Winger crystal in two dimensions
Predicted in 1930s, a Wigner crystal (WC) [1] is a remarkable solid phase of electrons stabilized by dominating long range Coulomb energy against quantum fluctuations (zero point energy) and disorder fluctuations [2]. Experimentally, observation of a Wigner crystal depends critically on achieving the condition that the Coulomb energy far exceeds the Fermi energy in the presence of little disorder. There have been Extensive experimental efforts made to confirm the presence of WCs in two-dimensional (2D) systems [3-7]. Most are based on detecting collecting modes. Nevertheless, collective modes alone are insufficient to make unambiguous conclusion because the phase diagram is complex and there are collective modes associated with intermediate phases.
Our approach is to study WC phases in both two- and one-dimensional (1D) systems in a zero magnetic field. This requires systems with ultra-dilute charge densities in order to reach the limit where interaction dominates. In collaboration with Loren Pfeiffer at Princeton University, we have realized ultra-dilute systems in undoped GaAs HIGFET [8] heterostructures where the carrier density varies from 7×10^{10} cm^{-2} down to approximately 6×10^{8} cm^{-2}. Because HIGFETs are undoped, the 2D systems are exceptionally clean because the major source of disorder is eliminated.
Our experiments target two aspects. The first is to identify the quantum liquid to solid phase transition. Through measuring the electrical resistance as a function of charge density and temperature which are varied independently, we have found a discontinuity in the temperature dependence when the Wigner-Seitz radius is beyond 40. This is consistent with the critical point predicted theoretically. In addition, the melting transition includes an intermediate phase, similar to the Kosterlitz-Thouless picture [9]. Second, we detected the collective pinning modes by performed dc and dc+ac response. The collective modes is characterized by an enormous resistance, consistent with a manybody pinning on correlation length close to 0.5 mm [10].
Wigner crystal of lattice constant a on a crystal lattice