Inhomogeneous superconducting States of mesoscopic thin-walled cylinders in external magnetic fields.

We theoretically investigate the appearance of spatially modulated superconducting states in mesoscopic superconducting thin-wall cylinders in a magnetic field at low temperatures. Quantization of the electron motion around the circumference of the cylinder leads to a discontinuous evolution of the spatial modulation of the superconducting order parameter along the transition line T(c)(H). We show that this discontinuity leads to the nonmonotonic behavior of the specific heat jump at the onset of superconductivity as a function of temperature and field. We argue that this geometry provides an excellent opportunity to directly and unambiguously detect distinctive signatures of the Fulde-Ferrell-Larkin-Ovchinnikov modulation of the superconducting order.