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 electrons and holes in layered transition-metal dichalcogenides (TMDCs). 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. Due to the large energy scales involved in these CDW/EC systems, the critical temperatures are high and $T^{EC}_c \sim T^{CDW}_c \sim 100K$. Condensed free energy of this coupled CDW/EC system varies with the electron-hole separation resulting in a new type of force ${\cal F}_{EC}$ due to the condensation. We argue that ${\cal F}_{EC}$ can provide an alternative explanation to the existing theories for the periodic lattice distortion arising in $ 1 {\it T}$-$TiSe_2$ below $200 K$