Wigner crystallization in moiré materials

A new chapter in graphene and superconductivity research unfolded recently by a surprising discovery at MIT. Two sheets of graphene twisted at about 1◦, provide an unparalleled playground for studying strong-correlation physics including high-temperature superconductivity. The experiment showed that doping this twisted bilayer graphene (TBG) can result in an array of metallic, insulating, and superconducting states. Although it is clear that these states result from the emergent interaction caused by twisting, the origin of the insulating and superconducting states remains highly contentious to date. The existence of high-temperature superconductivity in TBG is unarguably the most exciting facet of this discovery. However, understanding its nature is highly reliant on the physics of the underlying the normal state. Chapter 2 discusses arguments against the initial proposal of this state being a Mott type insulator. Instead, Wigner crystallization is proposed as a viable mechanism for insulation. The key in reaching this conclusion is the computation of rs, the ratio of kinetic to the potential energy. A subsequent experiment at UCSB showed even the previously thought metallic states of a TBG can become insulating around an optimal pressure along the c-axis. In Chapter 3, we construct a tight-binding model that takes this transverse pressure into account and solve it numerically. Using the energetics of the band structure, we re-calculate rs as a function of pressure. Indeed, just like the insulating states, rs exhibits a similar optimal pressure region where it transitions from a metallic to a Wigner insulating phase. The aim of Chapter 4 is to develop an effective model to capture Wigner physics in moire systems independent of the material. We do so by using a variational method. We recover various elastic properties of the crystal by treating the crystallized electrons as particles stuck in a matrix of rigid springs. Here, we also analyze several material parameters and discuss the candidacy of a few transition metal dichalcogenides where large rs can be achieved, thereby facilitating formation of Wigner crystals.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Padhi, Bikash K.

Contributors dc:contributor

• Phillips, Philip W
• Fradkin, Eduardo
• Faulkner, Thomas
• Mason, Nadya

• Graphene
• Wigner Physics
• Mott Insulator
• Strongly correlated materials

Statement dc:rights

• Copyright 2022 Bikash Padhi

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/115335

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F115335