Strain-induced Berry phase in chiral superconductors

We study the topology of the order parameter in the intermediate phase between the superconducting and time-reversal symmetry breaking transitions of a $p_x+i{p}_y$ superconductor under strain. The application of in-plane strain reduces the underlying crystal symmetry and lifts the degeneracy of the critical temperature between the $p_x$ and $p_y$ orbitals, resulting in a Dirac cone structure in the thermodynamic phase diagram. When the strain is varied adiabatically along a closed path enclosing the Dirac cone, the order parameter acquires a Berry phase of $\pi$, which originates from a half rotation of the superconducting gap function. This half rotation leaves a topological signature in the superfluid stiffness tensor, making it directly observable through the geometry of vortices and the upper critical field.