Chiral twist on the high- Tc phase diagram in moiré heterostructures

Abstract

We show that the large orbital degeneracy inherent in Moiré heterostructures naturally gives rise to a 'high-Tc' like phase diagram with a chiral twist -wherein an exotic quantum anomalous Hall insulator phase is flanked by chiral d + id superconducting domes. Specifically, we analyze repulsively interacting fermions on hexagonal (triangular or honeycomb) lattices near Van Hove filling, with an SU(N f ) flavor degeneracy. This model is inspired by recent experiments on graphene Moiré heterostructures. At this point, a nested Fermi surface and divergent density of states give rise to strong (ln 2 ) instabilities to correlated phases, the competition between which can be controllably addressed through a combination of weak coupling parquet renormalization group and Landau-Ginzburg analysis. For N f = 2 (i.e. spin degeneracy only) it is known that chiral d + id superconductivity is the unambiguously leading weak coupling instability. Here we show that N f ≥ 4 leads to a richer (but still unambiguous and fully controllable) behavior, wherein at weak coupling the leading instability is to a fully gapped and chiral Chern insulator, characterized by a spontaneous breaking of time reversal symmetry and a quantized Hall response. Upon doping this phase gives way to a chiral d + id superconductor. We further consider deforming this minimal model by introducing an orbital splitting of the Van Hove singularities, and discuss the resulting RG flow and phase diagram. Our analysis thus bridges the minimal model and the practical Moiré band structures, thereby providing a transparent picture of how the correlated phases arise under various circumstances. Meanwhile, a similar analysis on the square lattice predicts a phase diagram where (for N f > 2) a nodal staggered flux phase with 'loop current' order gives way upon doping to a nodal d-wave superconductor.

Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene

“…The recent discovery of correlated insulating states and superconductivity in twisted bilayer graphene (TBG) [1][2][3][4] has opened a new window to exploring strong correlation effects in systems whose doping can be easily tuned, enabling the exploration of a rich range of interaction-driven phenomena. Although the underlying reason for the correlated physics is understood to arise from a relatively narrow electronic bandwidth induced by the long wavelength Moiré pattern [5,6], several details, including the symmetry breaking within the insulating phase and the nature and mechanism of pairing in the neighboring superconductor, remain under debate [7][8][9][10][11][12][13][14][15][16][17][18][19]. One of the difficulties in addressing these questions arises from the complexity of the theoretical treatment of TBG which involves at least a pair of narrow bands per spin per valley with a symmetry-protected band touching, leading to 8 bands in total.…”

“…The band structure of the model at θ = 1.33 • and U = 0,14,30,60, 90, 110. At U = 14, Chern number is exchanged by 3 between the conduction and valence band at three momenta which are located not along the symmetric cut.…”

Emergence and stability of spin-valley entangled quantum liquids in moiré heterostructures

“…Due to a high degree of control, e.g., in the regulation of the twist angle, tunable bandwidths or fillings, and a low level of disorder, such systems are discussed as ideal platforms for detailed studies of quantum many-body states. Despite a vast amount of concomitant theoretical activity [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35], the precise nature of the observed insulators and superconductors, however, remains to be explored and settled through the construction of faithful models and application of appropriate quantum many-body approaches.…”

Competing phases of interacting electrons on triangular lattices in moiré heterostructures

“…While this in itself is a non-trivial task, some universal aspects are shared by all models, including the focus on the emergent superlattice, the presence of several orbitals inherited from the valleys of the original bands and sizable further-neighbor interactions. Hence, a basic understanding of the correlated behavior may be developed by analyzing phenomenological models that capture the qualitative features of moiré flatbands [16][17][18][19][20][21][22][23][24][25][26][27][28][29] . In addition, this approach allows one to study multi-orbital effects in hexagonal systems in general.…”

“…Regarding the role of interactions, no consensus has been reached on whether the experimentally observed insulating states in TBG or trilayer graphene/hBN are due to Mott physics in the strong coupling limit or due to interaction-driven symmetry-breaking, e.g., based on Fermi-surface nesting close to van-Hove singularities [10][11][12]21,22 . For the lattice structure of the effective model, triangular and honeycomb geometries have been discussed.…”