bcc4Heas a coherent quantum solid

Abstract

In this work we investigate implications of the quantum nature of bcc 4 He. We show that it is a unique solid phase with both a lattice structure and an Off-Diagonal Long Range Order of coherently oscillating local electric dipole moments. These dipoles arise from the local motion of the atoms in the crystal potential well, and oscillate in synchrony to reduce the dipolar interaction energy. The dipolar ground-state is therefore found to be a coherent state with a well defined global phase and a three-component complex order parameter. The condensation energy of the dipoles in the bcc phase stabilizes it over the hcp phase at finite temperatures. We further show that there can be fermionic excitations of this ground-state and predict that they form an optical-like branch in the (110) direction. A comparison with 'super-solid' models is also discussed.

Velocity-dependent interactions and sum rule in bcc He

“…This mode turns out to be the anomalously soft T 1 (110) phonon, which agrees very well with the experimental data [2]. In addition our model predicts two new modes which are gapped (optic-like) [2,5]. One of these modes was recently observed in neutron scattering experiments [4].…”

“…The main surprise in this experiment was the discovery of a new, gapped excitation branch in bcc 4 He. This excitation was found at the energy predicted by a new model of the dynamic effects of the zero-point motion on the phonon spectra [2,5]. Usually a bcc lattice is not expected to support opticlike phonons, so the measurement of this new excitation branch provides support for the basic idea of the new model, namely the introduction of an additional degree of freedom in bcc He.…”

“…In previous papers [2,5] we have presented a new model to describe some of the correlations in the atomic zero-point motion in bcc Helium. The main point is that there is an anharmonic, low energy mode of atomic motion along the major axes of the bcc lattice, which is not described by the harmonic approximation.…”

“…The commutator (5) is performed at equal times [11]. When calculating the summation in (5) we have to specify the phase relation between the dipoles on different sites. If there is no correlation between the dipoles, the interaction X(k) is zero, and the correlation function of the atomic displacements described by these dipoles, i.e.…”

“…The momentum operators in (4) replace the usual kinetic energy term for the part of the atomic motion which is described by the dipolar degree of freedom. Using this double commutator (5) in the usual definition of the dynamic structure-factor S(ω, k) [8,12], we get that the new sum rule for the T 1 (110) phonon is…”