Controlling the Orbital Hall Effect in Gapped Bilayer Graphene in the Terahertz Regime

We study the orbital Hall effect (OHE) in the AC regime using bilayergraphene (BLG) as a prototypical material platform. While the unbiased BLG hasgapless electronic spectra, applying a perpendicular electric field creates anenergy band gap that can be continuously tuned from zero to high values. Byexploiting this flexibility, we demonstrate the ability to control the behaviorof AC orbital Hall conductivity. Particularly, we demonstrate that the orbitalHall conductivity at the neutrality point changes its signal at a criticalfrequency, the value of which is proportional to the perpendicular electricfield. For BLG with narrow band gaps, the active frequency region for the ACOHE may extend to a few terahertz, which is experimentally accessible withcurrent technologies. We also consider the introduction of a perpendicularmagnetic field in the weak coupling regime using first-order perturbationtheory to illustrate how the breaking of time-reversal symmetry enables theemergence of AC charge Hall effect in the charge-doped situation and modifiesthe AC orbital Hall conductivity. Our calculations suggest that BLG with narrowbandgaps is a practical candidate for investigating time-dependent orbitalangular momentum transport.