A low-disorder, two-dimensional electron system (2DES) subjected to a large perpendicular magnetic field and cooled to very low temperatures provides a rich platform for studies of many-body quantum phases. The magnetic field quenches the electrons kinetic energy and quantizes the energy into a set of Landau levels, allowing the Coulomb interaction to dominate. In excited Landau levels, the fine interplay between short- and long-range interactions stabilizes bubble phases, Wigner crystals with more than one electron per unit cell. Here we present the screening properties of bubble phases, probed via a simple capacitance technique where the 2DES is placed between a top and a bottom gate and the electric field penetrating through the 2DES is measured. The bubbles formed at very low temperatures screen the electric field poorly as they are pinned by the residual disorder potential, allowing a large electric field to reach the top gate. As the temperature is increased, the penetrating electric field decreases and, surprisingly, exhibits a pronounced minimum at a temperature that appears to coincide with the melting temperature of the bubble phase. We deduce a quantitative phase diagram for the transition from bubble to liquid phases for Landau level filling factors $4leq uleq5$.
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