Tilted Dirac cones and their topology in holographic materials

Abstract

We explore strongly correlated materials with tilted Dirac cone by introducing a method to realize this spectral feature within a holographic setup. Following the work by Moradpouri et al, we construct an asymptotically AdS spacetime by uplifting the vielbein of Volovik et al. to tilt the flat spacetime light cone. We then couple the resulting metric to holographic fermions and compute their spectral functions, confirming the presence of a tilted Dirac cone in momentum space. We also calculate the topological number using the holographic Green's function and find that the Chern number is independent of the tilting parameter. Additionally, we show that the optical conductivity exhibits a Drude peak even at zero chemical potential, revealing nontrivial strong-coupling effects absent in field-theoretic models.