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

## TL;DR

This paper proposes that high-temperature superconductivity in potassium-doped p-Terphenyl arises from quantum Fano resonances near a Lifshitz transition, with numerical evidence showing a narrow energy window for maximum Tc.

## Contribution

It introduces a novel mechanism involving shape resonances for high Tc in organic superconductors and provides numerical support for the role of Lifshitz transitions in enhancing Tc.

## Key findings

- High Tc (up to 123K) occurs near a Lifshitz transition in p-Terphenyl.
- Superconducting gaps exhibit Fano resonance behavior near the transition.
- Predicted experimental signatures include variations in isotope coefficients and gap ratios.

## Abstract

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 Tc in an organic superconductor overcoming the previous record of Tc=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 multi gap equation shows that high Tc 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, Tc=123K, the condensate in the appearing new small Fermi surface pocket is in the BCS-BEC crossover while the Tc 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 2Delta/Tc as a function of Tc.