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. The irregular arrangement of atoms in a liquid forms the aperiodic dispersion of rotons that played a pivotal role in understanding fractional quantum Hall liquid (magneto-rotons) and the supersolidity of Bose-Einstein condensates. Even for a two-dimensional electron or dipole liquid in the absence of a magnetic field, their repulsive interactions were predicted to form a roton minimum that can be used to trace the transition to Wigner crystals and superconductivity, but it has not been observed. Here, we report the observation of such electronic rotons in a two-dimensional dipole liquid of alkali-metal ions doping charges to surface layers of black phosphorus. Our data reveal a striking aperiodic dispersion of rotons characterized by a local minimum of energy at a finite momentum. As the density of dipoles decreases, where interactions dominate over kinetic energy, the roton gap reduces to 0 as in crystals, signalling Wigner crystallisation. 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 Fermi liquids. Our results reveal that the primary origin of electronic rotons (and the pseudogap) is strong correlations.