Lloyd Engel

High magnetic field  Wigner solid phases  in GaAs two-dimensional electron systems are pinned by disorder, which  produces a pinning mode, whose frequency is a   measure of the disorder that pins the  solid.  Wee studded the pinning modes of series of  ultralow disorder GaAs quantum wells which are similar except for their  varying well widths,  $d$.  The pinning mode frequencies, $f_{pk}$,  decrease strongly as $d$   increases, with the widest well exhibiting  $f_{pk}$ as low as 38 MHz.    The degree of reduction of $f_{pk}$ with increasing $d$ can be explained by tails of the growth-direction wave function impinging into the alloy-disordered  Al$_x$Ga$ _{1-x}$As barriers that contain the quantum wells,   as long as  the model for the  confinement includes the Coulomb repulsion effect of the quantum well being populated.   Wells of 40 and 50 nm width   exhibit distinct shifts of the pinning resonance in the reentrant  range of the solid,  at   fillings just above that of the 1/5 fractional quantum Hall effect; these changes may indicate   phase transitions within the solid.