Semimetal-superfluid quantum phase transitions in 2D and 3D lattices with Dirac points

Abstract

We study the superfluid properties of attractively interacting fermions hopping in a family of 2D and 3D lattices in the presence of synthetic gauge fields having π-flux per plaquette. The reason for such a choice is that the π-flux cubic lattice displays Dirac points and that decreasing the hopping coefficient in a spatial direction (say, t_z) these Dirac points are unaltered: it is then possible to study the 3D-2D interpolation towards the π-flux square lattice. We also consider the lattice configuration providing the continuous interpolation between the 2D π-flux square lattice and the honeycomb geometry. We investigate by a mean field analysis the effects of interaction and dimensionality on the superfluid gap, chemical potential and critical temperature, showing that these quantities continuously vary along the patterns of interpolation. In the two-dimensional cases at zero temperature and at half filling there is a quantum phase transition occurring at a critical (negative) interaction U_c presenting a linear critical exponent for the gap as a function of |U-U_c|. We show that in three dimensions this quantum phase transition is again retrieved, pointing out that the critical exponent for the gap changes from 1 to 1/2 for each finite value of t_z.

Published in Journal of Physics B, Special Issue on Non Abelian Gauge Fields

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Cited by in corpus (11)

• Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials
• Unruh effect for interacting particles with ultracold atoms
• Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices
• Charge-Density Wave Order on a $\pi$-flux Square Lattice
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Antiferromagnetic transitions of Dirac fermions in three dimensions
• Breakdown of the Peierls substitution for the Haldane model with ultracold atoms
• Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials
• Superconductivity and pair density waves from nearest-neighbor interactions in frustrated lattice geometries
• Synthesis of Majorana mass terms in low-energy quantum systems
• Critical magnetic flux for Weyl points in the three-dimensional Hofstadter model