Winding charge density wave: intertwining of structural chirality and phase topology of electronic order

We propose a class of chiral charge density waves (CDWs), dubbed winding CDWs, that exhibit macroscopic chirality despite a single ordering wavevector. In screw-symmetric chiral crystals, chiral phonons drive a Peierls instability that selects a definite crystal angular momentum channel, thereby endowing the CDW with an integer azimuthal phase winding dictated by the selection rule governing electron-phonon coupling. We further extend this framework to achiral crystals with discrete rotational symmetry and demonstrate that spontaneous symmetry breaking stabilizes a winding CDW with either handedness, realizing an achiral-to-chiral phase transition. Our results reveal a fundamental link between the geometry of chiral structures and the phase topology of electronic orders.