Unitarity bound violation in holography and the Instability toward the Charge Density Wave

We study the spectral function of fermions in a holographic set up with bulk Dirac mass in the regime beyond the conformal unitarity bound, and find that spectral function has the dispersion relation with tachyonic behavior, indicating an instability. Based on linearity between the density and the position of the tip of the k-gap, we suggest that this instability is toward the charge density wave(CDW) and the position of the tip can be identified as the wave vector of CDW. For the physical origin, we point out the similarity of unitarity violation in our non-Fermi Liquid theory and nesting phenomena in the Fermi liquid theory as the mechanism of CDW instability.