Abstract
We describe a mechanism by which the longitudinal thermal conductivity $\kappa_{xx}$, measured in an in-plane magnetic field, oscillates as a function of field angle in layered nodal superconductors. These oscillations occur when the spin-orbit splitting at the nodes is larger than the nodal scattering rate, and are complementary to vortex-induced oscillations identified previously. In sufficiently anisotropic materials, the spin-orbit mechanism may be dominant. As a particular application, we focus on the cuprate high-temperature superconductor YBa$_2$Cu$_3$O$_{6+x}$. This material belongs to the class of Rashba bilayers, in which individual CuO$_2$ layers lack inversion symmetry although the crystal itself is globally centrosymmetric. We show that spin-orbit coupling endows $\kappa_{xx}/T$ with a characteristic dependence on magnetic field angle that should be easily detected experimentally, and argue that for underdoped samples the spin-orbit contribution is larger than the vortex contribution. A key advantage of the magneto-thermal conductivity is that it is a bulk probe of spin-orbit physics, and therefore not sensitive to inversion breaking at surfaces.
Highlights
Nodal superconductors are characterized by an energy gap that vanishes at point or line “nodes” on the Fermi surface
This effect will be present whether or not the superconductor is quasi-two-dimensional, but must be disentangled from Doppler shift contributions if circulating vortex currents are not negligible. This is a bulk measurement that is insensitive to inversion symmetry breaking at sample surfaces and is complementary to other recent proposals: Kaladzhyan et al showed that the dominant Friedel oscillation wave vectors associated with impurity scattering reflect the spin-splitting of the Fermi surface and can be used to obtain the spinorbit coupling constant [37], while Raines et al discussed the practicality of spin-Hall and Edelstein effects as probes of spin-orbit coupling (SOC) [38]
We have shown that spin-orbit coupling generates a characteristic field-angle dependence of the longitudinal thermal conductivity in nodal superconductors
Summary
Nodal superconductors are characterized by an energy gap that vanishes at point or line “nodes” on the Fermi surface. We show that the nodal structure of the d-wave superconducting gap allows for an elegant and straightforward observation of spin-orbit coupling through the longitudinal thermal conductivity in a transverse magnetic field This effect will be present whether or not the superconductor is quasi-two-dimensional (quasi-2D), but must be disentangled from Doppler shift contributions if circulating vortex currents are not negligible. This is a bulk measurement that is insensitive to inversion symmetry breaking at sample surfaces and is complementary to other recent proposals: Kaladzhyan et al showed that the dominant Friedel oscillation wave vectors associated with impurity scattering (as measured by scanning tunneling spectroscopy) reflect the spin-splitting of the Fermi surface and can be used to obtain the spinorbit coupling constant [37], while Raines et al discussed the practicality of spin-Hall and Edelstein effects as probes of SOC [38]. We make an estimate that suggests that magnetothermal oscillations in YBa2Cu3O6.5 are dominated by spin-orbit effects
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