We investigate the equilibrium state and the collective modes of an excitonic insulator (EI) in a Fabry-Pérot cavity. In an EI, two bands of a semiconductor or semimetal spontaneously hybridize due to the Coulomb interaction between electrons and holes, leading to the opening of a gap. The coupling to the electromagnetic field reduces the symmetry of the system with respect to phase rotations of the excitonic order parameter from $U\left(1\right)$ to $Z_2$. While the reduction to a discrete symmetry would, in general, lead to a gapped phase mode and enhance the stability of the ordered phase, the coupling to the cavity leaves the mean-field ground state unaffected. Its energy remains invariant under $U\left(1\right)$ phase rotations, in spite of the lower $Z_2$ symmetry imposed by the cavity. In a dipolar gauge, this can be traced back to the balancing of the linear light-matter coupling and the dipolar self-interaction at zero frequency. At nonzero frequency, however, the collective excitations do reflect the lower $Z_2$ symmetry. While our model is studied using a mean-field decoupling of the light-matter approximation (which is exact in the single-mode limit), the results show that fluctuations beyond mean field could play a crucial role in finding the true phase at finite temperature.

中文翻译：

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腔中U（1）对称激子绝缘子的集体激发

我们研究了Fabry-Pérot腔中激子绝缘子（EI）的平衡状态和集体模式。在EI中，由于电子和空穴之间的库仑相互作用，半导体或半金属的两个能带自发地杂化，从而导致间隙的打开。与电磁场的耦合降低了系统相对于激子阶跃参数的相位旋转的对称性。$ü（\mathrm{1个}）$ 至 ${ž}_2$。通常，减小到离散对称会导致间隙相位模式并增强有序相的稳定性，但与腔的耦合不会影响平均场基态。它的能量在$ü（\mathrm{1个}）$ 相位旋转，尽管较低 ${ž}_2$腔施加的对称性。在偶极测量仪中，这可以追溯到线性光-质耦合和零频率下的偶极自相互作用的平衡。但是，在非零频率下，集体激励确实反映了较低的${ž}_2$对称。虽然我们的模型是使用光物质近似的平均场去耦（在单模极限中精确）进行研究的，但结果表明，超出平均场的波动可能在有限温度下寻找真相方面起着至关重要的作用。