Optical response of two-dimensional Dirac materials with a flat band

Two-dimensional Dirac materials with a flat band have been demonstrated to possess plethora of unusual electronic properties, but the optical properties these are less studied. Utilizing $\alpha$-$\mathcal{T}_3$ lattice as prototypical system, where $0\le \alpha \le 1$ is tunable parameter and through conic intersection two cones arises for $\alpha > 0$, we investigate conductivity flat-band material systems analytically numerically. Motivated by fact that imaginary part can significant effects on response an important factor consideration developing based devices, led derive complete formula both real parts. Scrutinizing formula, uncover phenomena. First, value $\alpha$ in some range, types transitions coexist: one between another from cone, which generate multi-frequency transverse electrical propagating waves. Second, $\alpha=1$ so quasiparticles become pseudospin-1, flat-to-cone transition result resonant scattering. These results pave way exploiting $\alpha$-$T_3$ device applications terahertz frequency domain.