Domain wall junctions and networks in Dirac topological moiré materials

In this talk, we will discuss effective Dirac models for topological modes propagating along domain wall in the presence of large gapped domains, such as the AB/BA triangular domains in small-angle twisted bilayer graphene in the presence of a strong potential difference between layers, which has attracted interest in recent years.

We will rigorously define topological edge invariants associated with massive Dirac operators and their robustness with respect to perturbations and geometries such as domain wall junctions, and introduce discretization strategies for these nonstandard effective Dirac equations, both for the computation of edge invariants as well as the siulation of time-dependent wavepacket propagation on the network formed by the domain walls. Using numerical simulations, we will illustrate the robust behavior in the presence of strong disorder, curved and/or intersecting domain walls.