# Nuclear magnetic resonance line shapes of Wigner crystals in $^{13}$C-enriched graphene

## TL;DR

This paper theoretically analyzes the NMR line shapes of Wigner crystal states in $^{13}$C-enriched graphene under strong magnetic fields, highlighting how different crystal states affect the NMR signals and the importance of linewidth in detecting these states.

## Contribution

It introduces a detailed computation of NMR line shapes for various crystal ground states in graphene, considering hyperfine and orbital couplings, and assesses their detectability via NMR.

## Key findings

- Wigner and bubble crystals have distinct NMR line shapes from uniform states if linewidth is small.
- Orbital motion coupling contributes significantly to NMR frequency shifts in nonuniform states.
- Small linewidths can obscure the signatures of crystal states in NMR measurements.

## Abstract

Assuming that the nuclear magnetic resonance (NMR) signal from a $^{13}$C isotope enriched layer of graphene can be made sufficiently intense to be measured, we compute the NMR\ lineshape of the different crystals ground states that are expected to occur in graphene in a strong magnetic field. We first show that in nonuniform states, there is, in addition to the frequency shift due to the spin hyperfine interaction, a second contribution of equal importance from the coupling between the orbital motion of the electrons and the nuclei. We then show that, if the linewidth of the bare signal can be made sufficiently small, the Wigner and bubble crystals have line shapes that differ qualitatively from that of the uniform state at the same density while crystal states that have spin or valley pseudospin textures do not. Finally, we find that a relatively small value of the bare linewidth is sufficient to wash out the distinctive signature of the crystal states in the NMR line shape.