Quantum Matter

I will discuss the phenomenology of superconductors hosting both order parameter vortices and fractionally charged anyon excitations. I will demonstrate that in such systems superconductivity and topological order are intertwined under applied magnetic fields, leading to surprising observable consequences departing from traditional superconductivity from electronic pairing. In particular,  I will show that vortices nucleated by perpendicular magnetic fields must trap anyons in their cores. However, because only some vortices can trap an integer number of anyons, this places a constraint on the vortex phase winding. In general, rather than the expected hc/2e quantization of superconducting vortices, we find instead the enhanced flux quantum of hc/e, which I will argue should affect a wide range of observables. I will further develop a general Landau-Ginzburg theory describing vortex fluctuations and discuss the phase diagram as perpendicular magnetic field is increased, showing that condensation of the intertwined vortices leads to exotic insulating phases hosting neutral anyons and a nonvanishing thermal Hall effect.