Is SmB6 a failed superconductor?—Part I: long-wave length action

The theory of superfluids and superconductors is founded on London's idea of ``wavefunction rigidity", in which gradients of the condensate phase carry a persistent superflow. However, the theory of neutral superfluids reveals that a stable superflow also requires the topological quantization of circulation: when this is absent, as in the case of $^3$He-A, the superflow is unstable. Motivated with the controversial experimental results on SmB$_6$, we generalize this idea to charged superfluids, in which a higher dimensional order parameter manifold topologically destabilizes vortices, causing the rapid decay of supercurrents into a novel diamagnetic insulator. I will present a Ginzburg-Landau type long wavelength action of a `failed' superconductor and discuss how supercurrents decay through formation of space-time skyrmions. This work is done in collaboration with Po-Yao Chang, Piers Coleman and Alexei M. Tsvelik.