We investigate topological spin-up triplet excitonic condensation and its competition with other stabilities in a two-dimensional interacting electron-hole system taking into account Rashba spin-orbit coupling and external magnetic fields. Using an unrestricted Hartree-Fock approach, we self-consistently evaluate spin-selective excitonic condensate order parameters and the Chern number. The ground state phase diagram in the dependence on magnetic field and Coulomb interaction shows a spin-up triplet excitonic condensate (EC) with a nonzero Chern number, emerging uniquely away from the topologically trivial singlet and spin-down triplet EC regions. Strong spin-polarized triplet excitonic fluctuations preceding the condensation are further revealed through the signatures of the dynamical excitonic susceptibility spectra. Our results establish a class of topological quantum phases driven by excitonic coherence and suggest a realistic pathway to its realization in a distorted Janus monolayer of transition metal dichalcogenides or some twisted van der Waals heterostructures.

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• Excitons
• Quantum Hall effect
• Spin-orbit coupling
• Topological phase transition
• Zeeman effect
• Bose-Einstein condensates
• Topological materials
• Transition metal dichalcogenides
• Two-dimensional electron system
• Mean field theory
• Random phase approximation