Space-time Supercrystals from Non-Abelian Electric Translation Symmetries

Electronic supercrystals can form in spatial or temporal dimensions where traditional mechanisms usually require many-body interactions, such as Wigner crystals or discrete time crystals. We propose a novel approach for electronic supercrystals in 1+1D without requiring many-body interactions, but arising from the competition between characteristic space-time areas in periodically driven Su-Schrieffer-Heeger lattices under electric fields. Utilizing the non-Abelian dynamical symmetries described by the electric translation group, the area competition is characterized by fractal spectra and replicated bands, furnished with eigenstates crystallized in enlarged space-time unit cells forming space-time supercrystals under perturbations. We also report robust dynamical localization of electrons arising from the static topology of the SSH lattice.