Coupled Electronic and Lattice Charge Density Waves

The charge density wave (CDW) is a periodic modulation of electron density, driven by electronic or lattice instabilities. We investigate the CDW formation in the two-dimensional topological insulator TaIrTe₄ using density functional theory (DFT), mean field calculation, and free energy model. Our results show that density-tuned electron-phonon coupling (EPC) can stabilize or suppress the CDW, differing from conventional mechanisms based solely on Fermi surface nesting or phonon instabilities. The CDW forms in two stages: an initial charge modulation due to van Hove singularities (VHS), followed by lattice distortions induced by EPC. We develop a Landau functional with two order parameters, highlighting the key role of EPC in the lattice-driven transition.