We present a mechanism for the onset of a biaxial charge density wave (CDW) ground state in a quasi-2D metallic system with cubic symmetry, possessing a closed, isotropic Fermi surface. Unlike the quasi-1D systems, where the CDW appears solely as uniaxial, the quasi-2D systems, such as high-$T_c$ superconducting cuprates, intercalated graphite compounds, and transition-metal dichalcogenides, for example, may exhibit a multiaxial CDW state depending on the symmetry of the crystal lattice. The weakly coupled quasi-1D systems rely on the Fermi-surface nesting to facilitate Peierls instability, while in quasi-2D systems, completely parting from the nesting paradigm, the Kohn anomaly is triggered by considerably strong electron-phonon coupling, with pseudogap and a logarithmic type of van Hove singularity below the Fermi energy forming in turn. The zero-temperature CDW state appears as a Lifshitz type of quantum transition for electron-phonon coupling stronger than the critical value, which is determined by the properties of the electron band with a Fermi surface reconstructed by the self-consistent order parameter. A comparison between biaxial and uniaxial CDW states is addressed.

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• Charge density waves
• Density of states
• Fermi surface
• Nesting
• 2-dimensional systems