Counterflow Conductivity and Quantum Geometry in Excitonic Condensates

Excitons are bound electron-hole pairs that Bose condense to form an excitonic condensate with macroscopic phase coherence. Motivated by recent experiments in TMDs, we focus on inter-layer excitons and investigate the effects of particle-hole asymmetry and quantum geometry on the condensate within a mean-field framework. We make connections between phase stiffness, Coulomb drag and counterflow conductivity, and highlight how they are enhanced by the quantum geometry of Bloch wavefunctions. We then add deviations from particle-hole symmetry in excitons and uncover an effective magnetic field that aids in pairing but quenches stiffness. Combining quantum geometry, particle-hole asymmetry with different pairing symmetries of the excitons, we comment on various regimes that optimize the BKT temperature. Our mean-field results have direct implications on the ongoing search for excitonic condensates in Moire materials.