Pablo Jarillo-Herrero – Quantum electronic transport and thermodynamic measurements in magic angle twisted bilayer and trilayer graphene.

Oskar Vafek – Correlations and topology in the magic angle twisted bilayer graphene narrow bands. We will cover RG treatment of the projection onto the narrow bands and the flow towards the chiral limit, results from DMRG, non-Abelian Dirac node braiding and theory of cascade transitions.

Titus Neupert– Topology Bands from homotopy theory. The lectures will introduce Wilson loops and homotopy invariants, such as (mirror) Chern numbers, winding numbers etc., to define and identify topological bands in crystalline solids. The relation between Wilson loops and Wannier functions can be used to discern stable, fragile, and delicate topological phases. Wilson loops can further be used to prove the bulk-boundary correspondence of topological phases. We will discuss explicitly the 1D Su-Schrieffer-Heeger chain, (mirror) Chern insulators, and higher-order topological insulators. Finally, I will comment on the topological classification of non-Hermitian Hamiltonians.

Cécile Repellin– Interaction-driven insulators in flat-band moire superlattices
This set of lecture will focus on the correlated insulators arising in multilayer moire graphene materials, when the valence or conduction band (the active band) is sufficiently flat. Examples of such materials include magic angle twisted bilayer graphene, ABC trilayer graphene, twisted double bilayer graphne, twisted monolayer-bilayer graphene, and more. I will distinguish scenarios corresponding to insulators with three different topological natures. First, we will consider an integer filling of the active band, where a quantized anomalous Hall effect and emergent orbital ferromagnetism have been experimentally observed in several materials, and can be attributed to spontaneous spin and valley polarization due to Coulomb repulsion (flat-band ferromagnetism). Secondly, we will discuss the insulating phases that can arise through the interplay of topology and strong interactions: topological charge density waves, which appear at fractional filling of the active band, with an integer quantized Hall conductance, and fractional Chern insulators, whose filling and Hall conductance are fractional, and have anyonic excitations. We will review experimental evidence for these phases, the band parameters favoring them, as well as the theoretical methods (numerical and analytical) permitting the understanding of their conditions of emergence.

Sami Mitra – Roles of journals in general and PRL in particular in disseminating physics results through a cascading sequence involving journal editors, referees, conference chairs, journalists, department chairs, deans, funding agencies, and others.