Paramagnetic Meissner, vortex, and onionlike ground states in a finite-size Fulde-Ferrell superconductor

We theoretically find that a finite-size Fulde-Ferrell (FF) superconductor (which is characterized by spatially nonuniform ground state $\mathrm{\ensuremath{\Psi}}\ensuremath{\sim}\text{exp}(\ensuremath{-}i{\mathbf{q}}_FF\mathbf{r})$ and $|\mathrm{\ensuremath{\Psi}}|(r)=\text{const}$ in the bulk case, where $\mathrm{\ensuremath{\Psi}}$ is a superconducting order parameter) has paramagnetic Meissner, vortex, and ``onion'' ground states with $|\mathrm{\ensuremath{\Psi}}|(r)\ensuremath{\ne}\text{const}$. These states are realized due to boundary effect when the lateral size of a superconductor $L\ensuremath{\sim}1/{q}_FF$. We argue that predicted states could be observed in a thin disk/square made of a superconductor--ferromagnet--normal metal trilayer with $L\ensuremath{\simeq}150--600\phantom{\rule{4pt}{0ex}}\text{nm}$.