Topological Superfluid Responses of Superconducting Dirac Semimetals

Abstract

We demonstrate that topological constraints do not only dictate the geometric part of the superfluid stiffness, but can also govern the total superfluid stiffness. By introducing a general adiabatic approach for superfluid responses, we showcase such a possibility by proving that the stiffness of a superconducting Dirac cone in two dimensions (2D) is proportional to its topological charge. By relying on the emergent Lorentz invariance of Dirac electrons, we unify the superfluid stiffness and quantum capacitance in these systems. Based on this connection, we further predict a topological origin for the quantum capacitance of a Josephson junction where 2D massless Dirac electrons are sandwiched between two conventional superconductors. We show that the topological responses persist upon effecting strain, are resilient against weak disorder, and can be experimentally controlled via a Zeeman field. Remarkably, the nonuniversal topological quantization of the two superfluid responses, yet implies the universal topological quantization of the admittance modulus of the superconducting Dirac system in units of conductance. The quantum admittance effect arises when embedding the superconducting Dirac system in an ac electrical circuit with a frequency tuned at the absorption edge. These findings are in principle experimentally observable in graphene-superconductor hybrids.