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### Recent Research

Signatures of the topological spin of Josephson vortices in topological superconductors

Photo Credit: Eytan Grosfeld

Realization of non-abelian quasi-particles known as Majorana fermions is an ongoing challenge for physicists exploring topological states of matter. Towards achieving this goal, we recently suggested that Josephson vortices in topological Josephson junctions (TJJ) would constitute such Majorana fermions and retain the exchange statistics of bulk vortices. We corroborated this hypothesis by finding the universal exchange phase of Josephson vortices. In order to do so, we derived the Hamiltonian governing the dynamics of a soliton in an annular Josephson junction. Our next step was to develop a procedure to calculate the Berry connection of systems that posses particle-hole symmetry. The procedure was applied to confirm that the Abelian phase due to the an exchange between a vortex in the bulk of a p-wave superconductor and a Josephson vortex is π/8. In addition, we suggested an experiment to measure it by.

On the effective theory of vortices in two-dimensional spinless chiral p-wave superfluids

As the search for quantum computers evolves, new methods to realize an universal topological quantum computation are a explored. Vortex defects in a 2D spinless chiral p-wave superfluid bind Majorana zero modes that endow them with non-Abelian exchange statistics. Motivated by its potential for topological quantum information processing, we developed a ${\mathbb{U}(1) \times \mathbb{Z}_2}$ effective gauge theory for vortices in a ${p_x+ip_y}$ superfluid in two dimensions. The combined gauge transformation binds ${\mathbb{U}(1)}$ and ${\mathbb{Z}_2}$ defects so that the total transformation remains single-valued and manifestly preserves the particle-hole symmetry of the action. The ${\mathbb{Z}_2}$ gauge field introduces a complete Chern-Simons term in addition to a partial one associated with the ${\mathbb{U}(1)}$ gauge field. The theory reproduces the known physics of vortex dynamics such as a Magnus force proportional to the superfluid density. It also predicts a universal Abelian phase, ${\exp(i\pi/8)}$, upon the exchange of two vortices, modified by non-universal corrections due to the partial Chern-Simon term that are screened in a charged superfluid.