Effects of strain on the stability of the metallic rutile and insulating M1 phases of vanadium dioxide

We present a systematic density-functional theory study of the effects of strain on the structural and electronic properties in vanadium dioxide (VO$_2$), with particular emphasis on its effect on the relative stability of the metallic rutile and the insulating monoclinic M1 phases. We consider various strain conditions that can be related to epitaxial strain present in VO$_2$ films grown on different lattice planes. Our calculations confirm the dominant role of $c$ axis strain, i.e., along the direction of the V-V dimerization in the M1 phase. Our analysis suggests that this effect stems primarily from the weakening of the lattice stiffness, with the hopping along the $c$ axis playing a minor role. We also confirm that, in strain scenarios that deform the basal plane, the $c$ axis strain still has a dominant effect on the phase stability.