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

TL;DR

This paper analyzes the optical conductivity of two-dimensional Dirac materials with a flat band, revealing coexistence of multiple optical transitions and resonant scattering phenomena, with implications for terahertz optical device applications.

Contribution

The study provides an analytical and numerical investigation of the optical conductivity in $ ext{alpha}$-$ ext{T}_3$ lattices, including both real and imaginary parts, highlighting unique transition phenomena.

Findings

Coexistence of flat band to cone and cone-to-cone optical transitions.

Resonant scattering at $ ext{alpha}=1$ with pseudospin-1 quasiparticles.

Potential for terahertz optical device applications.

Abstract

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