Density of states near a vortex core in ferromagnetic superconductors: Application to STM measurements

We investigate numerically the local density of states (LDOS) in the vicinity of a vortex core in a ferromagnetic superconductor. Specifically, we investigate how the LDOS is affected by the relative weight of the spin bands in terms of the superconducting pairing and we also examine the effect of different pairing symmetries for the superconducting order parameter. Our findings are directly related to scanning tunneling microscopy measurements and may thus be highly useful to clarify details of the superconducting pairing in recently discovered ferromagnetic superconductors.

Figure 1

(Color online) Schematic of the model.

Figure 2

(Color online) The ratio $R$ between the majority- and minority-spin gaps as a function of $h/\mu$ as obtained from a self-consistent, mean-field solution [Eq. (15)].

Figure 3

(Color online) Normalized LDOS in the vortex core for a $p_x$-wave symmetry $\left[\chi \left(\theta \right)=\text{cos}\theta \right]$ using several values of $h/\mu$.

Figure 4

(Color online) Normalized LDOS in the vortex core for a chiral $p$-wave symmetry $\left[\chi \left(\theta \right)={\text{e}}^{\text{i}\theta }\right]$ using several values of $h/\mu$.

Figure 5

(Color online) Total and spin-resolved LDOS in the vortex core for the (a) $p_x$-wave symmetry symmetry $\left[\chi \left(\theta \right)=\text{cos}\theta \right]$ and the (b) chiral $p$-wave symmetry $\left[\chi \left(\theta \right)={\text{e}}^{\text{i}\theta }\right]$. We have used $h/\mu =0.15$ here.

Figure 6

(Color online) Normalized LDOS in the vicinity of the vortex core at three different quasiparticle energies, using $R=2$ with a $p_x$-wave symmetry $\left[\chi \left(\theta \right)=\text{cos}\theta \right]$. A twofold symmetry is observed in agreement with the symmetry of the order parameter.

Figure 7

(Color online) Normalized LDOS in the vicinity of the vortex core at three different quasiparticle energies, using $R=2$ with a chiral $p$-wave symmetry $\left[\chi \left(\theta \right)={\text{e}}^{\text{i}\theta }\right]$. A circular symmetry is observed in agreement with the symmetry of the order parameter.

Figure 8

(Color online) Normalized LDOS in the vicinity of the vortex core at three different values of the inelastic-scattering rate $\delta ={\tau }^{-1}$, using a $p_x$-wave symmetry with $h/\mu =0.15$.