Possible Fano resonance for high-T c multi-gap superconductivity in p-Terphenyl doped by K at the Lifshitz transition

Recent experiments have reported the emergence of high-temperature superconductivity with critical temperature T c between 43 K and 123 K in a potassium-doped aromatic hydrocarbon para-Terphenyl or p-Terphenyl. This achievement provides the record for the highest T c in an organic superconductor overcoming the previous record of T c = 38 K in Cs 3 C 60 fulleride. Here we propose that the driving mechanism is the quantum resonance between superconducting gaps near a Lifshitz transition which belongs to the class of Fano resonances called shape resonances. For the case of p-Terphenyl our numerical solutions of the multigap equation shows that high T c is driven by tuning the chemical potential by K doping and it appears only in a narrow energy range near a Lifshitz transition. At the maximum critical temperature, T c = 123 K, the condensate in the appearing new small Fermi surface pocket is in the BCS-BEC crossover while the T c drops below 0.3 K where it is in the BEC regime. Finally, we predict the experimental results which can support or falsify our proposed mechanism: a) the variation of the isotope coefficient as a function of the critical temperature and b) the variation of the gaps and their ratios 2Δ/ T c as a function of T c .