Universal phase diagrams with superconducting domes for electronic flat bands

TL;DR

This paper reveals universal phase diagrams with superconducting domes for flat band systems, showing how critical temperatures depend on doping and the nature of the order, with implications for materials like graphite and graphene.

Contribution

It introduces universal curves for critical temperatures in flat band systems based on doping and order type, explaining the coexistence and competition of superconductivity and magnetism.

Findings

Superconducting critical temperatures follow universal doping-dependent curves.

Superconducting orders persist further than magnetic or charge orders.

Superconducting domes are likely near magnetic or charge orders even if initially suppressed.

Abstract

Condensed matter systems with flat bands close to the Fermi level generally exhibit, due to their very large density of states, extraordinary high critical ordering temperatures of symmetry breaking orders, such as superconductivity and magnetism. Here we show that the critical temperatures follow one of two universal curves with doping away from a flat band depending on the ordering channel, which completely dictates both the general order competition and the phase diagram. Notably, we find that orders in the particle-particle channel (superconducting orders) survive decisively further than orders in the particle-hole channel (magnetic or charge orders) because the channels have fundamentally different polarizabilities. Thus, even if a magnetic or charge order initially dominates, superconducting domes are still likely to exist on the flanks of flat bands. We apply these general results to both the topological surface flat bands of rhombohedral ABC-stacked graphite and to the van Hove singularity of graphene.