Edge excitations of symmetry protected topological states in two-dimensions.

Symmetry protected topological (SPT) states in two-dimensions (2D) exhibit counter-propagating edge modes with well-defined quantum numbers. The symmetry is important for the robust longitudinal quantization as it prevents back-scattering. These states appear in Dirac semi-metals in the quantum Hall regime at the charge neutrality point and in 2D topological insulators. In this talk, I will discuss the role of interactions and disorder on the edge excitations and longitudinal conductance of SPT states in 2D. The longitudinal conductance is robust to intra-edge and inter-edge interactions and symmetry preserving edge disorder. However, symmetry breaking edge disorder results to localization of the edge modes. The localization length depends on the topological properties of the SPT states. I will also discuss the formation of exotic ordered states along the edges induced by interactions and symmetry breaking edge disorder.