Laser-induced topological phases in monolayer amorphous carbon

Driving non-topological materials out of equilibrium using time-periodic perturbations, such as circularly-polarized laser light, is a compelling way to engineer topological phases. At the same time, topology has traditionally only been considered for crystalline materials. Here we propose an experimentally feasible way of driving monolayer amorphous carbon topological. We show that circularly polarized laser light induces both regular and anomalous edge modes at quasienergies $0$ and $\pm π$, respectively. We also obtain complete topological characterization using an energy- and space-resolved topological marker based on the spectral localizer. Additionally, by introducing atomic coordination defects in the amorphous carbon, we establish the importance of the local atomic structure in topological amorphous materials. Our work establishes amorphous systems, including carbon, as a versatile and abundant playground to engineer topological phases.