Symmetric tensor coupling in holographic mean-field theory: deformed Dirac cones

We extend the holographic mean-field theory to rank-two symmetric tensor field as an external source coupled with fermion. We classify the roles of symmetric tensor coupling according to the effect on the spectral density: cone-angle change, squashing, and tilting of the spectral light cones. The over-tilted light cone is also achieved in a generalized prescription, which consistently retains the causality condition. Our results provide agreements between the holographic spectra with those observed in real materials, such as type-II Dirac cones and strained graphene.