Instabilities of a birefringent semimetal

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-neighbor and next-nearest-neighbor repulsive interactions in this model and demonstrate robustness of the birefringent semimetal 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 plateaus 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.

Figure 1

Unit cell of tight-binding model.

Figure 2

Phase diagram in the presence of nearest-neighbor interactions as a function of $V_1$ and $\beta$.

Figure 3

Hopping pattern corresponding to nonzero ${\zeta }_{35}$ order parameter. The amplitude of all diagonal hopping integrals is identical, and equal to $\alpha$.

Figure 4

Phase diagram as a function of $\beta$ and $V_2$ for next-nearest-neighbor interactions, showing the birefringent semimetal phase and the quantum anomalous Hall (QAH) phase. The inset shows the dispersion for $\alpha =0.3$ and $\beta =0.3$.

Figure 5

Phase diagram as a function of $V_1$ and $V_2$ at $\beta =0.5$.

Figure 6

Landau level energy eigenvalues as a function of $\beta$ for $n=0$ to $n=20$.

Figure 7

Eight-site unit cell and hopping parameters for the three-dimensional birefringent fermion model.