Phonon-Induced Emergent Charge Order in Cuprates

Charge-density modulations are inevitably accompanied by a distortion of the crystalline lattice. Electronic or phononic origins of charge order are therefore difficult to distinguish. Here we propose a mechanism which traces the charge-density wave formation in underdoped cuprates to the incipient softening of a bond-buckling phonon. The momentum dependence of its coupling to the electrons in the copper oxygen planes favourably selects the incommensurate and axial ordering wavevector. But, it requires strong electronic correlations via their cuprate specific renormalization of the weight and the dispersion of quasiparticles to enable a unique enhancement of the charge susceptibility near the B_1g -phonon selected wavevector. The frequency of the B_1g phonon softens by a few percent, and a lattice instability with concomitant finite range charge-density wave correlations will form locally, if nucleated by materials’ defects or dopant disorder.