We provide a framework to compute the dynamics of massive Dirac fermions using holography. To this end we consider two bulk Dirac fermions that are coupled via a Yukawa interaction and propagate on a gravitational background in which a mass deformation is introduced. Moreover, we discuss the incorporation of this approach in semiholography. The resulting undoped fermionic spectral functions indeed show that the Yukawa coupling induces a gap in the holographic spectrum, whereas the semiholographic extension is in general gapped but additionally contains a quantum critical point at which the effective fermion mass vanishes and a topological phase transition occurs. Furthermore, when introducing doping, the fermionic spectral functions show a quantum phase transition between a gapped material and a Fermi liquid.

We investigate the effect of order parameter fluctuations in the holographic superconductor. In particular, following an introduction to the concept of intrinsic dynamics and its implementation within holographic models, we compute the intrinsic spectral functions of the order parameter in both the normal and the superconducting phase, using a fully backreacted bulk geometry. We also present a vector-like large-N version of the Ginzburg-Landau model that accurately describes our long-wavelength results in both phases. Our results indicate that the holographic superconductor describes a relativistic multi-component superfluid in the universal regime of the BEC-BCS crossover.

We present an alternative way of computing nonrelativistic single-particle spectra from holography. To this end, we introduce a mass gap in a holographic Dirac semimetal and subsequently study the nonrelativistic limit of the resulting spectral functions. We use this method to compute the momentum distributions and the equation of state of our nonrelativistic fermions, of which the latter can be used to extract all thermodynamic properties of the system. We find that our results are universal and reproduce many experimentally and theoretically known features of an ultracold Fermi gas at unitarity.