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 43K and 123K 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 = 38K in Cs3C60 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 0.3K 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 2 Delta/T-c as a function of T-c. Copyright (C) EPLA, 2017