(a) The configuration of a double-layer cluster. (b) The structure of each layer in the double-layer cluster or a single layer. The separation between adjacent spheres is D = 2a+0.002 μm. (c) Optical torques exerted on the PT-symmetric double-layer structure with the refractive indexes of the lower lossy and upper gain layers are n = 2± 0.005i, respectively. The insert figure displays the opposite torques of the two layers at resonance. (d) Optical torques exerted on a single lossy layer (n_lossy = 2+0.005i), the lower lossless layer (n_lossless = 2) in a lossless–lossless double-layer cluster, and a partial view of the black line in panel (c) are shown for comparison. Optical torques obtained by the upper lossless layer (n_lossless = 2) in a lossless–lossless double-layer cluster, and a partial view of the red line in panel (c) are also shown in panel (e) for comparison. Black dotted vertical lines in panels (d) and (e) are guides of eyes to highlight the optical twist.