Intertwined Order and Holography: The Case of Parity Breaking Pair Density Waves

We present a minimal bottom-up extension of the Chern-Simons bulk action for holographic translational symmetry breaking that naturally gives rise to pair density waves. We construct stationary inhomogeneous black hole solutions in which both the U(1) symmetry and spatially translational symmetry are spontaneously broken at a finite temperature and charge density. This novel solution provides a dual description of a superconducting phase intertwined with charge, current, and parity orders.