Space-time Supercrystals from Non-Abelian Electric Translation Symmetries

TL;DR

This paper introduces a novel mechanism for forming electronic space-time supercrystals in 1+1D systems driven periodically, using non-Abelian electric translation symmetries, without requiring many-body interactions.

Contribution

It demonstrates how space-time supercrystals can emerge from symmetry and area competition in driven SSH lattices, expanding understanding of non-equilibrium topological phases.

Findings

Fractal spectra and replicated bands characterize the area competition.

Eigenstates form enlarged space-time unit cells, creating supercrystals.

Robust dynamical localization linked to static topology of the SSH lattice.

Abstract

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.