The ternary chalcogenide superconductor ${\mathrm{Bi}}_2{\mathrm{Rh}}_3{\mathrm{Se}}_2$ was discovered to have charge density wave (CDW) order and electron-phonon coupling (EPC). However, it is still debated whether the phase transition at $\sim 240\mathrm{K}$ is a CDW one. Here, we systematically performed Raman scattering investigations on single-crystal ${\mathrm{Bi}}_2{\mathrm{Rh}}_3{\mathrm{Se}}_2$. Angle-resolved polarized Raman spectroscopic measurements reveal the in-plane anisotropic EPC in ${\mathrm{Bi}}_2{\mathrm{Rh}}_3{\mathrm{Se}}_2$, which inhibits the Raman intensity. Temperature-dependent x-ray diffraction and Raman measurements indicate the existence of the incommensurate (ICCDW) and commensurate (CCDW) CDW orders below $\sim 250$ and $\sim 170$ K, respectively, in ${\mathrm{Bi}}_2{\mathrm{Rh}}_3{\mathrm{Se}}_2$. The appearance of zone-folded phonon modes at $\sim 170$ K confirms the CCDW-induced $2\times 2$ reconstruction of the Brillouin zone. Semiquantitative analysis based on Landau theory of second-order phase transitions of CDW-correlated and uncorrelated phonon modes reflects extensive coupling between the phonons and CDW orders. Our findings elucidate the existence of CCDW and ICCDW and confirm the critical role of EPC in CDW transitions in ${\mathrm{Bi}}_2{\mathrm{Rh}}_3{\mathrm{Se}}_2$.

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• Charge density waves
• Lattice dynamics
• Phonons
• Quasiparticles & collective excitations
• Transition temperature
• Chalcogenides
• Raman spectroscopy