Antichiral edge states in an exciton polariton strip

We present a scheme to obtain antichiral edge states in an exciton-polariton honeycomb lattice with strip geometry, where the modes corresponding to both edges propagate in the same direction. Under resonant pumping the effect of a polariton condensate with nonzero velocity in one linear polarization is predicted to tilt the dispersion of polaritons in the other, which results in an energy shift between two Dirac cones, and the otherwise flat edge states become tilted. Our simulations show that due to the spatial separation from the bulk modes the edge modes are robust against disorder.

Figure 1

Schematic view of the system under consideration. A graphene like polariton strip with zigzag edges, which can be fabricated with different technologies [25, 26, 27], is subjected to an $x$ linearly polarized optical field. $y$ linearly polarized polaritons propagate at both edges in the same direction compensated by counterpropagating polaritons through the bulk. Since the edge and bulk modes are spatially separated, the edge states are robust against scattering with disorder.

Figure 2

Dispersion of the $y$ polarized polaritons calculated from Eq. (6) corresponding to the stable states. All the states marked in blue correspond to the bulk states and states marked in red correspond to the edge states. Parameters: ${\omega }_0=15,k_0=\pi ,{\varepsilon }_x=0,{\varepsilon }_y=A_0^2,A_0=3.6,{\mathrm{\Gamma }}_x={\mathrm{\Gamma }}_y=0.23,V_0=17.7,\zeta =0.1$.

Figure 3

Dispersion of the $y$ polarized polaritons calculated from Eqs. (4) and (5) in the presence of white noise which corresponds to the photoluminescence spectrum obtainable in experiments. The blue dot corresponds to the state which is excited to probe the pulse propagation.

Figure 4

Propagation of the polaritons in a graphene zigzag strip consisting of $32\times 23$ unit cells with both edges slightly deformed. Polaritons propagate through both edges in the same direction and go around the defects without being backscattered, (a) and (b). Once the polaritons reach the left end they couple to the counterpropagating bulk modes and the intensity is transferred back to the right end (c). When the polaritons reach the right end through the bulk they again couple to the edge modes and start to propagate through the edges robustly until they again reach the left end (d). The energy and wave vector of the pulse correspond to the blue dot shown in Fig. 3. Due to the finite lifetime of the polaritons the intensity decreases with time, which is compensated by rescaling of the intensity at each time step. Parameters: $F_0=2,\sigma =2,\tau =4,t_0=0$.

Figure 5

Propagation of (a) an edge state and (b) a bulk state in the presence of disorder. Due to the absence of backscattering the edge state does not spread too much whereas the bulk state spreads indicating backscattering. The green line represents the mean position of the pulse and the dashed green lines represent the square root of variance.