NMR Probing of Wigner Solids in High Magnetic Fields

Trevor David Rhone1,2, Lars Tiemann1,2, Naokazu Shibata3, and Koji Muraki1,2
1Physical Science Laboratory, 2Japan Science and Technology Agency, 3Tohoku University

In two-dimensional electron systems subject to strong magnetic fields, various quantum phases emerge due to electron interaction. While it is believed that electrons form Wigner solids in the low filling factor regime, where the sequence of fractional quantum Hall states terminates, experimental evidence for Wigner solids has been limited to microwave absorption measurements which show the presence of pinning-mode resonances characteristic of a solid. Here we focus on another defining feature of a solid - translational symmetry breaking. We use NMR to probe on a nanometer scale the spatial variation of probability density resulting from electron solidification, and to obtain microscopic information including the spatial extent of lattice electrons [1].

Figure 1 shows the filling factor dependence of longitudinal resistance and resistively detected NMR spectra of 75As taken at various filling factors at 6.4 T. At ν = 1/3, where the electron system is in a fractional quantum Hall liquid phase, the measured NMR spectrum matches a simulation assuming a uniform electron system. In contrast, at ν < 1/3 and in the vicinity of ν = 2, the measured spectra cannot be explained by the uniform model. Instead, a model assuming the formation of Wigner crystal domains of electrons or electrons/holes added to ν = 2 reproduces the measured spectra exceedingly well. The difference in the spectral lineshapes for ν = 1.9 and 2.1, which share the same effective filling of 0.1, is a manifestation of the distinct single-particle wavefunctions for the respective Landau levels. This highlights NMR’s ability to resolve probability density variation on a nanometer scale.

L. Tiemann*, T. D. Rhone*, N. Shibata, and K. Muraki, Nature Phys. 10, 648 (2014). (*: These authors contributed equally to this work.)

Fig. 1. (a) Filling factor dependence of longitudinal resistance. (b)-(d) Resistively detected NMR spectra of 75As taken at various filling factors. The horizontal axis is the frequency shift with respect to the resonance frequency at ν = 2. Dashed lines represent simulations assuming uniform electron systems. Solid lines are numerical fits using a model incorporating the presence of Wigner crystal domains. Insets: illustrations of occupied Landau levels for (b) ν = 0.2, (c) 1.9, and (d) 2.1.