Charge density wave (CDW) phenomena in low-dimensional rare-earth chalcogenides have drawn considerable interest owing to their interplay with lattice instabilities, electronic correlations, and magnetism. ${\mathrm{EuTe}}_4$, which contains both mono- and bilayer Te pseudosquare nets together with Eu–Te zigzag layers, provides a unique platform for exploring these effects. Using first-principles calculations, angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy/spectroscopy (STM/STS), and low-temperature thermodynamic measurements, we map the full CDW-induced reconstruction of its electronic structure. ARPES reveals a highly anisotropic low-energy CDW gap that maximizes along $\overline{\mathrm{\Gamma }}\text{−}\overline{\mathrm{Y}}$ and minimizes along $\overline{\mathrm{\Gamma }}\text{−}\overline{\mathrm{X}}$, accompanied by a second, higher-binding-energy gap originating from band folding. STM directly visualizes the incommensurate CDW with Te-trimer formation and a dominant modulation vector ${\mathit{q}}_{\mathrm{CDW}}\approx 0.38{\mathit{b}}^{*}$, and spectroscopy confirms a wide CDW-induced suppression of states. A similar ${\mathit{q}}_{\mathrm{CDW}}$ corresponds to the imaginary soft modes in the calculated phonon spectrum. Heat capacity measurements identify an antiferromagnetic transition at $T_{\mathrm{N}}\approx 6.9\mathrm{K}$. Together, these results establish a comprehensive picture of the multigap, momentum-dependent CDW state in ${\mathrm{EuTe}}_4$.

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• Charge density waves
• Electronic structure
• Fermi surface
• Layered crystals
• Angle-resolved photoemission spectroscopy
• Density functional calculations