Dipole-Obstructed Cooper Pairing: Theory and Application to $j=3/2$ Superconductors

Like electrons, Cooper pairs can carry a monopole charge if the pairing electrons come from two or more Fermi surfaces with different Chern numbers. In such an instance, a superconductor is necessarily nodal due to an inherent topological pairing obstruction. In this work, we show that a similar obstruction is also possible when there is only one Fermi surface involved in the pairing process. By developing a Chern-vorticity theorem, we have identified a class of Fermi surfaces with a quantized dipolar Berry flux pattern, where all intra-Fermi-surface Cooper pairings are ``dipole-obstructed" and nodal. As a real-world application, we find that the dipole obstruction plays a crucial role in stabilizing the superconducting nodal structure for $j=3/2$ half-Heusler compounds.