Unconventional superconductors under rotating magnetic field I: density of states and specific heat

The thermal conductivity of heavy-fermion superconductor CeCoIn$_5$ was measured with a magnetic field rotating in the tetragonal a-b plane, with the heat current in the anti-nodal direction, $J$ || [100]. We observe a sharp resonance in thermal conductivity for the magnetic field at an angle $\theta$ $\sim$ 12$^{\circ}$, measured from the heat current direction [100]. This resonance corresponds to the reported resonance at an angle $\theta'$ $\sim$ 33$^{\circ}$ from the dire...

We show that the density of states and the thermodynamic properties of a 2D d-wave superconductor in the vortex state with applied magnetic field $\bf H$ in the plane depend on the angle between $\bf H$ and the order parameter nodes. Within a semiclassical treatment of the extended quasiparticle states, we obtain fourfold oscillations of the specific heat, measurement of which provides a simple probe of gap symmetry. The frequency dependence of the density of states and the t...

Experiments on several novel superconducting compounds have observed oscillations of the specific heat when an applied magnetic field is rotated with respect to the crystal axes. The results are commonly interpreted as arising from the nodes of an unconventional order parameter, but the identifications of nodal directions are sometimes controversial. Here we show with a semiclassical model calculation that when the magnetic field points in the direction of the nodes, either m...

We consider, within BCS weak coupling theory, the instability of a $d_{x^2-y^2}$-wave superconductor to a state of mixed symmetry $d+iq$, $q=d_{xy},s$. In zero magnetic field we show that there is a large and physically reasonable range of interaction strengths for which a pure $d_{x^2-y^2}$ state is stable down to T=0. In this case a magnetic field, assumed to couple to quasiparticles via their Doppler shifts in the vortex superflow field, is shown to induce a phase transiti...

We report field-orientation specific heat studies of the pressure-induced heavy fermion superconductor CeRhIn5. Theses experiments provide the momentum-dependent superconducting gap function for the first time in any pressure-induced superconductor. In the coexisting phase of superconductivity and antiferromagnetism, field rotation within the Ce-In plane reveals four-fold modulation in the density of states, which favors a d-wave order parameter and constrains a theory of the...

The density of states of a 2D d-wave superconductor in the vortex state with applied magnetic field $\bf H$ in the plane is shown to exhibit fourfold oscillations as a function of the angle of the field with respect to the crystal axes. We find further that the frequency dependence of the density of states and the temperature dependence of transport coefficients obey different power laws, thus leading to different magnetic scaling functions, for field in the nodal and anti-no...

Over the past two decades, unconventional superconductivity with gap symmetry other than s-wave has been found in several classes of materials, including heavy fermion (HF), high-T_c, and organic superconductors. Unconventional superconductivity is characterized by anisotropic superconducting gap functions, which may have zeros (nodes) along certain directions in the Brillouin zone. The nodal structure is closely related to the pairing interaction, and it is widely believed t...

We analyse the combined effect of orbital and Pauli depairing on the superconducting state, and apply the results to the heavy fermion CeCoIn$_5$. We find that: a) standard extrapolation based on the slope of $H_{c2}(T)$ in the vicinity of the transition temperature to T=0 does not always give accurate values of the orbital upper critical field; b) critical value of the Maki parameter, $\alpha$, that determines onset of the first order transition depends on the Fermi surface ...

The appearance of spin-density-wave (SDW) magnetic order in the low-temperature and high-field corner of the superconducting phase diagram of CeCoIn$_5$ is unique among unconventional superconductors. The nature of this magnetic $Q$ phase is a matter of current debate. Here, we present the thermal conductivity of CeCoIn$_5$ in a rotating magnetic field, which reveals the presence of an additional order inside the $Q$ phase that is intimately intertwined with the superconducti...

The specific heat oscillation in the mixed state of type II superconductors is studied theoretically when rotating field within a plane containing gap minimum and maximum. The calculations are performed microscopically by solving quasi-classical Eilenberger equation for vortex lattices. The field dependence of the oscillation amplitude can discriminate between the nodal and anisotropic gap with a finite minimum and the oscillation phase gives the gap minimum position on the F...