Persistent currents in two dimensions: New regimes induced by the interplay between electronic correlations and disorder

Using the persistent current I induced by an Aharonov-Bohm flux in square lattices with random potentials, we study the interplay between electronic correlations and disorder upon the ground state (GS) of a few polarized electrons (spinless fermions) with Coulomb repulsion. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\bf K}$\end{document} being the total momentum, we show that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$I \propto {\bf K}$\end{document} in the continuum limit. We use this relation to distinguish between the continuum regimes, where the lattice GS behaves as in the continuum limit and I is independent of the interaction strength U when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\bf K}$\end{document} is conserved, and the lattice regimes where I decays as U increases. Changing the disorder strength W and U, we obtain many regimes which we study using the map of local currents carried by three spinless fermions. The decays of I characterizing three different lattice regimes are described by large U perturbative expansions. In one of them, I forms a stripe of current flowing along the axis of the diamagnetic Wigner molecule induced by large electronic correlations. This stripe of current persists in the continuum limit. The quantum melting of the diamagnetic molecule gives rise to an intermediate “supersolid” regime where a paramagnetic correlated pair co-exists with a third particle, before the total melting. The concepts of stripe and of supersolid which we use to describe certain regimes exhibited by three spinless fermions are reminiscent of the observations and conjectures done in other fields at the thermodynamic limit (stripe for high-Tc cuprates, supersolid for Helium quantum solids).