Anomalous angular dependence of the upper critical induction of   orthorhombic ferromagnetic superconductors with completely broken p-wave   symmetry
  We employ the Klemm-Clem transformations to map the equations of motion for the Green functions of a clean superconductor with a general ellipsoidal Fermi surface (FS) characterized by the effective masses $m_1, m_2$, and $m_3$ in the presence of an arbitrarily directed magnetic induction ${\bm B}=B(\sin\theta\cos\phi,\sin\theta\sin\phi,\cos\theta)$ onto those of a spherical FS. We then obtain the transformed gap equation for a transformed pairing interaction $\tilde{V}(\hat{\tilde{\bm k}},\hat{\tilde{\bm k}}')$ appropriate for any orbital order parameter symmetry. We use these results to calculate the upper critical induction $B_{c2}(\theta,\phi)$ for an orthorhombic ferromagnetic superconductor with transition temperatures $T_{\rm Curie}>T_c$. We assume the FS is split by strong spin-orbit coupling, with a single parallel-spin ($\uparrow\uparrow$) pairing interaction of the \textit{p}-wave polar state form locked onto the $\hat{\bm e}_3$ crystal axis normal to the spontaneous magnetization ${\bm M}_0\perp\hat{\bm e}_3$ due to the ferromagnetism. The orbital harmonic oscillator eigenvalues are modified according to $B\rightarrow B\alpha$, where $\alpha(\theta,\phi)=\sqrt{m_3/m}\sqrt{\cos^2\theta+\gamma^{-2}(\phi)\sin^2\theta}$, $\gamma^2(\phi)=m_3/(m_1\cos^2\phi+m_2\sin^2\phi)$ and $m=(m_1m_2m_3)^{1/3}$. At fixed $\phi$, the order parameter anisotropy causes $B_{c2}$ to exhibit a novel $\theta$-dependence, which for $\gamma^2(\phi)>3$ becomes a double peak at $0^{\circ}<\theta^{*}<90^{\circ}$ and at $180^{\circ}-\theta^{*}$, providing a sensitive bulk test of the order parameter orbital symmetry in both phases of URhGe and in similar compounds still to be discovered. 
Christopher L\"orscher, Jingchuan Zhang, Qiang Gu, and Richard A.   Klemm
cond-mat.supr-con cond-mat.str-el