Aharonov-Bohm effect in the superconducting LOFF state

We study the Aharonov-Bohm oscillations of the transition temperature, paraconductivity, and specific heat of a thin ring in the regime of the inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell superconducting state. We found that, in contrast to the uniform superconductivity, the magnetic flux might increase the critical temperature of the Larkin-Ovchinnikov-Fulde-Ferrell state. The degeneracy of the inhomogeneous superconducting state reveals in a double peak structure of the Aharonov-Bohm oscillations. The text was submitted by the authors in English.