Twist Electron Dynamics

Structural symmetries of crystals uniquely influence the quasiparticle behaviors. Here, I will discuss the consequences of twist symmetry on the electronic band structures of materials. We build a tight binding Hamiltonian from density functional theory inputs in terms of the underlying twist symmetry. This twist dynamics unravels symmetry-enforced band degeneracies and non-trivial topologies in terms of pseudoangular momenta of the electronic bands.  Inclusion of spin-orbit coupling requires electron spin be included as a component of the total angular momentum. The dynamics and symmetry signatures will be illustrated in a variety of material classes.