Highly unconventional behavior of the thermodynamic response functions has been experimentally observed in a narrow gap semiconductor samarium hexaboride. Motivated by these observations, we use renormalization group technique to investigate many-body instabilities in the f-orbital narrow gap semiconductors with band inversion in the limit of weak coupling. By projecting out the double occupancy of the f-states we formulate a low-energy theory describing the interacting particles in two hybridized electron- and hole-like bands. The interactions are assumed to be weak and short-ranged. We take into account the difference between the effective masses of the quasiparticles in each band. Upon carrying out the renormalization group analysis we find that there is only one stable fixed point corresponding to the excitonic instability with time-reversal symmetry breaking for small enough mismatch between the effective masses.

已经在窄间隙半导体六硼化钐中通过实验观察到热力学响应函数的高度非常规行为。受这些观察的启发，我们使用重整化群技术来研究f轨道窄隙半导体中的多体不稳定性，在弱耦合的极限下具有能带反转。通过投影出f的双重占用-states 我们制定了一个低能理论，描述了两个杂化的电子和类空穴带中的相互作用粒子。假设相互作用是弱的和短程的。我们考虑了每个带中准粒子的有效质量之间的差异。在进行重整化群分析时，我们发现只有一个稳定的不动点对应于激子不稳定性，因为有效质量之间的失配足够小，时间反演对称性破缺。