Elastic constants of incommensurate solid 4He from diffusion Monte Carlo simulations

We study the elastic properties of incommensurate solid He-4 in the limit of zero temperature. Specifically, we calculate the pressure dependence of the five elastic constants (C-11, C-12, C-13, C-33, and C-44), longitudinal and transversal speeds of sound, and the T = 0 Debye temperature of incommensurate and commensurate hcp He-4 using the diffusion Monte Carlo method. Our results show that under compression, the commensurate crystal is globally stiffer than the incommensurate, however at pressures close to melting (i.e., P similar to 25 bar) some of the elastic constants accounting for strain deformations of the hcp basal plane (C-12 and C-13) are slightly larger in the incommensurate solid. Also, we find that upon the introduction of tiny concentrations of point defects, the shear modulus of He-4 (C-44) undergoes a small reduction.