Gate-controlled optical bistability via tunable self-action feedback in a semiconductor quantum dot-graphene nanodisk...

We theoretically examine how electrostatic gating can tune the steady-state response of a semiconductor quantum dot (SQD)-graphene nanodisk hybrid between monostable and bistable regimes. The model combines the optical Bloch dynamics of a driven two-level SQD with a gate-dependent polarizability of the graphene nanodisk. Through this polarizability, the gate voltage controls the SQD self-action, represented by the complex feedback parameter G(Vg) = GR(Vg) + iGI(Vg). The bistable response results from saturation of the SQD transition combined with graphene-mediated feedback. As Vg is varied, G(Vg) traces a trajectory in the complex feedback plane relative to the saddle-node boundary. Bistability occurs only along the part of this trajectory for which the steady-state input-output relation has two physical turning points. Within this segment, adiabatic sweeps of gate voltage or input intensity remain on a stable branch until a turning point is reached, giving a hysteresis loop. The stability of these branches is verified from the local Jacobian eigenvalues. The same turning-point criterion locates the gate-detuning domain for fixed-input branch switching and identifies the coupling-dephasing window in which the feedback trajectory can reach the bistable domain. These results identify gate-controlled complex self-action as the mechanism governing the opening and closing of the bistability window and the associated branch switching in the SQD-graphene nanodisk hybrid.