In this work, a thorough exploration has been carried out to unravel the role
of electron-phonon interaction (EPI) in a Bernevig-Hughes-Zhang (BHZ) quantum
spin Hall (QSH) insulator subjected to a time-periodic step drive. It is
observed that upon inclusion of the EPI, the system demonstrates emergent
Floquet QSH (FQSH) phases and several topological phase transitions therein,
mediated solely by the interaction strength. Quite intriguingly, the emergence
of topological zero ($\pi$) modes in the bulk that remains otherwise gapless in
the vicinity of the $\pi$ (zero) energy sector is observed, thus serving as a
prime candidate of robust topology in gapless systems. With other invariants
being found to be deficient in characterizing such coexistent phases, a
spectral localizer (SL) is employed, which distinctly ascertains the nature of
the (zero or $\pi$) edge modes. Following the SL prescription, a real-space
Chern marker computed by us further provides support to such \textit{gapless}
Floquet topological scenario. Our results can be realized in advanced optical
setups that may underscore the importance of EPI-induced Floquet features.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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