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|®=const$ in the bulk case, where $\mathrm{\Psi }$ is a superconducting order parameter) has paramagnetic Meissner, vortex and ‘onion’ ground states with $\mathrm{\mid }\mathrm{\Psi }\mathrm{\mid }(r)\mathrm{\ne }const$. 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 $L \simeq 150-600 nm$.