Possible Sliding Regimes in Twisted Bilayer WTe$_2$

Inspired by the observation of increasingly one-dimensional (1D) behavior with decreasing temperature in small-angle twisted bilayers of WTe$_2$ (tWTe$_2$), we theoretically explore the exotic sliding regimes that could be realized in tWTe$_2$. At zero displacement field, while hole-doped tWTe$_2$ can be thought of as an array of weakly coupled conventional two-flavor 1D electron gases (1DEGs), the electron-doped regime is equivalent to coupled four-flavor 1DEGs , due to the presence of an additional "valley'' degree of freedom. In the decoupled limit, the electron-doped system can thus realize phases with a range of interesting ordering tendencies, including $4k_F$ charge-density-wave and charge-$4e$ superconductivity. Dimensional crossovers and cross-wire transport due to inter-wire couplings of various kinds are also discussed. We find that a sliding Luther-Emery liquid with small inter-wire couplings is probably most consistent with current experiments on hole-doped tWTe$_2$.