1) The study provides evidence of a pinned quantum Wigner crystal (WC) in a two-dimensional system of holes in GaAs at filling factor ν = 1/3. 2) Below 30 mK, the holes are pinned within a narrow current range with resistance over 1 GΩ, and the resistance suddenly drops by over 3 orders of magnitude just above this threshold, consistent with melting. 3) Heating also destroys the pinning in a non-activated way that does not match disorder models, proving the existence of a pinned WC that undergoes a second-order melting transition with increasing temperature.

1. Pinning and melting of a quantum Wigner Crystal
1
T. Knighton, 2
A. Serafin, 1
Z. Wu, 1
V. Tarquini, 2
J. S. Xia, 2
N. S. Sullivan, 1
J. Huang, 3
L. N. Pfeiffer,
3
K. West
1
Wayne State University, Detroit, MI, USA
2
National High Field Magnetic Laboratory and University of Florida, Gainesville, FL, USA
3
Princeton University, Princeton, NJ, USA
Quantum Wigner crystals (WC) are one of the most remarkable and sought-after interaction-driven phenomena
[1]. For two-dimensional (2D) systems, the competing kinetic energy is quenched by application of a perpendicular
magnetic field (B) at low temperatures (T). This leads to enhanced interaction in the fractional quantum Hall
regime where reentrant insulating phases (RIP) have been considered as candidates for WC. Previous studies
looked at non-linear IV characteristics, noise generation, and microwave resonances in the 2D charges showing
some evidence for collective modes [2]. Nevertheless, a WC must be a tremendous insulator due to manybody
pinning. Unambiguous demonstration of rigorous pinning and melting transition are important proofs which have
not yet been produced. For this study, high mobility (𝜇 = 3.0 × 106
cm2
/Vs) dilute 2D holes (𝑝 = 4.5 ×
1010
cm−2
) in a 20nm GaAs/AlGaAs/GaAs square well are cooled using a novel immersion cell technique to a base
temperature of 10 mK at the Microkelvin Lab at National High Magnetic Field Laboratories. Figure 1(a) shows the
RIP observed near filling factor 𝜈 = 1/3 using standard lock-in techniques. Fixing B-field at the center of the peak,
we use an electrometer level DC source capable of resolving micro-volt signals and femto-amp currents. Figure
1(b) shows a set of curves taken for at a series of fixed T ranging from 10 mK to 500 mK. There is a striking
threshold behavior below 30 mK where the holes are pinned within a narrow range of ±5 pA having equivalent
resistance greater than 1 GΩ. Just above this threshold, the resistance plummets by more than 3 orders of
magnitude. Pinning is also destroyed by heating [Fig. 1(c)], consistent with a melting transition. This occurs in a
non-activated fashion that cannot be fit to any disorder-driven mechanisms such as hopping models for non-
interacting or interacting charges. This is proof of the existence of a pinned WC that appears to undergo a second-
order transition upon heating, in agreement with previous theoretical studies [3].
Figure 1: (a) Quantum Hall Effect. (b) DC measurement of small-signal IV characteristics. (c) Sub-threshold non-
activated resistance as a function of temperature on a semi-log scale.
[1] E. P. Wigner, Phys. Rev.46, 1002 (1934)
[2] V. J. Goldman et al., Phys. Rev. Lett. 65, 2189; Y. P. Chen et al., Nature Physics 2, 452 - 455 (2006)
[3] Boris Spivak and Steven A. Kivelson, Phys. Rev. B 70, 155114