Nucleation of merons in double quantum dots with spontaneous interlayer phase coherence

We have investigated how merons nucleate in the spontaneous interlayer phase coherent state of double quantum dots when a distortion with a reflection symmetry is present in the lateral confinement potential. When the lateral confinement strength is large enough merons with a negative topological charge nucleate in the ground state. For weaker values of the lateral confinement strength both density depletions and positively charged merons are present. These density depletions form an ordered structure. When the strength of the distortion increases some of these density depletions can transform into merons. In the presence of merons the resulting electron density in one of the layers is the mirror image of the electron density of the other layer. Even when a random disorder potential is present both density depletions and merons can coexist.