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

Abstract

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 .

Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials

“…The system remains a semimetal also when local attractive interactions are added, up to a critical value of the interaction strength, due to the vanishing density of states [64], as discussed in a variety of 2D and 3D lattices, including the 3D π-flux model [65].…”

Topological phase transitions driven by non-Abelian gauge potentials in optical square lattices

“…The structure of Dirac points is unaltered when passing from a two-dimensional square to a three-dimensional cube with π-flux for each plaquette [13][14][15]. In two dimensions, one can explicitly see the similarity between the tight-binding models on the honeycomb and the π-flux square lattices by considering a continuous path smoothly interpolating between these two lattices and showing that the Dirac points are well defined across this path [16].…”

Charge-Density Wave Order on a $π$-flux Square Lattice

“…In this section, we present a mean-field theory approach to solve the Holstein model. Semi-metal to superfluid transitions have previously been investigated with MFT in 2D and 3D [24,25]. Here we focus on the semimetal to CDW transition.…”