Vortex-lattice melting and paramagnetic depairing in the nematic superconductor FeSe

The full H−T phase diagram in the nematic superconductor FeSe is mapped out using heat-capacity and thermal-expansion measurements down to 0.7 K and up to 30 T for both field directions. A clear thermodynamic signal of an underlying vortex-melting transition is found in both datasets and could be followed down to low temperatures. The existence of significant Gaussian thermal superconducting fluctuations is demonstrated by a scaling analysis, which also yields the mean-field upper critical field H$_{c2}$(T). For both field orientations, H$_{c2}$(T) shows Pauli-limiting behavior. Whereas the temperature dependence of the vortex-melting line is well described by the model of Houghton et al. [Phys. Rev. B 40, 6763 (1989)] down to the lowest temperatures for H ⊥ FeSe layers, the vortex-melting line exhibits an unusual behavior for fields parallel to the planes, where the Pauli limitation is much stronger. Here, the vortex-melting anomaly is only observed down to T$_{*}$≈2–3 K, and then merges with the H$_{c2}$(T) line as predicted by Adachi and Ikeda [Phys. Rev. B 68, 184510 (2003)]. Below T$_{*}$, H$_{c2}$ (T) also exhibits a slight upturn possibly related to the occurence of a Fulde-Ferrell-Larkin Ovchinnikov state