New free energy related signatures of the condensed excitons in Double Quantum Wells (DQW) are predicted and experiments are proposed to measure the effects. These signatures are related to the measurement of a conceptually new kind of force ($approx
10^{-9} N$) due to the condensate. This force, which may be coined as the Exciton Condensate (EC)-force is attractive and reminiscent of the Casimir force between two perfect metallic plates, but also distinctively different from it by its driving mechanism and dependence on the parameters of the condensate. The proposed experiments here are based on a recent experimental work on a driven micromechanical oscillator with a proven high quality factor. The free energy related measurements are immune to the commonly agreed drawbacks of the existing photoluminescence experiments. In this regard, the proposed experiments are highly decisive about the EC.
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 ide
ntical 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.
