Puzzling evidence for surface superconductivity in the layered dichalcogenide Cu_10%TiSe₂

We report on specific heat and magnetotransport measurements performed on superconducting Cu_10%TiSe₂ single crystals. We show that superconductivity persists in transport measurements up to magnetic fields H_R well above the upper critical field H_c2 deduced from the calorimetric measurements. Surprisingly this "surface" superconductivity is present for all magnetic field orientations, either parallel or perpendicular to the layers. For H∥ab, the temperature dependence of the H_R/H_c2 ratio can be well reproduced by solving the Ginzburg-Landau equations in presence of a surface layer with reduced superconducting properties. Unexpectedly this temperature dependence does not depend on the field orientation.