Interlayer magnetoresistance in multilayer Dirac electron systems: motion and merging of Dirac cones

We theoretically study the effect of the motion and the merging of Dirac cone on the interlayer magnetoresistance in multilayer graphene like systems. This merging, which could be induced by a uniaxial strain, gives rise in monolayer Dirac electron system to a topological transition from a semi-metallic phase to an insulating phase where Dirac points disappear. Based on a universal Hamiltonian proposed to describe the motion and the merging of Dirac points in two dimensional Dirac electron crystals, we calculate the interlayer conductivity of a stack of deformed graphene like layers using Kubo formula in the quantum limit where only the contribution of the $n=0$ Landau level is relevant. A crossover from a negative to a positive interlayer magnetoresistance is found to take place as the merging is approached. This sign change of the magnetoresistance could also result from a coupling between the Dirac valleys which is enhanced as the magnetic field amplitude increases. Our results may describe the behavior of the magnetotransport in the organic conductor $\alpha$-(BEDT)${}_2$I${}_3$ at high pressure where the merging of Dirac cones could be observed.