NMR profiling of quantum electron solids in high magnetic fields

When the motion of electrons is restricted to a plane under a perpendicular magnetic field, a variety of quantum phases emerge at low temperatures, the properties of which are dictated by the Coulomb interaction and its interplay with disorder. At very strong magnetic field, the sequence of fractional quantum Hall liquid phases(1) terminates in an insulating phase, which is widely believed to be due to the solidification of electrons into domains possessing Wigner crystal(2) order(3-11). The existence of such Wigner crystal domains is signalled by the emergence of microwave pinning-mode resonances(10,11), which reflect the mechanical properties characteristic of a solid. However, the most direct manifestation of the broken translational symmetry accompanying the solidification-the spatial modulation of particles' probability amplitudes-has not been observed yet. Here, we demonstrate that nuclear magnetic resonance provides a direct probe of the density topography of electron solids in the integer and fractional quantum Hall regimes. The data uncover quantum and thermal fluctuations of lattice electrons resolved on the nanometre scale. Our results pave the way to studies of other exotic phases with non-trivial spatial spin/charge order.