Topologically Charged Vortices at Superconductor-Quantum Hall Interfaces

Abstract

We explore interface states between a type-II $s$-wave superconductor (SC) and a $ν= 1$ quantum Hall (QH) state. We show that the effective interaction gives rise to two emergent Abelian Higgs fields, representing paired electrons localized at the SC-QH interface. These fields interact with each other in the presence of a Chern-Simons term originating from the QH sector. The Chern-Simons term leads to a topological contribution to the photon mass and imparts a \emph{fractional} topological charge of $e/2$ to the interface vortices. The topological mass modifies the vortex lattice at the interface, while the topological charge leads to formation of vortex quadruplets. We predict that these effects lead to a \emph{topological} Abrikosov lattice at the interface.

Figures (2)

• Figure 1: Illustration of vortex lattice formation in quadruplets.
• Figure 2: Numerical vortex solutions \ref{['vortex_ansatz']} (see also Eqs. (83) in SM) for $n=1$ and $e=1$. Parameters: solid lines--$\sqrt{2}\tilde{\kappa}_1=2.35$, $\sqrt{2}\tilde{\kappa}_2=0.56$, $\sqrt{2}\kappa=2.23$, $\delta_2/\delta_1=0.24$; dashed lines--$\sqrt{2}\tilde{\kappa}_1=0.85$, $\sqrt{2}\tilde{\kappa}_2=0.55$, $\sqrt{2}\kappa=1.02$, $\delta_2/\delta_1=0.66$.