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

¹ RICMASS, Rome International Center for Materials Science Superstripes - Via dei Sabelli 119A, 00185 Rome, Italy
² Institute for Microelectronics and Microsystems, IMM, Consiglio Nazionale delle Ricerche CNR Via del Fosso del Cavaliere 100, 00133 Roma, Italy
³ Institute of Crystallography, IC, Consiglio Nazionale delle Ricerche CNR - via Salaria, Km 29.300, 00015 Monterotondo Roma, Italy
⁴ Department of Chemistry, University of Liverpool - Liverpool, L69 7ZD, UK
⁵ School of Pharmacy, Physics Unit, University of Camerino - Camerino, Italy
⁶ National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) 115409 Moscow Kashirskoe shosse 31, Russia
⁷ Latvian Academy of Sciences - Akadēmijas Laukums 1, Rīga, LV-1050 Latvia

Received: 25 May 2017
Accepted: 22 June 2017

Abstract

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 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 0.3 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.