We study the effect of electron-atomic phonon coupling on the location of the Fermi Liquid to Wigner Crystal transition in the two-dimensional electron gas realized in various material platforms. Based on dimensional estimates of the relevant parameters, we conclude that (as conventionally assumed) atomic phonons are negligible in traditional semiconductor quantum well systems, but likely play a significant role in various recently synthesized atomically thin two-dimensional materials.

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• Electron-phonon coupling
• Two-dimensional electron system
• Wigner crystal
• Perturbation theory