Nuclear Magnetic Resonance Line Shapes of Electron Crystals in ¹³C Graphene

Inhomogeneous electronic states such as Wigner and Skyrme crystals are expected to form in graphene in a small range of filling factor near integer fillings [1]. In these states, the spatial variation of the spin density leads to an inhomogeneous broadening of the nuclear magnetic resonance (NMR) line shape of the ¹³C nuclei. In GaAs quantum wells, Wigner crystals in different Landau levels have NMR line shapes that are qualitatively different [2]. It is thus natural to ask if this also hold for Wigner crystals in graphene. In this talk, we first show that in graphene, one must consider, in addition to the spin hyperfine interaction (both contact and dipolar), a second contribution of equal importance that arises from the coupling between the orbital motion of the electrons and the nuclei i.e. one must consider both the Knight and the chemical shifts. Taking this fact into account, we compute the line shape of different crystals and discuss the conditions, such as the linewidth of the bare resonance, needed to differentiate between different types of Wigner and Skyrme crystals.
[1] R. Cote, J.-F. Jobidon, and H. A. Fertig, Phys. Rev. B 78, 085309 (2008).
[2] L. Tiemann, T. D. Rhone, N. Shibata and K. Muraki, Science 335, 828 (2012).