Disorder-induced currents as signatures of chiral superconductivity

Abstract: Chiral superconductors are expected to carry a spontaneous, chiral and perpetual current along the sample edge. However, despite the availability of several candidate materials, such a current has not been observed in experiments. In this article, we suggest an alternative probe in the form of impurity-induced chiral currents. We first demonstrate that a single non-magnetic impurity induces an encircling chiral current. Its direction depends on the chirality of the order parameter and the sign of the impurity potential. Building on this observation, we consider the case of multiple impurities, e.g., realized as adatoms deposited on the surface of a candidate chiral superconductor. We contrast the response that is obtained in two cases: (a) when the impurities are all identical in sign and (b) when the impurities have mixed positive and negative signs. The former leads to coherent currents within the sample, arising from the fusion of individual current loops. The latter produces loops of random chirality that lead to incoherent local currents. These two scenarios can be distinguished by measuring the induced magnetic field using recent probes such as diamond NV centres. We argue that impurity-induced currents may be easier to observe than edge currents, as they can be tuned by varying impurity strength and concentration. We demonstrate these results using a toy model for $p_x \pm i p_y$ superconductivity on a square lattice. We develop an improved scheme for Bogoliubov deGennes (BdG) simulations where both the order parameter as well as the magnetic field are determined self-consistently.