Effects of interedge scattering on the Wigner crystallization in graphene nanoribbons

TL;DR

This study explores how interedge coupling influences Wigner crystallization in graphene nanoribbons, revealing size-dependent effects, edge correlations, and differences between electron and hole crystallization.

Contribution

It demonstrates the impact of nanoribbon width and interedge interactions on Wigner crystallization, including an even-odd electron number effect and edge decoupling under electric fields.

Findings

Wider ribbons exhibit strong Wigner localization for even electron numbers.

Interedge correlations enable simultaneous crystallization on both edges.

Wigner crystallization also occurs for holes, but less strongly.

Abstract

We investigate the effects of coupling between the two zigzag edges of graphene nanoribbons on the Wigner crystallization of electrons and holes using a combination of tight-binding, mean field Hubbard and many-body configuration interaction methods. We show that the thickness of the nanoribbon plays a crucial role in the formation of Wigner crystal. For ribbon widths smaller than 16 \mbox{\AA}, increased kinetic energy overcomes the long-range Coulomb repulsion and suppresses the Wigner crystallization. For wider ribbons up to 38 \mbox{\AA} wide, strong Wigner localization is observed for even number of electrons, revealing an even-odd effect also found in Coulomb blockade addition spectrum. Interedge correlations are found to be strong enough to allow simultaneous crystallization on both edges, although an applied electric field can decouple the two edges. Finally, we show that Wigner crystallization can also occurs for holes, albeit weaker than for electrons.