Elementary Excitations, Spectral Weights and Experimental Signatures of a Supersolid and a Fulde-Ferrell-Larkin-Ovchinnikov State

Abstract

We construct a Ginsburg Landau (GL ) theory to study the phases of liquid, solid, superfluid, especially a possible supersolid and phase transitions among these phases in a unified framework. In this GL, we put the two competing orders between the solid component and the superfluid component on the same footing. We only introduce two parameters: v which is the repulsive interaction between the normal component and the local superfluid mode and g which is a periodically changing chemical potential for the local superfluid mode. The microscopic origins of v and g are given. By using this GL action, we study the superfluid to supersolid transition, normal solid to the supersolid transition and analyze the conditions for the existence of the supersolid. The non-classical rotational inertial (NCRI) in the SS state is calculated and found to be isotropic in bcc and f cc lattice, but weakly anisotropic in hcp lattice. We study the elementary low energy excitation inside a supersolid. We find that there are one upper branch and one lower branch longitudinal "supersolidon" modes inside the SS, while the transverse modes in the SS stay the same as those inside the NS. We also determine the corresponding spectral weights of the two branches. We work out the experimental signatures of these elementary excitations in Debye-Waller factor, density-density correlation, vortex loop interaction and specific heat. The estimated excess entropy due to vacancies seems consistent with data measured in the specific experiment in Helium 4. Detecting the two supersolidon modes by various equilibrium and thermodynamic experiments such as X-ray scattering, neutron scattering, acoustic wave attenuation and heat capacity can prove or disapprove the existence of a supersolid in Helium 4. A toy model of supersolid wavefunction is analyzed. The difference and similarities with lattice supersolid are clearly demonstrated. Elementary excitations inside a Fulde -Ferrell-Larkin-Ovchinnikov (FFLO) state of superfluid are also discussed.

Goldstone and Higgs modes of photons inside a cavity

“…The Goldstone modes have been detected in a quantum anti-ferromagnet7, a superfluid891011 and also in cold atom systems121314151617. However, the massive Higgs mode is much more difficult to detect in experiments.…”

Classification of a Supersolid: Trial Wavefunctions, Symmetry Breakings and Excitation Spectra

“…The classical hydrodynamics will break down at very low temperature where quantum fluctuations dominate. The quantum phenomenological Ginsburg-Landau theories [19][20][21] in both 3d and 2d were written down. They can be applied to study possible supersolids in 3 dimensional 4 He system and possible exciton supersolids in 2 dimensional electron-hole bilayer systems.…”

“…Here, we will review the nature of low energy excitations in the SS, namely, focus on the (4) in the above. We refer (1)-(3) to the original papers [19][20][21]29 . The part (5) is new and will be discussed in Sect.II-B.…”

“…So detecting these "supersolidons " in Fig.1b by possible inelastic neutron scattering experiments or acoustic attenuation experiments could be smoking gun experiments to confirm a supersolid in any continuous systems. The experimental implications of the supersolidons on X-ray scatterings, density-density correlation functions, specific heats wee discussed in 20,21 . However, it is well known that the GL theory is a phenomenological theory.…”

“…The effective Hamiltonian also hold on lattice scales. When neglecting the vortex excitations, the Eqn.12 is quadratic, the standard Bogliubov transformation can be used to extend the supersolidon dispersion relation in Fig.1b to the whole BZ zone including near to the BZ boundary G in the Fig 1c. The vortex excitations inside a supersolid were discussed in 21 .…”