Interaction-Driven Phenomena And Wigner Transition In Two-Dimensional Systems

The formation of a quantum Wigner Cyrstal (WC) is one of the most anticipated predictions of electron-electron interaction. This is expected to occur in zero magnetic field when the Coulomb energy $E_C$ dominates over the Fermi energy $E_F$ (at a ratio $r_s \equiv E_C/E_F \sim 37$) for temperatures $T \ll E_F / k_B$. The extremely low $T$ and ultra dilute carrier concentrations necessary to meet these requirements are difficult to achieve. Alternatively, a perpendicular magnetic $B$-field can be used to quench the kinetic energy. As $B$ increases, various energies compete to produce the ground state. High purity systems with large interaction $r_s\u3e1$ tend to exhibit reentrant insulating phases (RIP) between the integer and fractional Hall states. These are suspected to be a form of WC, but the evidence is not yet conclusive. We use transport measurements to identify a conduction threshold in the RIP at filling factor $\nu = 0.37$ (close to the 1/3 state) that is several orders of magnitude larger than the pinning observed in many other systems. We analyze the temperature and electric $E$-field dependence of this insulating phase and find them to be consistent with a second-order phase transition to WC. The measurements are performed on dilute holes $p=4\times10^{10}$~cm$^{-2}$ of mobility $\mu = 1/pe\rho \sim 2.5 \times 10^{6}$~cm$^2$/Vs in 20~nm GaAs/AlGaAs quantum square wells. We also discuss various other projects related to the study of topological states and strongly interacting charges: direct testing of the bulk conduction in a developing quantum Hall state using a corbino-disk-like geometry (or ``anti-Hall bar ); preliminary results for ultra dilute charges in undoped heterojunction insulated gated field effect transistors; quantum capacitance measurement of the density of states across the vanadium dioxide metal insulator transition; progress towards a scanning capacitance measurement using the tip of an atomic force microscope; and graphene devices for optical detection