Subharmonic intersubband polaritonic responses in metagate-tuned strongly-modulated graphene

We show that an extreme modulation of carrier density in monolayer graphene deforms the underlying Dirac band dispersion and results in subharmonic inter-subband transition responses in optical conductivity. In our proposed system, hBN-encapsulated graphene is placed on top of a one-dimensional metagate with a periodicity of $L$. Besides the metagate-tuning, a backgate placed beneath the metagate is used as the second gate, further modulating carrier density on regions in graphene that are not directly screened by the metagate. With strong carrier density modulation, graphene optical conductivity, computed by Kubo formula applied to deformed electronic band structures, shows resonances at frequencies $\nu v_F G_0$, where $\nu=0.5,1,1.5,...$, $v_F$ is the fermi velocity of Dirac electrons, and $G_0$ is the reciprocal lattice vector $2\pi/L$. We find that these half-integer subharmonic resonances are caused by transitions between subbands that are equispaced by $0.5v_F G_0$ near the fermi sea. As a result, there appear new polaritonic peaks in far-field reflection spectra that cannot be predicted by local or perturbative-nonlocal graphene conductivity models. Our study opens up an avenue for exploring emergent polaritons in two-dimensional materials with engineered band structures.