often difficult to completely achieve the aforementioned goal, the existence of superconducting nodes, one of the few important experimental signatures of unconventional superconductivity, plays a vital role in exploring the possibility of unconventional superconductivity. The interplay between supe...

The spin-density wave (SDW) can be considered as a pair of charge density waves (CDWs), one composed only of electrons with up-spins and the other only of electrons with down-spins. The high-temperature superconductivity found in cuprates and pnictides may then be ascribed to BCS-type pairing between these SDWs, which is then no longer simple Cooper pairing between independent singlet electrons but rather involves collective interaction between Cooper pairs. The pseudo-gap ma...

The thermal conductivity, $\kappa$, of the heavy fermion superconductor UPt$_3$ was measured down to T$_c$/10. The absence of a linear term in the temperature dependence as T$\rightarrow$0 strongly suggests there are no zero energy quasiparticle excitations, in contradiction with the gapless behaviour often inferred from specific heat. A non-vanishing anisotropy ratio $\kappa_c$/$\kappa_b$ as T$\rightarrow$0 establishes a new property of the gap structure: the presence of nod...

In contrast to multigap superconductors (e.g. MgB$_{2}$), the low-temperature properties of nodal superconductors are dominated by nodal excitations. Here we extend for a variety of nodal superocnductors the earlier work by Simon and Lee and K\"ubert and Hirschfeld. The scaling relations seen in the thermodynamics and the thermal conductivity will provide an unequivocal test of nodal superconductivity.

Unconventional superconductors are most frequently identified by the observation of power-law behaviour on low-temperature thermodynamic or transport properties, such as specific heat. Here we show that, in addition to the usual point and line nodes, a much wider class of different nodal types can occur. These new types of nodes typically occur when there are transitions between different types of gap node topology, for example when point or line nodes first appear as a funct...

Point contact Andreev reflection spectra have been taken as a function of temperature and magnetic field on the polycrystalline form of the newly discovered iron-based superconductor Sr2ScFePO3. A zero bias conductance peak which disappears at the superconducting transition temperature, dominates all of the spectra. Data taken in high magnetic fields show that this feature survives until 7T at 2K and a flattening of the feature is observed in some contacts. Here we inspect wh...

We present a theoretical study of the superconducting gap function in PrOs4Sb12 using a symmetry-based approach. A three-component order parameter in the triplet channel best describes superconductivity. The gap function is non-degenerate and the lower branch has four cusp nodes at unusual points of the Fermi surface, which lead to power law behaviours in the density of states, specific heat and nuclear spin relaxation rate.