Intertwined superfluid and density wave order in two dimensional 4He

Superfluidity is a manifestation of the operation of the laws of quantum mechanics on a macroscopic scale. The conditions under which superfluidity becomes manifest have been extensively explored experimentally in both quantum liquids (liquid 4He being the canonical example) and ultra-cold atomic gases ( 1, 2), including as a function of dimensionality ( 3,4). Of particular interest is the hitherto unresolved question whether a solid can be superfluid ( 5, 6). Here we report the identification of a new state of quantum matter with intertwined superfluid and density wave order in a system of two-dimensional bosons subject to a triangular lattice potential. Using a torsional oscillator we have measured the superfluid response of the second atomic layer of 4He adsorbed on the surface of graphite, over a wide temperature range down to 2 mK. Superfluidity is observed over a narrow range of film densities, emerging suddenly and subsequently collapsing towards a quantum critical point. The unusual temperature dependence of the superfluid density in the limit of zero temperature and the absence of a clear superfluid onset temperature are explained, self-consistently, by an ansatz for the excitation spectrum, reflecting density wave order, and a quasi-condensate wave function breaking both gauge and translational symmetry. 1. Leggett, A. J., Quantum Liquids (Oxford University Press, London, 2006). 2. Nozieres P & Pines , D., The Theory of Quantum Liquids Vol. II (Addison-Wesley, 1990). 3. Bishop, D. J. & Reppy, J. D., Study of the superfluid transition in two-dimensional 4He films. Phys. Rev. Lett. 40, 1727-1730 (1978). 4. Hadzibabic, Z., Kruger, P., Cheneau, M., Battelier, B. & Dalibard, J., Berezinskii-Kosterlitz-Thouless crossover in a trapped atomic gas. Nature 441, 1118-1121 (2006). 5. Leggett, A. J., Can a solid be superfluid? Phys. Rev. Lett. 25, 1543-1546 (1970). 6. Balibar, S., The enigma of supersolidity. Nature 464, 176-182 (2010).