# Correlated and Topological Phases in flat bands of two-dimensional crystals

Yafis Barlas

Assistant Professor of Physics

University of Nevada, Reno

Title: Correlated and Topological Phases in flat bands of two-dimensional crystals

Abstract: Due to their vanishing density of states and gapless semi-metallic behavior at charge neutrality, honeycomb lattice two-dimensional (2D) crystals are ideal candidates to host topological states. Even more interesting are twisted or strained 2D crystals, as the electron dispersion in these systems can be weakly dispersing, (i.e exhibit a small bandwidth) or completely flat. In these situations, the interplay of topology and correlation driven phases in flat bands of 2D crystals can result in emergent topological order. Similarly, at high magnetic fields, multi-layer graphene and twisted bilayer graphene exhibit topological bands and various correlated states. In this talk, I will discuss a new class of interacting and non-interacting symmetry protected topological phases stabilized by mirror symmetry in 2D Dirac semi-metals. This quantum parity Hall state, exhibits two one-dimensional counter-propagating metallic edge states, distinguished by even or odd parity under the system’s mirror reflection symmetry. I will also discuss some of our results in twisted 2D crystals at high magnetic fields.