Berry curvatures of two-dimensional electron-hole system in external magnetic field

Abstract

The Berry-curvature signatures and topological transitions of excitonic condensates (ECs) in a two-dimensional electron-hole system including intraband Rashba spin-orbit coupling under an external magnetic field is investigated. Within an unrestricted Hartree-Fock approach, we self-consistently determine spin-resolved EC order parameters. The Berry curvature and Chern number are then evaluated by using the Fukui-Hatsugai-Suzuki method. At a weak field, the Berry curvature is antisymmetric guaranteeing a vanishing total Berry flux over the Brillouin zone and system settles in trivially topological state. Increasing the external magnetic field breaks timereversal symmetry that produces asymmetric curvature and quantizes the Chern number \(C = 2\), identifying a topological spin-up triplet EC phase. Once the field is sufficiently strong, opposite Chern numbers from the occupied bands cancel each other, restoring a trivial topological state. Our results reveal a magnetic-field driven route to stabilize topological spin-up triplet EC state in two-dimensional materials with strong Rashba spin-orbit coupling.