Sharp Tunneling Resonance from Vibrations of a 2D Wigner Crystal

Microwave conductivity measurements show a rigidity of the 2D electron system around filling factor 1 that may arise from a Wigner crystal of quasiparticles, but these measurements could not determine if a long-range ordered crystal exists. One might expect that the broken symmetry from a Wigner crystal would result in features in the tunneling spectrum that would vary with the interparticle spacing and magnetic field strength. However, measurements of electrons tunneling into 2D system under strong perpendicular magnetic fields face technical challenges; e.g. the lateral conductivity can vanish, prohibiting the tunneled electrons from moving out of the system. We used a method of capacitively detected pulsed tunneling that overcomes this and other issues, allowing accurate measurements of tunneling of 2D holes and electrons in GaAs at 20 mK and in high magnetic field. For 2D holes, we discovered sharp and filling factor dependent resonances that are antisymmetric in energy and density around filling factor 1. Careful study shows similar resonances around filling factors 0 and 2. Analysis of the resonance structure agrees with a picture of holes that are dressed by interactions with vibrational degrees of freedom of the crystal. The dependence of the energy of the resonance on quasiparticle density shows a divergence and upon the approach to the from filling factor 1 to the quantum phase transition tot he 4/5 quantum Hall state and fits closely with a theory by Archer, Park, and Jain (PRL 111, 146804 (2013)). The sharpness of the resonance points to a remarkably long-range ordered Wigner Crystal with lattice correlation length of ~15 lattice spacings. Electron samples also show a similar tunneling resonance appearing near filling factor 1, but it only appears under application of a strong field parallel to the 2D system, along with the perpendicular field.