Continuum-edge bifurcations and a fragile reentrant acoustic plasmon in imbalanced electron bilayers

Using the zero-temperature random-phase approximation (RPA), we determine the momentum intervals in which the acoustic plasmon of an electron bilayer remains above both particle-hole continua. We evaluate the continuum-edge determinant through an analytic threshold limit and count all undamped poles from the inertia of a symmetric inverse response whose frequency derivative is positive de nite. For equal masses we prove that the pole count cannot increase with momentum when the static interaction matrix decreases in the positive-semide nite order; the 432-case survey provides a numerical check. A narrow reentrant strip appears when the layer masses differ: for rs = 4, d = 4aB, w = 0.15aB, and density imbalance   delta= 0.25, it spans 0.868255 < m2=m1 < 0.869471. At m2=m1 = 0.8683, a 721-point momentum scan gives 2 > 1 >2 >1 >0. The eigenvectors identify the returning pole as an out-of-phase mode, and every pole-residue matrix is positive semide nite and rank one. The pocket is born through the smooth tangency of a pair of edge zeros and terminates at a cusp where the binding continuum switches from one layer to the other. It survives in the strict-2D limit, with a con nement-derived in nite-square-well form factor, and at a second (rs; d) point, although its position is model dependent. At the canonical mass its largest separation from the continuum is only 1.064 *10-4 effective Hartree, or 2.795 *10-4 of the mode frequency; a GaAs-like conversion gives 1.17  eV (13.5 mK). We therefore regard the pocket as a fragile collisionless-RPA bifurcation rather than an experimentally established mode.