Effect of superconductivity on the shape of flat bands

¹ Petersburg Nuclear Physics Institute of NRC “Kurchatov Institute” - Gatchina, 188300, Russia
² Clark Atlanta University - Atlanta, GA 30314, USA
³ Racah Institute of Physics, Hebrew University - Jerusalem 91904, Israel
⁴ Ioffe Physical Technical Institute, RAS - St. Petersburg, 194021, Russia

^(a) vrshag@thd.pnpi.spb.ru (corresponding author)

Received: 18 November 2021
Accepted: 6 April 2022

Abstract

For the first time, basing both on experimental facts and our theoretical consideration, we show that Fermi systems with flat bands should be tuned with the superconducting state. Experimental measurements on magic-angle twisted bilayer graphene of the Fermi velocity V_F as a function of the temperature T_c of superconduction phase transition have revealed , where N_s(0) is the density of states at the Fermi level. We show that the high-T_c compounds exhibit the same behavior. Such observation is a challenge to theories of high-T_c superconductivity, since V_F is negatively correlated with T_c, for . We show that the theoretical idea of forming flat bands in strongly correlated Fermi systems can explain this behavior and other experimental data collected on both and twisted bilayer graphene. Our findings place stringent constraints on theories describing the nature of high-T_c superconductivity and the deformation of flat band by the superconducting phase transition.