Effect of superconductivity on the shape of flat bands

Abstract

Recent experimental measurements on magic-angle twisted bilayer graphene of the Fermi velocity VF as a function of the temperature Tc of superconduction phase transition have revealed VF ∝ Tc ∝ 1/Ns(0), where Ns(0) is the density of states at the Fermi level. Such behavior is a challenge to theories of high-Tc superconductivity, since VF is negatively correlated with Tc, for Tc ∝ 1/VF ∝ Ns(0). We show that the theoretical idea of forming flat bands in a Fermi system, proposed three decades ago and revisited recently, can explain this behavior and other experimental data collected on twisted bilayer graphene with flat bands. 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.

On the effect of disorder in a $p$-wave flat-band superconductor

“…FBS has been proposed as a mechanism to achieve high T C in carbon-based materials [3], such as graphite with rhombohedral stacking [4][5][6], twisted bylayer graphene [7] and strained graphene [8]. Experimental signatures of FBS have been found in bilayer graphene [9], where a zero-resistance state is observed when the angle between the two graphene sheets in the twisted bilayer is equal to certain magic values at which the single-particle spectrum exhibits a flat band near the Fermi energy.…”

“…FBS has also been considered as the mechanism leading to the observation of high-T C in highly oriented pyrolytic graphite [10][11][12]. Other systems where FBS could play a significant role include strongly correlated materials [2,7,13] and interfaces of topological II-VI semiconductors [14]. So far FBS has been investigated in the context of spinsinglet pairing.…”