Topological Structure of a Vortex in the Fulde-Ferrell-Larkin-Ovchinnikov State

We find theoretically that the vortex core in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is quite different from the ordinary core for a simple topological reason. The intersection point of a vortex and nodal plane of the FFLO state empties the excess spins. This leads to observable consequences in the spatial structure of the spontaneous magnetization. We analyze this topological structure based on the low lying excitation spectrum by solving a microscopic Bogoliubov–de Gennes equation to clarify its physical origin.

Figure 1

Spatial structures of $\mathrm{Re}[\Delta (\mathbf{r})/{\Delta }_0]$ (a) and $m(r,z)/{\rho }_0$ (b). ${\rho }_0$ is the density in the uniform BCS state at $T=0$. Note that $m(r,z)$ is missing near the origin $r=z=0$.

Figure 2

Schematic view of the vortex line and nodal plane.

Figure 3

Spectral evolutions of $N_{\uparrow }(\mathbf{r},E)$ along the paths ($A\to B\to C\to D\to A$) shown in Fig. 2. Density plot (upper) and stereographic view (lower) are displayed. In the energy scale, $E=0$ corresponds to the Fermi energy $\mu$.

Figure 4

The local density of states for spin up (solid lines) and spin down (dashed lines) components at the positions $B$ (a), $A$ (b), and $D$ (c).