Quantum wires are the physical platform of choice to study Luttinger liquids, 1D conducting metals with a variety of unique properties, including spin-charge separation. When electrons propagate along periodic arrays of parallel 1D channels, they form a smectic phase. 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 in the transverse direction to the wires. This work shows that the smectic metal phase is stable in the ideal quantum wire limit. For a finite lateral spread, as expected in realistic quantum wires, we find a critical Coulomb coupling separating the strong coupling smectic metal from a weak coupling Fermi liquid phase, where the wires collapse into an isotropic 2D metal. We conjecture that the absence of superconductivity should be a generic feature of similar microscopic models in moire heterostructures. See: arXiv:2202.11744 (2022)

The merging of two Dirac cones describes a topological phase transition known as Lifshitz transition. At the transition, the electronic spectrum is characterized by massive quadratic dispersion in one direction, while it remains linear in the other. The elementary electronic quasiparticles at the transition are known as semi-Dirac fermions. The role of long-range Coulomb interactions in the renormalization of the spectrum of semi-Dirac fermions is an outstanding problem. This work shows that the leading self-energy corrections to the mass of the quasiparticles resum to all orders in perturbation theory, leading to a restoration of the Dirac cone, as in graphene. The Berry phase associated with the restored critical Dirac spectrum is zero - a property guaranteed by time-reversal symmetry and unchanged by renormalization. Our results are in contrast with the behavior that has been found within the large-N approach. Read more: Physical Review B 103, 045403 (2021)

Semi-Dirac fermions are low energy quasiparticles that disperse either as Galilean invariant particles or as relativistic ones depending in what direction they propagate. We investigate instabilities of semi-Dirac fermions towards charge, spin-density wave and superconducting orders, driven by short-range interactions. We analyze the critical behavior of the Yukawa theories for the different order parameters using Wilson momentum shell RG. We show that the order-parameter correlations inherit the electronic anisotropy of the semi-Dirac fermions, leading to correlation lengths that diverge along the spatial directions with distinct exponents, even at the mean-field level. We speculate that the proximity to the critical point may stabilize novel modulated order phases. Read more: Phys. Rev. B 100, 155101 (2019)

We address the role of short range interactions for spinless fermions in the hyperhoneycomb lattice, a three dimensional (3D) structure where all sites have a planar trigonal connectivity. For weak interactions, the system is a line-node semimetal. In the presence of strong interactions, we show that the system can be unstable to a 3D quantum anomalous Hall phase with loop currents that break time reversal symmetry, as in the Haldane model. We find that the low energy excitations of this state are Weyl fermions connected by surface Fermi arcs. See: Phys. Rev. B 97, 201101(R) (2018)

We consider the extended half-filled Hubbard model on the honeycomb lattice for second nearest neighbors interactions. Using a functional integral approach, we find that collective fluctuations suppress topological states and instead favor charge ordering, in agreement with previous numerical studies. However, we show that the critical point is not of the putative semimetal-Mott insulator variety. Due to the frustrated nature of the interactions, the ground state is described by a novel hidden metallic charge order with semi-Dirac excitations. We conjecture that this transition is not in the Gross-Neveu universality class. Read more: Phys. Rev. B 98, 161120(R) (2018)