Composite Fermions Waltz to the Tune of a Wigner Crystal

Abstract

When the kinetic energy of a collection of interacting two-dimensional (2D) electrons is quenched at very high magnetic fields so that the Coulomb repulsion dominates, the electrons are expected to condense into an ordered array, forming a quantum Wigner crystal (WC). Although this exotic state has long been suspected in high-mobility 2D electron systems at very low Landau level fillings ($ν<<1$), its direct observation has been elusive. Here we present a new technique and experimental results that directly probe the magnetic-field-induced WC. We measure the magneto-resistance of a bilayer electron system with unequal layer densities at high magnetic fields. One layer has a very low density and is in the WC regime ($ν<<1$), while the other ("probe") layer is near $ν=1/2$ and hosts a sea of composite fermions, quasi-particles formed by attaching two flux-quanta to each interacting electron. The composite fermions feel the periodic electric potential of the WC in the other layer and exhibit magneto-resistance maxima whenever their cyclotron orbit encircles certain integer number of the WC lattice points. The positions of the maxima reveal that the WC has a triangular lattice and yield a direct measure of its lattice constant. Our results provide a striking example of how one can probe an exotic many-body state of 2D electrons using equally exotic quasi-particles of another many-body state.