Many-body instabilities and mass generation in slow Dirac materials

Some Kondo insulators are expected to possess topologically protected surface states with linear Dirac spectrum: the topological Kondo insulators. Because the bulk states of these systems typically have heavy effective electron masses, the surface states may exhibit extraordinarily small Fermi velocities that could force the effective fine structure constant of the surface states into the strong coupling regime. Using a tight-binding model, we study the many-body instabilities of these systems and identify regions of parameter space in which the system exhibits spin density wave and charge density wave order.

Figure 1

Plots of the band structure given by Eq. (3) along the diagonal of the square Brillouin zone using four different values of the parameter $A [1/4$ (solid, black), $1/8$ (dashed, red), $1/16$ (dashed-dot, blue), and $1/32$ (dotted, green)] in two different momentum ranges [(a) from $\mathbf{k}=(-1/5a,-1/5a)$ to $\mathbf{k}=(1/5a,1/5a)$ and (b) from $\mathbf{k}=(-\pi /a,-\pi /a)$ to $\mathbf{k}=(\pi /a,\pi /a)]$. All energies are in units of the bandwidth.

Figure 2

Plot of the phases for the self-consistent solutions found in different regions of the $A,V_0$ plane. Note that the region below the line $A=V_0$ appears to favor the formation of nontrivial order, consistent with ${\alpha }_c\approx 1$. The region enclosed by the red dashed line favors the formation of spin density wave order while in the region enclosed by the black solid line we find both spin density wave and charge density wave solutions. Outside of these regions the solution is paramagnetic (PM).

Figure 3

Plot of the density modulations over a $10\times 10$ real space unit cell, as observed in the SDW and CDW regions shown in Figs. 2 and 4.

Figure 4

Plot of the phases for the self-consistent solutions found in different regions of the $A,V_0$ plane for attractive on-site interaction. In the region enclosed to the right of the solid black line the self-consistent solutions possessed charge density wave order; outside of this region the solution was paramagnetic (PM).