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 non-monotonic 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. 
K. Aoyama, R. Beaird, D. E. Sheehy, and I. Vekhter
cond-mat.supr-con