Conductance spectra of ferromagnetic superconductors: Quantum transport in a ferromagnetic metal/non-unitary ferromagnetic superconductor junction

Recent findings of superconductors that simultaneously exhibit multiple spontaneously broken symmetries, such as ferromagnetic order or lack of an inversion center and even combinations of such broken symmetries, have led to much theoretical and experimental research. We consider quantum transport in a junction consisting of a ferromagnetic metal and a non-unitary ferromagnetic superconductor. It is shown that the conductance spectra provide detailed information about the superconducting gaps, and are thus helpful in determining the pairing symmetry of the Cooper pairs in ferromagnetic superconductors.

Figure 1

(Color online) Model system of an FM-FMSC interface in a slab geometry in the clean limit. Retroreflection symmetry is not broken since the hole carries the same spin as the incident electron. We have sketched gaps corresponding to the analog (Ref. 17) of the $A2$ phase in liquid ${}^3\mathrm{He}$.

Figure 2

(Color online) Plot of the conductance $G\left(E\right)$ for a FM/FMSC junction in the case of a metallic contact, the tunneling limit, and an intermediate case. The gaps are given by Eq. (15) in this case, for which $G\left(E\right)$ is found to be insensitive to $\{\alpha ,\beta \}$. In the above, $\{\alpha ,\beta \}=0$. The columns for each case provide the spectrum for $U_L=0.05E_F$, $U_L=0.5E_F$, and $U_L=-0.5E_F$, in descending order. For each figure, we have plotted several ratios between the magnitude of the superconducting gaps. These are given by $R_{\Delta }=\{2,3,4,5\}$, represented by the magenta (thick, full-drawn), blue (thick, dashed), green (thin, full-drawn), and red lines (thin, dashed), respectively.

Figure 3

(Color online) Plot of the conductance $G\left(E\right)$ for FM/FMSC junction with gaps given by Eq. (16), for which $G\left(E\right)$ is sensitive to $\{\alpha ,\beta \}$. We have chosen $Z=3$, and $R_{\Delta }=\{2,3,4,5\}$ are represented by the magenta, blue, green, and red lines, respectively.