The paradigm of Floquet engineering of topological states of matter can be generalized into the time-quasiperiodic scenario, where a lower-dimensional time-dependent system maps onto a higher-dimensional one by combining the physical dimensions with additional synthetic dimensions generated by multiple incommensurate driving frequencies. Differently from most previous works in which gapped topological phases were considered, we propose an experimentally realizable, one-dimensional chain driven by two frequencies, which maps onto a gapless Weyl semimetal in a synthetic dimension. Based on analytical reasoning and numerical simulations, we find that the nonadiabatic quantum dynamics of this system exhibit energy pumping behaviors characterized by universal functions. We also numerically find that such behaviors are robust against a considerable amount of spatial disorder.

• Received 20 October 2021
• Revised 19 November 2021
• Accepted 19 November 2021

DOI:https://doi.org/10.1103/PhysRevB.104.224301