Winger crystal in two dimensions 
Predicted in the 1930s, the Wigner crystal (WC) [1] represents a unique solid phase of electrons stabilized by dominant Coulomb interactions that outweigh quantum fluctuations (zero-point energy) and disorder effects [2]. Experimentally observing a Wigner crystal requires achieving conditions where the Coulomb energy significantly exceeds the Fermi energy while maintaining a low level of disorder. Numerous experimental efforts have aimed to confirm the existence of WCs in two-dimensional (2D) systems [3-7], primarily by detecting collective modes. However, collective modes alone are not sufficient for definitive identification due to the complex phase diagram and the presence of intermediate phases.
Our research focuses on studying WC phases in both two-dimensional (2D) and one-dimensional (1D) systems in the absence of a magnetic field. Achieving this requires ultra-dilute charge densities to reach a regime where interactions dominate. In collaboration with Loren Pfeiffer at Princeton University, we have developed ultra-dilute systems using undoped GaAs HIGFET [8] heterostructures, with carrier densities ranging from 7×10^{10} cm^{-2} to approximately 6×10^{8} cm^{-2}. The undoped nature of HIGFETs results in exceptionally clean 2D systems, as it eliminates the major sources of disorder.
Our experiments are designed to address two main objectives. First, we aim to identify the quantum liquid-to-solid phase transition by measuring electrical resistance as a function of charge density and temperature, which are varied independently. We have observed a discontinuity in the temperature dependence when the Wigner-Seitz radius exceeds 40, consistent with theoretical predictions of the critical point. Additionally, the melting transition appears to involve an intermediate phase, analogous to the Kosterlitz-Thouless scenario [9]. Second, we have detected collective pinning modes through both DC and DC+AC response measurements. The collective modes are characterized by a substantial resistance, indicative of many-body pinning with a correlation length near 0.5 mm [10].