Critical Behavior of Topological Kondo Insulators

A thermodynamic study of the Kondo insulator SmB$_6$ is pursued to elucidate the well-known anomalous low-temperature electronic-like specific heat contribution conjectured to arise from metallic surface states. A general thermodynamic description of topological Kondo insulators is developed using a mean-field slave-boson approximation and an approach inspired by Hill thermodynamics to study the phase transitions with the critical exponents of the model. The results show consistency with the Josephson hyper-scaling relation. We further apply this framework to SmB$_6$. By separating the bulk and boundary contributions to the heat capacity, we show that while the surface states contribute to an increase of the heat capacity upon lowering the temperature, the effect is immeasurably small. This suggests that an alternate explanation is required for the anomalous low-temperature contributions to the specific heat in this material.