Two-band model of ferromagnetic $p$-wave superconductors

We present results on the full angular and temperature dependencies of the upper critical induction, $B_{c2}(\theta,\phi,T)$, for a ferromagnetic $p$-wave completely broken symmetry state (CBS), in which parallel-spin electron pairing is pinned to only one crystal axis direction, $V(\hat{k},\hat{k}^{\prime})=V_{0}k_{z}k_{z}^{\prime}$, normal to the spontaneuous magnetization direction. We show that the angular dependence of $B_{c2}$ exhibits an anomalous peak at $\theta^{\star}<90^{\circ}$, due to a competition between order parameter anisotropy and effective mass anisotropy. We also propose a two-band model for ferromagnetic superconductors, where we have two ellipsoidal Fermi surfaces (FSs). Using this model, and by assuming a field-dependent anisotropic effective mass on one of the FSs, $m_{\uparrow,i}(B)$, we can fit the experimental data for the low-temperature specific heat $\gamma(B)$ of URhGe, which exhibits a peak at $\mu_0H\sim12$T in the $b$-axis direction. We provide quantitative fits to experiment, and propose that this model of a field-dependent effective mass can help to understand the reentrant phase of the ferromagnetic superconductor URhGe, and the upward curvature observed in $B_{c2}$ of UCoGe