Quantum ratchet effect in periodically driven dimer chain

In condensed matter physics, one of the major topics is to find out and classify interesting novel topological matters and phenomena. Topologically nontrivial systems can also be achieved by using periodical driving fields. On the other hand, ratchet effect can be used to realize directed transport in symmetrically-driven systems. Here, we promote a dimer chain by applying two mutually-parallel ac electric fields, and obtain an effective two-dimensional Hamiltonian in the low-frequency regime. We thereby derive Floquet quantum anomalous Hall conductance and then find a quantized ratchet effect in the resulting current along the chain. Our further analysis shows that these are originated from the electric fields only. This lengthwise quantized ratchet effect without magnetic field should be useful to designing novel high-performance electronic applications.