CDW-Exciton Condensate Competition and a Condensate Driven Force

We examine the competition between the charge-density wave (CDW) instability and the excitonic condensate (EC) in spatially separated layers of electrons and holes. The CDW and the EC order parameters (OPs), described by two different mechanisms and hence two different transition temperatures $T^{CDW}_c$ and $T^{EC}_c$, are self-consistently coupled by a microscopic mean field theory. We discuss the results in our model specifically focusing on the transition-metal dichalcogenides which are considered as the most typical examples of strongly coupled CDW/EC systems with atomic layer separations where the electronic energy scales are large with the critical temperatures in the range $T^{EC}_c \sim T^{CDW}_c \sim 100-200 K$. An important consequence of this is that the excitonic energy gap, hence the condensed free energy, vary with the layer separation resulting in a new type of force ${\cal F}_{EC}$. We discuss the possibility of this force as the possible driver of the structural lattice deformation observed in some TMDCs with a particular attention on the $ 1 {\it T}$-$TiSe_2$ below $200 K$.