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Many-body localization (MBL) has attracted significant attention due to itsimmunity to thermalization, role in logarithmic entanglement entropy growth,and opportunities to reach exotic quantum orders. However, experimentalrealization of MBL in solid-state systems has remained challenging. Here wereport evidence of a possible phonon MBL phase in disordered GaAs/AlAssuperlattices. Through grazing-incidence inelastic X-ray scattering, we observea strong deviation of the phonon population from equilibrium in samples dopedwith ErAs nanodots at low temperature, signaling a departure fromthermalization. This behavior occurs within finite phonon energy and wavevectorwindows, suggesting a localization-thermalization crossover. We support ourobservation by proposing a theoretical model for the effective phononHamiltonian in disordered superlattices, and showing that it can be mappedexactly to a disordered 1D Bose-Hubbard model with a known MBL phase. Our workprovides momentum-resolved experimental evidence of phonon localization,extending the scope of MBL to disordered solid-state systems.

Signature of Many-Body Localization of Phonons in Strongly Disordered Superlattices