Electronic rotons and Wigner crystallites in a two-dimensional dipole liquid.

Abstract

A key concept proposed by Landau to explain superfluid liquid helium is the elementary excitation of quantum particles called rotons^1-8. The irregular arrangement of atoms in a liquid leads to the aperiodic dispersion of rotons, which played a pivotal role in understanding fractional quantum Hall liquids (magneto-rotons)^9,10 and the supersolidity of Bose-Einstein condensates^11-13. Even for a two-dimensional electron or dipole liquid, in the absence of a magnetic field, the repulsive interactions have been predicted to form a roton minimum^14-19, which can be used to trace the transition to Wigner crystals^20-24 and superconductivity^25-27, although this has not yet been observed. Here, we report the observation of such electronic rotons in a two-dimensional dipole liquid of alkali-metal ions donating electrons to surface layers of black phosphorus. Our data reveal the striking aperiodic dispersion of rotons, which is characterized by a local minimum of energy at finite momentum. As the density of dipoles decreases so that interactions dominate over the kinetic energy, the roton gap reduces to 0, as in a crystal, signalling Wigner crystallization. Our model shows the importance of short-range order arising from repulsion between dipoles, which can be viewed as the formation of Wigner crystallites (bubbles or stripes) floating in the sea of a Fermi liquid. Our results reveal that the primary origin of electronic rotons (and the pseudogap) is strong correlations.