2026/07/31 by Minho Luke Kim, Xiao-Gang Wen · 1 citation
Physics and Astronomy · #cond-mat.str-el #cond-mat.mes-hall
6 pages plus appendices, 4+2 figures
arxiv created 2026/07/31 · arxiv updated 2026/08/04
We study Wigner crystals (WCs) induced by a strong Coulomb interaction from the ring-like Fermi surface of a Mexican-hat dispersion εk= c2k2+c4k4. We design orbital shape in order to minimize the energy of the WC, and find that a low ground-state energy requires an orbital shape with a depletion of electrons near k=0. To capture the Coulomb-induced correlations, we include a Jastrow factor as well as a factor describing the correlation between electrons and doped vacancies. Using variational Monte Carlo calculations, we calibrate the effective band parameters c2 and c4 to reproduce the two transitions observed experimentally as the electron density is lowered: from a spin-valley-polarized Fermi liquid with a disk-like Fermi surface, to one with a ring-like Fermi surface, and finally to a WC. We find that, even with an optimized orbital shape that depletes electrons near k=0, a WC with hole self-doping near k=0 can still be energetically favorable near the WC transition, provided that the electron-vacancy correlation is included. We also estimate the dispersion of the doped hole.