Instabilities of a birefringent semimetal

Abstract

Birefringent fermions arise as massless fermionic low energy excitations of a particular tight binding model for spinless fermions on a square lattice which have two "speeds of light" [M. P. Kennett, et al., Phys. Rev. A 83, 053636 (2011)]. We use mean field theory to study phases that can arise when there are nearest neighbour and next-nearest neighbour repulsive interactions in this model and demonstrate robustness of the birefringent semi-metal phase in the presence of weak interactions and identify transitions to staggered density and quantum anomalous Hall ordered phases. We consider the effect of coupling birefringent fermions to a magnetic field, and find analytic expressions for the corresponding Landau levels and demonstrate that their integer Quantum Hall effect displays additional plateaux beyond those observed for regular Dirac fermions, such as in graphene. We briefly discuss a tight-binding construction that leads to three dimensional birefringent fermions.

Emergence of asymmetric fermionic order in interacting birefringent fermions

“…In Fig. 3(b), when β < 0.8, the increasing of V can drive the system from BRS into the SQAH order with the critical V c keeping unchanged, which is consistent with the previous work [26]. While when β > 0.8, the AQAH order appears, which is guaranteed by the bifurcation of the boundary line between BRS and SQAH.…”

“…Compared with the previous work [26], where only the SQAH order is predicted to exist, here we find that when β is large enough, the NNN interactions tend to induce the AQAH order. This may be attributed to the fact that in this case, J − → 0, then the outer J − bands become asymptotic flatness and the linear region is much narrower (or see the DOS plot in Fig.…”

“…In the previous work [26], the authors assumed a priori the specific fermionic orders, and then performed the mean-field analysis based on the linear energy spectrum. Here we consider the finite-size lattice model, which enables us to take into account all the properties of the full spectrum and to explore new possible phases.…”

From Birefringent Electrons to a Marginal or Non-Fermi Liquid of Relativistic Spin- 1/2 Fermions: An Emergent Superuniversality

“…An important recent advance in condensed matter physics is the discovery of (quasi)-relativistic spin-1/2 fermions in graphene [2], on the surface of topological insulators [3][4][5], in Weyl materials [6] and in topological superconductors [7]. It is also conceivable to realize higher spin fermions as emergent quasiparticles in various solid state systems in the vicinity of band-touching points [8][9][10][11][12][13][14][15][16][17][18][19][20], which can be either symmetry protected or correspond to a fixed point description of a quantum phase transition between two topologically distinct insulators.Pseudo-spin-3/2 fermions [21] can be found in the close proximity of linear or bi-quadratic touching of valence and conduction bands [8]. We focus on the former situation where the quasiparticles display a birefringent spectrum with two distinct Fermi velocities, and therefore manifestly break Lorentz symmetry.…”

“…Such fermions can be realized from simple tight-binding models on a twodimensional generalized π-flux square lattice [9-11], honeycomb lattices [12,13], shaken optical lattices [14,15], as well as in three-dimensional strong spin-orbit coupled systems [16,17], such as anti-perovskites [18] and the CaAgBi family of materials [19]. In the present Letter we venture into the largely unexplored territory [11,12,20] that encompasses the response of such peculiar gapless fermionic excitations and their stability in the presence of electronic interactions.We now provide a brief summary of our main findings. Irrespective of their materials origin and dimensionality of the system, we show that the optical conductivity of non-interacting spin-3/2 fermions at zero temperature is identical to that of pseudo-relativistic spin-1/2 fermions.…”