Global Phase Diagram of the Normal State of Twisted Bilayer Graphene

Abstract

We investigate the full doping and strain-dependent phase diagram of the normal state of magic-angle twisted bilayer graphene (TBG). Using comprehensive Hartree-Fock calculations, we show that at temperatures where superconductivity is absent the global phase structure can be understood based on the competition and coexistence between three types of intertwined orders: a fully symmetric phase, spatially uniform flavor-symmetry-breaking states, and an incommensurate Kekulé spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all nonzero integer fillings of the moiré unit cell, is found to be ubiquitous for noninteger doping as well. We demonstrate that the corresponding electronic compressibility and Fermi surface structure are consistent with the "cascade" physics and Landau fans observed experimentally. This suggests a unified picture of the phase diagram of TBG in terms of IKS order.

Kekulé spiral order in magic-angle graphene: a density matrix renormalization group study

“…Indeed, a previous DMRG study at ν = 0 predicts a phase transition from the strong-coupling Kramers-intervalley coherent insulator to a semimetallic phase at only ε Gr ∼ 0.2% [28], consistent with the experimental finding that gapped and semimetallic phases compete [7,9,11,12,[16][17][18][39][40][41][42]. Away from charge neutrality, a comprehensive self-consistent Hartree-Fock (SCHF) study found that strain drives a transition into an "incommensurate-Kelulé spiral (IKS) order" [1,29]. At |ν| = 3, the IKS order is a spin-polarized insulating state that preserves time reversal, but breaks U (1) valley and -crucially -has moiré-incommensurate translation breaking.…”

“…In this work we use accurate density matrix renormalization group (DMRG) [24,[26][27][28] calculations at ν = −3 to demonstrate that realistic heterostrain qualitatively changes the low-temperature physics in a way that leads to excellent agreement with experiment. In particular, performing large-scale, unbiased calculations that include all spin and valley degrees of freedom, we find that heterostrain stabilizes a spin-polarized C = 0 "incommensurate Kekulé spiral" order [1,29] and a "normal metal", with important implications for the wider TBG phase diagram.…”

Moiré Phonons in Magic-Angle Twisted Bilayer Graphene

“…Twisted bilayer graphene (TBG) system around the magic angle is an ideal platform to realize various intriguing quantum phases , such as the correlated insulators, − quantum anomalous Hall states, and ,,− unconventional superconductivity. ,− ,,− Around magic angle 1.05°, there are two topologically nontrivial flat bands contributed by each valley and spin degrees of freedom. − A lot of the unusual phenomena, including correlated insulators and quantum anomalous Hall effects, can be attributed to the presence of such topologically nontrivial flat bands in the electronic degrees of freedom. The electron–electron (e–e) Coulomb interactions dominates over the kinetic energy near magic angle, and the interplay between the strong Coulomb correlations and the nontrivial topology of the flat bands give rise to diverse correlated insulator states and topological states, which have been extensively studied from the theoretical point of view over the past few years. − …”

Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state

“…Introduction -Quantum moiré systems, bestowed with the quantum geometry of wavefunctions -manifested in the distribution of Berry curvature in the flat bands -and strong long-range Coulomb electron interactions, exhibit a rich quantum phase diagram including correlated insulating, unconventional metallic and superconducting phases, thanks to the high tunability by twisting angles, gating and tailored design of the dielectric environment . In addition to this complex ground-state phase diagram with possibly different pairing mechanism and symmetry breaking patterns [9,[36][37][38][39], recent theoretical studies [14,32,[40][41][42] indicates that correlated flat bands also exhibit unique thermodynamic and quantum dynamic responses, fundamentally different from conventional correlated electron lattice model systems, such as the Hubbard-type model.…”