Measurements of the basal-plane resistivity rho_a(T,H) performed on highly oriented pyrolitic graphite, with magnetic field H parallel to the c-axis in the temperature interval 2 - 300 K and fields up to 8 T, provide evidence for the occurrence of both field - induced and zero-field superconducting instabilities. Additionally, magnetization M(T,H) measurements suggest the occurrence of Fermi surface instabilities which compete with the superconducting correlations.
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