Condensed Matter Seminar: "Melting of two-dimensional Wigner Crystals"
(sign-up)Jian Huang, Wayne State University
Physics - Condensed Matter
A Wigner Crystal (WC) is an exciting platform for learning fundamental concepts of long-range orders that is key to magnetism, superconductivity, superfluidity, and topological matters. This solid phase of electrons is expected to emerge only when the inter-particle Coulomb energy dominates the zero-point energy. Even though such a condition can be intuitively assumed in ultra-dilute two-dimensional (2D) systems where the ratio of the Coulomb energy Eee and the Fermi energy EF, rs=Eee/EF, reaches values close to the anticipated onset point, the experimental realization of it has proven to be an outstanding challenge. The tininess of Eee and EF makes a WC fragile even to moderate random disorders that usually overwhelm the interaction effect by driving an Anderson localization or a glass. Moreover, random disorder and quantum fluctuations are important factors that reduces the melting point even below what can be reached with modern low temperature (T) experimental capabilities. Consequently, a WC has not been rigorously demonstrated. Important questions in relations to Mermin-Wagner theorem and the Kosterlitz-Thouless (KT) transition , with possible intermediate phases such as hexatic  or microemulsions  including bubble and stripe phases, remain to be explored.
We utilize ultra-high purity p-GaAs 2D systems in which the carrier density can be continuously tuned from 5x1010 cm-2 down to 7x108 cm-2. Effective sample cooling down to 10 mK is achieved via a state-of-the-art helium-3 immersion cell technique. Delicate dc and dc+ac transport study reveals benchmark signatures in terms of both many-body pinning and melting transitions. Rigorously pinned WCs are characterized by enormous (G?) pinning strength, even stronger than those found in charge density waves (CDWs), consistent with a macroscopic correlation length. Melting occurs under both pressure and temperature variations both of which confirm two-stage characteristics: 1st stage-discontinuous WC-intermediate phase transition; 2nd stage-smooth intermediate phase-liquid transition. Remarkably, the 1st stage transition, in contrast to the KT model, exhibits first-order characteristics according to the steep discontinuous drop in the pinning strength and it occurs at T below a melting temperature (Tm) of 30 mK. The 2nd stage is a smooth crossover occurring around 120mK, consistent with numerous previous results. Tm, being only ¼ of the classical estimate, is likely a confirmation of the disorder effect influencing melting.
 J.M. Kosterlitz, J. M., and D. J. Thouless, Journal of Physics C: Solid State Physics 5(11), L124(1972)
 David R. Nelson and B. I. Halperin, Physical Review B 19, 2457 (1979)
 B.I. Spivak and S. A. Kivelson, Physical Review B 43, 3740 (1991)
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