Holographic Calculation of the Magneto-Transport Coefficients in the Dirac Semimetals

We use the holographic analogy to calculate magneto-thermoelectric transport coefficients of the strongly interacting electrons. The examples of the real materials which supposedly contain strongly interacting electron-hole fluid include graphene, the topological insulators or three-dimensional compounds with the Dirac spectrum. In such systems the particles (electron and holes if the Fermi energy is located close to the Dirac point) behave as a strongly interacting fluid. This has been observed in graphene, where experimental signatures of the strong interactions have been observed, and is assumed to be valid for other systems. On the gravity side we have modeled the transport of such materials by two interacting vector fields. According to the gauge-gravity interpretation two vector fields represent electron and hole currents flowing in the system under the effect of electric field. The axionic field introduced into the gravity action provides momentum relaxation and gives finite values of DC transport coefficients. We have calculated charge conductivity and thermal conductivity tensors and tensor of the Wiedemann-Franz ratio. Our results favorably compare with the existing experimental data.