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Tracking shear mode dynamics across the glass transition in a 2D colloidal system

Long-wavelength collective shear dynamics are profoundly different in solids and liquids. According to the theoretical framework developed by Maxwell and Frenkel, collective shear waves vanish upon melting by acquiring a characteristic wave-vector gap, known as the $k$-gap. While this prediction has been supported by numerous simulations, experimental validation remains limited. Moreover, this phenomenon has been never tested across a continuous glass transition between a liquid phase and a glassy state with large but finite viscosity. In this work, we track the dispersion relation of collective shear modes in a two-dimensional colloidal system and provide direct experimental evidence for the emergence of a $k$-gap. This gap opens continuously at an effective temperature consistent with the onset of the glass transition and the vanishing of the static shear modulus. By extracting the instantaneous shear velocity from the experimental data, we uncover a shear relaxation time exhibiting a super-Arrhenius temperature dependence characteristic of glass-forming materials, accurately described by the Vogel-Fulcher-Tammann (VFT) relation. Our results confirm the predictions of the Maxwell-Frenkel framework and highlight their relevance across continuous melting processes originating from low-temperature amorphous solid phases.