Fig. 1: Designing vortex–antivortex pair in (PTO)_n/(STO)_m superlattice.

a Schematic illustration of a topological antivortex sandwiched between two adjacent vortices. b–e Four typical polar structures exist in (PTO)_n/(STO)_m superlattices for different combinations of m and n, as predicted by phase-field simulation. b For 4-u.c. thick STO (m = 4) sandwiched between two 4-u.c. thick PTO (n = 4), antiparallel a-domain is observed in PTO, while polarization in STO is negligibly small, exhibiting no nontrivial topological structure. c For m = 20 and n = 10, vortex array emerges in PTO, while polarization in STO remains negligibly small. d For m = 10 and n = 10, sign of topological structure appears in STO, with modestly increased polarization, while antivortex appears irregular. e For m = 4 and n = 10, perfect antivortex array with relatively large polarization is observed in STO, sandwiched between two vortices in adjacent PTO. f Phase-field computed phase diagram of four typical polar structures in (PTO)_n/(STO)_m superlattices, as represented by b–e.