Condensed Matter Seminar: Yizhi You, University of Illinois Urbana-Champaign, “Spatial symmetry breaking in FQH states and beyond, when geometry meets topology”

In this talk, I would introduce spontaneous nematicity in the background of fractional quantum Hall fluids where symmetry breaking phenomenon intertwined with topological phase of matter. The resulting nematic FQH state is characterized by an order parameter that represents these quadrupolar fluctuations, which play the role of fluctuations of the local geometry of the quantum fluid. We demonstrate that the low-energy effective theory of the nematic order parameter has z=2 dynamical scaling exponent, due to a Berry phase term of the order parameter, which is related to the nondissipative Hall viscosity. By investigating the spectrum of collective excitations, we demonstrate that the mass gap of the Girvin-MacDonald-Platzman mode collapses at the isotropic-nematic quantum phase transition. An interesting feature of the nematic phase is that it has topological defects carrying nontrivial braiding statistics and fractional charge inherited from the topological fluid nature. In addition, I would also mention the decorated nodal line condensation in pair density wave SC, where the topological phase emerges concurrently with symmetry recovery by decorated defect condensation.