# Quantum Melting of a Disordered Wigner Solid

**Authors:** Ziyu Xiang, Hongyuan Li, Jianghan Xiao, Mit H. Naik, Zhehao Ge, Zehao He, Sudi Chen, Jiahui Nie, Shiyu Li, Yifan Jiang, Renee Sailus, Rounak Banerjee, Takashi Taniguchi, Kenji Watanabe, Sefaattin Tongay, Steven G. Louie, Michael F. Crommie, Feng Wang  
**arXiv:** [2402.05456](https://arxiv.org/abs/2402.05456)  
**Date:** 2024-02-08  
**Summary page:** https://www.summarizepaper.com/en/paper/2402.05456v1/

## Key points

- Behavior of a two-dimensional electron gas (2DEG) in extreme coupling limits is well-understood
- Understanding of the intermediate region is limited
- At very low densities, strongly interacting electrons form a solid phase known as the Wigner crystal
- Wigner crystal transitions to a Fermi liquid at high densities
- Lack of microscopic probes for delicate quantum phases hinders understanding of the intermediate region
- Researchers used non-invasive scanning tunneling microscopy (STM) technique to image a disordered Wigner solid and its densification and melting behavior in a bilayer MoSe2
- Nanocrystalline domains of the Wigner solid were pinned by local disorder at low hole densities
- Increasing electrostatic gate voltages during densification process allowed quantum mechanical addition of holes
- Above a threshold hole density, the Wigner solid melted locally and created a mixed phase with coexisting solid and liquid regions
- Liquid regions gradually expanded and formed an apparent percolation network with further increase in density
- Local solid domains appeared to be pinned and stabilized by local disorder over a range of densities
- Observations consistent with microemulsion picture of Wigner solid quantum melting, where both solid and liquid domains emerge spontaneously and solid domains are pinned by local disorder
- Insights into behavior of intermediate-density 2DEGs provided, shedding light on transition from ordered crystalline structures to strongly correlated electron fluids
- Study contributes to understanding of quantum phases in condensed matter systems
- Provides experimental evidence for existence of disordered Wigner solids and their melting behavior
- Non-invasive STM technique opens up new possibilities for investigating delicate quantum phases

## Summary

The behavior of a two-dimensional electron gas (2DEG) in extreme coupling limits is well-understood, but our understanding of the intermediate region remains limited. At very low densities, strongly interacting electrons form a solid phase known as the Wigner crystal, which transitions to a Fermi liquid at high densities. However, at intermediate densities where the Wigner crystal melts into a strongly correlated electron fluid, our understanding is hindered by a lack of microscopic probes for delicate quantum phases. In this study, researchers report on their findings from imaging a disordered Wigner solid and its quantum densification and melting behavior in a bilayer MoSe2 using non-invasive scanning tunneling microscopy (STM) technique. They observed a Wigner solid with nanocrystalline domains that were pinned by local disorder at low hole densities. By slightly increasing electrostatic gate voltages during the densification process of the disordered Wigner solid, they were able to add holes quantum mechanically. As the hole density was increased above a threshold value (p ~ 5.7 * 10^12 cm^-2), they observed that the Wigner solid melted locally and created a mixed phase where solid and liquid regions coexisted. With further increase in density, the liquid regions gradually expanded and formed an apparent percolation network. Interestingly, local solid domains appeared to be pinned and stabilized by local disorder over a range of densities. These observations are consistent with a microemulsion picture of Wigner solid quantum melting, where both solid and liquid domains emerge spontaneously and solid domains are pinned by local disorder. The researchers provide valuable insights into the behavior of intermediate-density 2DEGs and shed light on the complex dynamics involved in the transition from ordered crystalline structures to strongly correlated electron fluids. This study contributes to our understanding of quantum phases in condensed matter systems and provides important experimental evidence for the existence of disordered Wigner solids and their melting behavior. The non-invasive STM technique used in this study opens up new possibilities for investigating delicate quantum phases and could lead to further advancements in the field of condensed matter physics.