Topological Phase Transitions of Flux Vortices Driven by Charge and Pair-Density Waves

Our experimental team recently observed charge order within magnetic vortices of an iron-based superconducting thin film, which is absent in the bulk. They also identified both topologically trivial and non-trivial flux vortices. Interestingly, a statistical correlation was found between the topological nature of the vortices and the phase of the charge order. Inspired by this discovery, we developed a theory about the topological phase transitions of the vortices driven by charge orders. We found that both charge density waves (CDW) and pair density waves (PDW) can induce vortex topological phase transitions linked to the phase of the order parameter:

(1) When the CDW dominates within the vortex, a sine-form CDW leads to inversion-symmetry breaking, which allows a mixing of spin-singlet and spin-triplet pairings in the superconducting order parameter. In the presence of spin-orbit coupling, when the amplitude of triplet pairing exceeds that of singlet pairing, the superconductor becomes an intrinsic topological superconductor, thereby triggering a topological phase transition.

(2) When the PDW dominates, within Ginzburg-Landau theory, a cosine-form PDW must undergo a phase dislocation to minimize the free energy. It can be shown that the dislocated PDW transforms the original vortex system away from a single vortex. Due to the change in the winding number, a topological phase transition of the vortex occurs.