Holographic fermions in external magnetic fields

Abstract

We study the Fermi-level structure of $2+1$-dimensional strongly interacting electron systems in external magnetic field using the gague/gravity duality correspondence. The gravity dual of a finite density fermion system is a Dirac field in the background of the dyonic AdS-Reissner-Nordstr\"om black hole. In the probe limit, the magnetic system can be reduced to the nonmagnetic one, with Landau-quantized momenta and rescaled thermodynamical variables. We find that at strong enough magnetic fields, the Fermi surface vanishes and the quasiparticle is lost either through a crossover to conformal regime or through a phase transition to an unstable Fermi surface. In the latter case, the vanishing Fermi velocity at the critical magnetic field triggers the non-Fermi-liquid regime with unstable quasiparticles and a change in transport properties of the system. We associate it with a metal--''strange-metal'' phase transition. Next, we compute the DC Hall and longitudinal conductivities using the gravity-dressed fermion propagators. For dual fermions with a large charge, many different Fermi surfaces contribute and the Hall conductivity is quantized as expected for integer quantum Hall effect (QHE). At strong magnetic fields, as additional Fermi surfaces open up, new plateaus typical for the fractional QHE appear. The somewhat irregular pattern in the length of fractional QHE plateaus resembles the outcomes of experiments on thin graphite in a strong magnetic field. Finally, motivated by the absence of the sign problem in holography, we suggest a lattice approach to the AdS calculations of finite density systems.