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Interactions between light and matter allow the realization ofout-of-equilibrium states in quantum solids. In particular, nonlinear phononicsis one of the efficient approaches to realizing the stationary electronic statein non-equilibrium. Herein, by using extended $ab~initio$ molecular dynamics,we identify that long-lived light-driven quasi-stationary geometry couldstabilize the topological nature in the material family of HgTe compounds. Weshow that coherent excitation of the infrared-active phonon mode results in adistortion of the atomic geometry with a lifetime of several picoseconds. Weshow that four Weyl points are located exactly at the Fermi level in thisnon-equilibrium geometry, making it an ideal long-lived metastable Weylsemimetal. We propose that such a metastable topological phase can beidentified by photoelectron spectroscopy of the Fermi arc surface states orultrafast pump-probe transport measurements of the nonlinear Hall effect.

Light-induced ideal Weyl semimetal in HgTe via nonlinear phononics