$\pi$ Phase Interlayer Shift and Stacking Fault in the Kagome Superconductor CsV${}_3$Sb${}_5$

The stacking degree of freedom is a crucial factor in tuning material properties and has been extensively investigated in layered materials. The kagome superconductor CsV${}_3$Sb${}_5$ was recently discovered to exhibit a three-dimensional CDW phase below TCDW ~94 K. Despite the thorough investigation of in-plane modulation, the out-of-plane modulation has remained ambiguous. Here, our polarization- and temperature-dependent Raman measurements reveal the breaking of C${}_6$ rotational symmetry and the presence of three distinct domains oriented at approximately 120°to each other. The observations demonstrate that the CDW phase can be naturally explained as a 2c staggered order phase with adjacent layers exhibiting a relative $\pi$ phase shift. Further, we discover a first-order structural phase transition at approximately 65 K and suggest that it is a stacking order-disorder phase transition due to stacking fault, supported by the thermal hysteresis behavior of a Cs-related phonon mode. Our findings highlight the significance of the stacking degree of freedom in CsV${}_3$Sb${}_5$ and offer structural insights to comprehend the entanglement between superconductivity and CDW.