Inter-Band Effects of Magnetic Field on Hall Conductivity in Multi Layered Massless Dirac Fermion System $\alpha$-(BEDT-TTF)${}_2$I${}_3$

We have discovered two-dimensional zero-gap material with a layered structure in the organic conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$ under high hydrostatic pressure. In contrast to graphene, the electron-hole symmetry is not good except at the vicinity of the Dirac points. Thus, temperature dependence of the chemical potential, $\mu$, plays an important role in the transport in this system. The experimental formula of $\mu$ is revealed. We succeeded in detecting the inter-band effects of a magnetic field on the Hall conductivity when $\mu$ passes the Dirac point.