  Layered transition metal dichalcogenides MoTe$_2$ and WTe$_2$ share almost
similar lattice constants as well as topological electronic properties except
their structural phase transitions. While the former shows a first-order phase
transition between monoclinic and orthorhombic structures, the latter does not.
Using a recently proposed van der Waals density functional method, we
investigate structural stability of the two materials and uncover that the
disparate phase transitions originate from delicate differences between their
interlayer bonding states near the Fermi energy. By exploiting the relation
between the structural phase transitions and the low energy electronic
properties, we show that a charge doping can control the transition
substantially, thereby suggesting a way to stabilize or to eliminate their
topological electronic energy bands.
