Stability of the smectic phase in arrays of parallel quantum wires

Abstract

Using bosonization, we study a microscopic 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 wavefunctions $\ell$ 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 taken into account. Perturbative studies on phenomenological models have shown that the smectic fixed point is unstable towards a variety of phases such as superconductivity, stripe, smectic and Fermi liquid phases. Here, we show that the considered microscopic 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 $\ell \to 0$. For finite $\ell$, we find a critical Coulomb coupling ${\alpha }_c$ 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 microscopic models. Finally, we discuss the physical realization of this model with moire heterostructures.

References in corpus (23)

• The electronic properties of graphene
• Emergence of Superlattice Dirac Points in Graphene on Hexagonal Boron Nitride
• Spin-Gap Proximity Effect Mechanism of High Temperature Superconductivity
• Topological confinement in bilayer graphene
• Stripe phases in high-temperature superconductors
• Adhesion and electronic structure of graphene on hexagonal boron nitride substrates
• Domain walls in gapped graphene
• Quantum Theory of the Smectic Metal State in Stripe Phases
• Zero Energy Modes and Gate-Tunable Gap in Graphene on hexagonal Boron Nitride
• Two dimensional anisotropic non Fermi-liquid phase of coupled Luttinger liquids
• Sliding Luttinger liquid phases
• One-Dimensional Luttinger Liquids in a Two-Dimensional Moiré Lattice
• Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene
• Local sublattice-symmetry breaking in rotationally faulted multilayer graphene
• Control of electron-electron interaction in graphene by proximity screening
• Volkov-Pankratov states in topological heterojunctions
• Tunable Luttinger liquid physics in biased bilayer graphene
• Luttinger liquids with boundaries: Power-laws and energy scales
• A Crossed Sliding Luttinger Liquid Phase
• Directional massless Dirac fermions in a layered van der Waals material with one-dimensional long-range order
• Correlated states of a triangular net of coupled quantum wires: Implications for the phase diagram of marginally twisted bilayer graphene
• Valley Order and Loop Currents in Graphene on Hexagonal Boron Nitride
• Chiral Luttinger liquids in graphene tuned by irradiation