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 $|Psi|(r) eq const$. 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 $L simeq 150-600 nm$.