Composite Fermions Waltz to the Tune of a Wigner Crystal

TL;DR

This study directly observes a Wigner crystal in a 2D electron system by measuring magneto-resistance in a bilayer setup, revealing the crystal's lattice structure through composite fermion behavior.

Contribution

The paper introduces a novel experimental technique to directly detect and characterize a Wigner crystal using composite fermions in a bilayer electron system.

Findings

Wigner crystal has a triangular lattice structure.

Magneto-resistance maxima correspond to composite fermions encircling WC lattice points.

Direct measurement of WC lattice constant was achieved.

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 ($\nu<<1$), 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 ($\nu<<1$), while the other ("probe") layer is near $\nu=1/2$ 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.