# Condensed Matter seminar: "The Berry curvature dipole of metals and the crossover from composite fermions to exciton superfluid”

The first part of this talk will summarise our progress in non-linear transport of metals. I will describe a non-linear Hall effect that is allowed by time reversal symmetry and is controlled by the "Berry curvature dipole” (the average of the Berry curvature gradient in momentum space). I will argue that such Berry curvature dipole offers a solution to the old problem of defining an “order parameter” for broken inversion symmetry in metals, by playing the role of a non-linear version of the Drude weight. I will also discuss a novel quantum rectification sum rule in which the frequency integrated rectification conductivity depends purely on the quantum geometry of the ground state wave-function controlled entirely by the non-abelian Berry connection. In the second part of the talk, I will describe our discovery of a remarkable connection between two celebrated fractionalized phases of matter: the composite fermion metal state realized in half-filled landau levels and the exciton superfluid realized in quantum Hall bilayers. Specifically, I will show that the exciton condensate is identical in all its universal properties to an interlayer paired state of composite fermions and that the two states can be smoothly connected in an analogous fashion to the BEC-BCS crossover.