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Electromagnetic responses of bilayer excitonic insulators: from exciton London equations to dipole and inverse dipole Hall effects

We develop a microscopic theory of the linear electromagnetic response of bilayer excitonic insulators relevant to electron-hole double-layer systems. Using a self-consistent Hartree-Fock description of the excitonic ground state and time-dependent Hartree-Fock for its dynamics, we compute the collective mode spectrum and the full first-order response to layer-symmetric (charge) and layer-antisymmetric (exciton) gauge fields. At zero magnetic field, we find that two gapped plasmon modes dominate the long-wavelength charge response, while the exciton channel is governed by a linearly dispersing phase (Goldstone) mode. From the Goldstone-dominated kernel we derive a London-like equation for the exciton condensate, demonstrating non-dissipative acceleration under a layer-antisymmetric electric field, which we identify as the direct evidence of exciton superfluid; in contrast, a normal exciton fluid shows a Drude-like, dissipative response. In a perpendicular magnetic field, the Goldstone mode develops a magnetic-roton minimum that signals an instability toward a finite-momentum stripe-ordered excitonic insulator. Besides, charge and exciton motions become coupled under the field, giving rise to dipole and inverse dipole Hall effects in which a charge (exciton) bias induces a transverse exciton (charge) current. As a manifestation of the exciton superfluidity, these mixed Hall responses remain finite even in the DC limit. Our findings provide concrete targets for microwave and transport probes of bilayer exciton superfluidity.