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High-order terahertz (THz) sideband generation (HSG) in semiconductors is aphenomenon with physics similar to high-order harmonic generation but in a muchlower frequency regime. It was found that the electron-hole pairs excited by aweak optical laser can accumulate Berry phases along a cyclic path under thedriving of a strong THz field. The Berry phases appear as the Faraday rotationangles of the emission signal under short-pulse excitation in monolayerMoS$_2$. In this paper, the theory of Berry phase in THz extreme nonlinearoptics is applied to biased bilayer graphene with Bernal stacking, which hassimilar Bloch band features and optical properties to the monolayer MoS$_2$,such as time-reversal related valleys and valley contrasting optical selectionrules. The bilayer graphene has much larger Berry curvature than monolayerMoS$_2$, which leads to a giant Faraday rotation of the optical emission($\sim$ 1 rad for a THz field with frequency 1 THz and strength 8 kV/cm). Thisprovides opportunities to use bilayer graphene and low-power THz lasers forultrafast electro-optical devices.

Giant Faraday rotation induced by Berry phase in bilayer graphene under strong terahertz fields