Stability of the smectic phase in arrays of parallel quantum wires

Abstract

Using bosonization, we study a model of parallel quantum wires constructed from two-dimensional Dirac fermions in the presence of periodic topological domain walls. The model accounts for the lateral spread of the wave functions $\ensuremath{\ell}$ in the transverse direction to the wires. The gapless modes confined to each domain wall are shown to form Luttinger liquids, which realize a well-known smectic non-Fermi liquid fixed point when interwire Coulomb interactions are considered. Perturbative studies on phenomenological models have shown that the smectic fixed point is unstable toward a variety of phases such as superconductivity, stripe, smectic, and Fermi liquid phases. Here, we show that the considered model leads to a phase diagram with only smectic metal and Fermi liquid phases. The smectic metal phase is stable in the ideal quantum wire limit $\ensuremath{\ell}\ensuremath{\rightarrow}0$. For finite $\ensuremath{\ell}$, we find a critical Coulomb coupling separating the strong coupling smectic metal from a weak coupling Fermi liquid phase. We conjecture that the absence of superconductivity should be a generic feature of similar models. We discuss the relevance of this model for quantum wires created with moir\'e heterostructures.