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    Universal dark-selective control in stationary bright-dark exciton condensates

    Yingda Chen1, Wen-Kai Lou2,*, Yongyong Cai3,†, Yibo Han4, and Kai Chang5,6,‡

    • *Contact author: wklou@semi.ac.cn
    • †Contact author: yongyong.cai@bnu.edu.cn
    • ‡Contact author: kchang@zju.edu.cn

    Phys. Rev. B 114, 125303 – Published 7 August, 2026

    DOI: https://doi.org/10.1103/78zs-9f9w

    Abstract

    Dark exciton condensates offer a long-lived platform, yet controlling their density and spatial profile remains a central challenge. We develop a spatially resolved selectivity framework for driven-dissipative bright-dark condensates controlled by the bright-dark detuning Δbd. Within an open-condensate Gross-Pitaevskii framework with effective bright-branch injection and detailed-balance-consistent spin-flip rates, stationarity imposes a universal overlap-renormalized conversion constraint on the dark fraction, rather than on the bare population ratio alone. In the long-lived dark-branch regime this constraint reduces to Q≃exp(Δbd/kBT), while the bright component remains largely buffered by pump and radiative loss. Confinement then determines how the same constraint is realized in real space: soft traps yield ringlike dark accumulation, whereas hard-wall confinement produces boundary layers, radial quantization, and boundary-sensitive annular interfaces under weak pumping, with the corresponding radial branches dynamically selected or destabilized by the pump aperture. The extracted selectivity collapses across top-hat and Gaussian pumps, establishing a compact route to spatially resolved, dark-selective nonequilibrium regimes in van der Waals heterostructures.

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