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Robust Ground State and Artificial Gauge in DQW Exciton Condensates under Weak Magnetic Field

Exciton condensate is a vast playground in studying a number of symmetries that are of high interest in the recent developments in topological condensed matter physics. In DQWs they pose highly nonconventional properties due to the pairing of non identical fermions with a spin dependent order parameter. Here, we demonstrate a new feature in these systems: the robustness of the ground state to weak external B-field and the appearance of the artificial spinor gauge fields beyond a critical field strength where, negative energy pair-breaking quasi particle excitations are created in certain $k$ regions (DX-pockets). The DX-pockets are the Kramers symmetry broken analogs of the negative energy pockets examined in the 60s by Sarma, where they principally differ from the latter in their non-degenerate energy bands due to the absence of the time reversal symmetry. They respect a disk or a shell-topology in $k$-space or a mixture between them depending on the B-field strength and the electron-hole mismatch. The Berry connection between the artificial flux and the TKNN number is made. The artificial spinor gauge field describes a collection of pure spin vortices in real space when the B-field has only inplane components.