Green's tensors for anisotropic elasticity: Application to quantum dots

Real-space Green's tensors for the calculation of the strain in systems containing buried quantum dots of arbitrary shape and composition, including the cubic anisotropy of elastic constants, are presented, to the best of our knowledge, for the first time. The Green's tensors an obtained as a series with very good accuracy obtained using the first two terms. The Green's function for the hydrostatic strain is of a simple form and it is shown that the cubic anisotropy leads to a nonzero hydrostatic strain outside a dot. The axial strain is shown to depend on the orientation of the dot in the crystal.