Universal phase diagrams with superconducting domes for electronic flat bands

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.c 1 2T − c . We are able to establish the general phase diagram exactly for any interactions in an ideally flat band system. Remarkably, we also show that the results remain valid arXiv:1611.04893v2 [cond-mat.supr-con]

Engineered electronic states in atomically precise artificial lattices and graphene nanoribbons

“…1b The flat bands are interesting as they are prone to electronic instabilities and spontaneous symmetry breaking at (near) half filling. Depending on whether the electron-electron interactions are attractive or repulsive, this would result in the system becoming superconducting or magnetic, respectively [36][37][38][39][40]. Finally, the presence of a flat band depends not only on the lattice symmetry but also on which hoppings are included in the model.…”

Quantum collision theory in flat bands

“…These systems are very interesting also from a few-body point of view due to their non-trivial scattering properties [34][35][36][37]. We note that truly flat bands are also of great interest in the context of graphene [38,39].…”

Interaction-Driven Surface Chern Insulator in Nodal Line Semimetals

“…The nodal line carries a π Berry flux [21], resulting in drumhead-like surface states (DSS) [26]. In the presence of chiral symmetry, such DSS are perfectly flat, so that any residual electronic interaction would overcome the surface kinetic energy, providing a perfect platform to realize strongly correlated and symmetry-broken surface states [2,48,[50][51][52]. Very recently, the spontaneous magnetization in the flat band of zigzag graphene nanoribbon was observed [53][54][55][56], indicating that the same physics may exist in the DSS, a higher-dimensional analogy of the 1D flat band in graphene nanoribbon [11].In this Letter, we show that a surface 2D Chern insulator can emerge from electronic interaction in a NLSM.…”