Bandwidth-controlled quantum phase transition between an easy-plane quantum spin Hall state and an s-wave superconductor

The quantum spin Hall state can be understood in terms of spontaneous O(3) symmetry breaking. Topological skyrmion configurations of the O(3) order parameter vector carry a charge 2e, and as shown previously, when they condense, a superconducting state is generated. We show that this topological route to superconductivity survives easy-plane anisotropy. Upon reducing the O(3) symmetry to $\mathrm{O}(2)\ifmmode\times\else\texttimes\fi{}\phantom{\rule{4pt}{0ex}}{\mathrm{Z}}_{2}$, skyrmions give way to merons that carry a unit charge. On the basis of large-scale auxiliary field quantum Monte Carlo simulations, we show that at the particle-hole symmetric point, we can trigger a continuous and direct transition between the quantum spin Hall state and $s$-wave superconductor by condensing pairs of merons. This statement is valid in both strong and weak anisotropy limits. Our results can be interpreted in terms of an easy-plane deconfined quantum critical point. However, in contrast to the previous studies in quantum spin models, our realization of this quantum critical point conserves $\text{U}(1)$ charge such that skyrmions are conserved.