Excitons in topological Kondo insulators: Theory of thermodynamic and transport anomalies in ${\mathrm{SmB}}_6$

Kondo insulating materials lie outside the usual dichotomy of weakly versus correlated—band versus Mott—insulators. They are metallic at high temperatures but resemble band insulators at low temperatures because of the opening of an interaction-induced band gap. The first discovered Kondo insulator (KI) ${\mathrm{SmB}}_6$ has been predicted to form a topological KI (TKI). However, since its discovery thermodynamic and transport anomalies have been observed that have defied a theoretical explanation. Enigmatic signatures of collective modes inside the charge gap are seen in specific heat, thermal transport, and quantum oscillation experiments in strong magnetic fields. Here, we show that TKIs are susceptible to the formation of excitons and magnetoexcitons. These charge neutral composite particles can account for long-standing anomalies in ${\mathrm{SmB}}_6$.

Figure 1

At low temperatures strong correlations lead to the formation of fermionic quasiparticles that have the schematically shown band structure (for $k_z=0$) of a broad-brimmed Mexican hat. Because of the large DOS at the band edges it is very susceptible to the formation of excitons.

Figure 2

Shown for $B=0$ as a function of $q_x$ with $q_y=0$. The full exciton dispersion of the two-dimensional TKI is plotted in the inset. Because of the special band structure the dispersion minima are always at nonzero momenta but their precise energy depends on the interaction strength. We have used parameters $W=\mu =-3.2$, $\alpha =0.15$, $\gamma =0.1$, $U=2.75$ (in units of hopping $t$), which give a dispersion with a small gap that can best explain experiments on ${\mathrm{SmB}}_6$.

Figure 3

The upper panel shows the specific heat for $B=0$, plotted as $C/T$, as a function of scaled temperature $T/\mathrm{\Delta }$ with the fermionic band gap $\mathrm{\Delta }$. For comparison, we plot the behavior of noninteracting excitons, $C_{\text{Exc}}^0$, with a dispersion with a perfect degenerate ringlike minimum (black dot dashed) or in the self-consistent lattice dispersion (black dashed). We use the same parameters as in the upper panel of Fig. 3 (with ${\mathrm{\Delta }}_{\mathrm{deg}}/\mathrm{\Delta }=1/20$, ${\mathrm{\Delta }}_{\text{Exc}}={\mathrm{\Delta }}_{\mathrm{deg}}/10$, $g=0.004t$) and scale the exciton contribution by a factor $1/4$. The lower panel shows the thermal conductivity plotted as $\kappa /T$.

Figure 4

The energy of MEXC, which is mainly given by the LL gap for weak MEXC binding, changes periodically as a function of inverse magnetic field; see Eq. (7). Therefore, the free energy of the exciton system $F$ (blue) varies periodically together with the corresponding magnetization $M$ (red) (the same parameters as before and $\gamma /W=0.025$). The schematic temperature dependence is shown in the inset.