Steve Simon

Abstract:

We consider fractional quantum Hall states in systems where two flat Chern number $C=\pm 1$ bands are labeled by an approximately conserved 'valley' index and interchanged by time reversal symmetry. At filling factor $\nu=1$ this setting admits an unusual hierarchy of correlated phases of excitons, neutral particle-hole pair excitations of a fully valley-polarized `orbital ferromagnet' parent state where all electrons occupy a single valley. Excitons experience an effective magnetic field due to the Chern numbers of the underlying bands. This obstructs their condensation in favor of a variety of crystalline orders and gapped and gapless liquid states. All these have the same quantized charge Hall response and are electrically incompressible, but differ in their edge structure, orbital magnetization, and hence valley and thermal responses. We explore the relevance of this scenario for Moir\'e heterostructures of bilayer graphene on a hexagonal boron nitride substrate.

Abstract:

We investigate the full doping and strain-dependent phase diagram (absent superconductivity) 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 Kekul\'e spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all non-zero integer fillings of the moir\'e unit cell, is found to be ubiquitous for non-integer 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.

Abstract:

We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to non-local inter-layer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials, and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wavevectors. We find that at all non-zero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal symmetric and spatially non-uniform order. This order, which we dub the 'incommensurate Kekul\'e spiral' (IKS) order, spontaneously breaks both the emergent valley-charge conservation and moir\'e translation symmetries, but preserves a modified translation symmetry $\hat{T}'$ -- which simultaneously shifts the spatial coordinates and rotates the $U(1)$ angle which characterizes the spontaneous inter-valley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order.

Abstract:

We consider a model of hard-core bosons on a lattice, half-filling a Chern band such that the system has a continuous transition between a fractional Chern insulator (FCI) and a superfluid state (SF) depending on the bandwidth to bandspacing ratio. We construct a parton-inspired trial wavefunction ansatz for the ground states that has remarkably high overlap with exact diagonalization in both phases and throughout the phase transition. Our ansatz is stable to adding some bosonic interactions beyond the on-site hard core constraint. We confirm that the transition is well described by a projective translation symmetry-protected multiple parton band gap closure, as has been previously predicted. However, unlike prior work, we find that our wavefunctions require anomalous (BCS-like) parton correlations to describe the phase transition and SF phase accurately.