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We describe a mechanism by which the longitudinal thermal conductivity$\kappa_{xx}$, measured in an in-plane magnetic field, oscillates as a functionof field angle in layered nodal superconductors. These oscillations occur whenthe spin-orbit splitting at the nodes is larger than the nodal scattering rate,and are complementary to vortex-induced oscillations identified previously. Insufficiently anisotropic materials, the spin-orbit mechanism may be dominant.As a particular application, we focus on the cuprate high-temperaturesuperconductor YBa$_2$Cu$_3$O$_{6+x}$. This material belongs to the class ofRashba bilayers, in which individual CuO$_2$ layers lack inversion symmetryalthough the crystal itself is globally centrosymmetric. We show thatspin-orbit coupling endows $\kappa_{xx}/T$ with a characteristic dependence onmagnetic field angle that should be easily detected experimentally, and arguethat for underdoped samples the spin-orbit contribution is larger than thevortex contribution. A key advantage of the magneto-thermal conductivity isthat it is a bulk probe of spin-orbit physics, and therefore not sensitive toinversion breaking at surfaces.

Intrinsic Mechanism for Magneto-Thermal Conductivity Oscillations in Spin-Orbit-Coupled Nodal Superconductors