Holographic Description of Strongly Correlated Electrons 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 AdS/CFT correspondence. The gravity dual of a finite density fermion system is a Dirac field in the background of the dyonic AdS-Reissner-Nordstrom black hole. In the probe limit the magnetic system can be reduced to the non-magnetic 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. We compute the DC Hall and longitudinal conductivities using the gravity-dressed fermion propagators. As expected, the Hall conductivity is quantized according to integer Quantum Hall Effect (QHE) at weak magnetic fields. At strong magnetic fields, new plateaus typical for the fractional QHE appear. Our pattern closely resembles the experimental results on graphite which are described using the fractional filling factor proposed by Halperin.