**Imaging nematic quantum Hall states and their interacting boundary modes **

Two-dimensional quantum Hall systems offer a versatile platform for realizing phenomena that can emerge from a confluence of electronic interactions, symmetry breaking and topology. In this talk, I will discuss scanning tunneling microscope experiments which explore the role of electron-electron interactions and their tunability on the surface of bismuth. Our spectroscopic measurements reveal a number of exotic ordered states that arise from spontaneous valley ordering of bismuth surface states in a large magnetic field. Specifically, we observe a nematic phase with broken rotational symmetry and a ferroelectric phase that carries a dipole moment. We use the scanning tunneling microscope to directly visualize the wavefunctions of these broken symmetry phases. Furthermore, we image local nematic domains and find counter-propagating one-dimensional quantum Hall edge modes at their boundaries. We can change the number of edge modes at the domain walls to realize strikingly different regimes where the boundary is either metallic or insulating, in accordance with theory for a new class of interacting Luttinger liquids.

Host: Jen