Probing the Melting of a Two-dimensional Quantum Wigner Crystal via its Screening Efficiency

One of the most fundamental and yet elusive collective phases of an interacting electron system is the quantum Wigner crystal (WC), an ordered array of electrons expected to form when the electrons Coulomb repulsion energy eclipses their kinetic (Fermi) energy. In low-disorder, two-dimensional (2D) electron systems, the quantum WC is known to be favored at very low temperatures ($T$) and small Landau level filling factors ($ u$), near the termination of the fractional quantum Hall states. This WC phase exhibits an insulating behavior, reflecting its pinning by the small but finite disorder potential. An experimental determination of a $T$ vs $ u$ phase diagram for the melting of the WC, however, has proved to be challenging. Here we use capacitance measurements to probe the 2D WC through its effective screening as a function of $T$ and $ u$. We find that, as expected, the screening efficiency of the pinned WC is very poor at very low $T$ and improves at higher $T$ once the WC melts. Surprisingly, however, rather than monotonically changing with increasing $T$, the screening efficiency shows a well-defined maximum at a $T$ which is close to the previously-reported melting temperature of the WC. Our experimental results suggest a new method to map out a $T$ vs $ u$ phase diagram of the magnetic-field-induced WC precisely.