Holographic phonons by gauge-axion coupling

In this paper, we show that a simple generalization of the holographic axion model can realize spontaneous breaking translational symmetry by considering special gauge-axion higher derivative term. The finite real part and imaginary stress tensor imply dual boundary system is viscoelastic solid. By calculating quasi-normal modes making comparison with predictions from elasticity theory, verify existence phonons pseudo-phonons, where latter realized introducing weak explicit symmetry, in transverse channel. Finally, discuss how phonon dynamics affects charge transport.