Speaker: Sankar Das Sarma (CMTC) Title: Wigner solid or Anderson solid? Abstract: Wigner showed in 1934 that electrons in metals, which are normally a Fermi gas or Fermi liquid even at T=0 because of the large zero point energy of fermions, would crystallize into a quantum solid at low enough densities where their Coulombic potential energy dominates the zero point kinetic energy [1]. Recent experiments in many 2D doped semiconductors claim the observation of this electronic Wigner crystal. On the other hand, Anderson showed in 1958 that disorder arising from random defects and impurities would cause spatial localization of the electrons due to the destructive interference of the electron waves from disorder if the disorder is strong enough [2]. The 2D semiconductors satisfy both criteria: the electron density is low enough for the Wigner criterion of low density crystallization to be satisfied and the disorder is strong enough, because in doped semiconductors electrons are produced by impurities (so low electron density implies effective strong disorder due to quenched unintentional impurities), for the Anderson localization to occur. So, the question arises about which is the more appropriate description for the low-density disordered 2D doped semiconductors where the electrons are spatially localized into a solid. Is it a Wigner solid (ie, a 'crystalline' solid) due to the strong Coulomb interaction among the electrons or is it an Anderson solid (ie, an 'amorphous' solid) due to the strong quantum interference imposed by the impurities? We will answer this question by using several different theoretical approaches, finding that the low-disorder Wigner solid (adiabatically connected to the Wigner crystal at zero electron density) crosses over to the high-disorder Anderson solid (adiabatically connected to the random spatially localized electron system at infinite electron density), and the resultant system at finite disorder is akin to a structural glass made of electrons which are spatially randomly located, but with strong short-range order imposed by the Coulomb coupling. We will focus on a recent STM experiment from UC, Berkeley [3] to discuss the problem in depth using complementary theoretical approaches since the Hamiltonian involving both strong interaction and strong disorder is not amenable to any field theoretic solutions as everything flows to unidentifiable strong coupling regimes.
[1] E. Wigner, "On the interaction of electrons in metals", Phys. Rev. 46, 1002 (1934). [2] P. W. Anderson, "Absence of diffusion in certain random lattices", Phys. Rev. 109, 1492 (1958). [3] Ge et al., "Visualizing the Impact of Quenched Disorder on 2D Electron Wigner Solids", arXiv:2510.12009 (2025).