Chiral plasmon in gapped Dirac systems

We study the electromagnetic response and surface electromagnetic modes in a generic gapped Dirac material under pumping with circularly polarized light. The valley imbalance due to pumping leads to a net Berry curvature, giving rise to a finite transverse conductivity. We discuss the appearance of nonreciprocal chiral edge modes, their hybridization and waveguiding in a nanoribbon geometry, and giant polarization rotation in nanoribbon arrays.

Figure 1

Optically induced valley polarization: (a) Polarization selective pumping leads to different populations in the $K$ and $K^{\prime }$ valleys. (b) DC electronic carrier concentration in the two valleys as a function of the pump electric field. (c) DC ${\sigma }_{xy}$ in the two valleys as a function of the right circular polarized pump electric field.

Figure 2

(a) Chiral plasmon dispersion in bulk and semi-infinite MDS. (b) Selective excitation of edge modes using circular and linear polarized dipoles placed at the origin: Line plots of electric field $E_x$ in the plane and perpendicular to the edge. The vertical offset is $6\times {10}^{18}\mathrm{V}$/m. (c) $\left|E\right|$ field (normalized to max) profile for a $\widehat{x}$-polarized emitter located near the edge of semi-infinite Dirac material ($x<0$) at $\omega =0.1\mathrm{eV}$. Both of these field profiles show nonreciprocal emission into the edge mode. The dipoles are placed $10\mathrm{nm}$ above the MDS.

Figure 3

Guided modes in freestanding MDS ribbons. Ribbon width is assumed to be $w=100\mathrm{nm}$. The gray dashed lines represent solutions of $k_{B}w+{\varphi }_R=n\pi$, where $k_B$ is the bulk plasmon momentum in MDS and ${\varphi }_R\approx -3\pi /4$ [35], which explains the cutoff for all the guided modes (except the edge mode). The black solid lines represent the bulk plasmon in a continuous sheet of MDS (same as Fig. 2). The color plots below represent the real part of the electric field along the ribbon at the indicated $q$.

Figure 4

Transmission and polarization rotation in freestanding MDS ribbons: (a) Transmission (vertical offset is one unit). Inset: Schematic of the configuration. Note that in general the transmitted wave is expected to be elliptically polarized as opposed to linear as shown here. (b) Polarization rotation spectrum for different ribbon sizes $w$ (vertical offset is 6 degrees). For ribbon arrays, a filling factor of 50% has been assumed.