Paramagnetic Meissner, vortex and 'onion' ground states in Fulde-Ferrell finite-size superconductor

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