Abstract:
We investigate the spin-ordered states in multilayer massless Dirac fermion systems under magnetic fields, in which the intralayer interaction is ferromagnetic owing to the exchange interaction, while the interlayer interaction is antiferromagnetic arising from the interlayer hopping and the on-site Coulomb repulsion. The possible spin-ordered states are examined within the mean field theory, and we apply it to alpha-(BEDT-TTF)2I3, which is a multilayer massless Dirac fermion system under pressure. In the weak interlayer coupling regime the system exhibits a ferromagnetically spin-ordered state with the effective Zeeman g-factor less than two contrasting to that observed in the single-layer graphene.

Abstract:
We report the first observation of Shubnikov-de Haas (SdH) oscillations and quantized Hall resistance in the multilayered massless Dirac fermion system $\alpha$-(BEDT-TTF)$_2$I$_3$ with tilted cones. Holes were injected into the thin crystal fixed on a polyethylene naphthalate (PEN) substrate by contact electrification. The detection of SdH oscillations whose phase was modified by Berry's phase $\pi$ strongly suggested that the carrier doping was successful in this system. We succeeded in detecting the quantum Hall effect (QHE) with the steps which is the essence of two dimensional Dirac fermion systems. The number of effectively doped layers was examined to be two in this device. We reveal that the correlation between effective layers plays an important role in QHE.

Abstract:
We present the theory of the inplane magnetoresistance in two-dimensional massless Dirac fermion systems including the Zeeman splitting and the electron-electron interaction effect on the Landau level broadening within a random phase approximation. With the decrease in temperature, we find a characteristic temperature dependence of the inplane magnetoresistance showing a minimum followed by an enhancement with a plateau. The theory is in good agreement with the experiment of the layered organic conductor \alpha-(BEDT-TTF)_2I_3 under pressure. In-plane magnetoresistsnce of graphene is also discussed based on this theory.

Abstract:
The inter-layer magnetoresistance in a multilayered massless Dirac fermion system, $\alpha$-(BEDT-TTF)$_2$I$_3$, under hydrostatic pressure was investigated. We succeeded in detecting the zero-mode (n=0) Landau level and its spin splitting in the magnetic field normal to the 2D plane. We demonstrated that the effective Coulomb interaction in the magnetic field intensifies the spin splitting of zero-mode Landau carriers. At temperatures below 2K, magnetic fields above several Tesla break the twofold valley degeneracy.

Abstract:
The effect of disorder on the Landau levels of massless Dirac fermions is examined for the cases with and without the fermion doubling. To tune the doubling a tight-binding model having a complex transfer integral is adopted to shift the energies of two Dirac cones, which is theoretically proposed earlier and realizable in cold atoms in an optical lattice. In the absence of the fermion doubling, the $n=0$ Landau level is shown to exhibit an anomalous sharpness even if the disorder is uncorrelated in space (i.e., large K-K' scattering). This anomaly occurs when the disorder respects the chiral symmetry of the Dirac cone.

Abstract:
A zero-gap state with a Dirac cone type energy dispersion was discovered in an organic conductor α-(BEDT-TTF) 2I 3 under high hydrostatic pressures. This is the first two-dimensional (2D) zero-gap state discovered in bulk crystals with a layered structure. In contrast to the case of graphene, the Dirac cone in this system is highly anisotropic. The present system, therefore, provides a new type of massless Dirac fermion system with anisotropic Fermi velocity. This system exhibits remarkable transport phenomena characteristic to electrons on the Dirac cone type energy structure.

Abstract:
We report on the experimental results of interlayer magnetoresistance in multilayer massless Dirac fermion system $\alpha$-(BEDT-TTF)$_2$I$_3$ under hydrostatic pressure and its interpretation. We succeeded in detecting the zero-mode Landau level (n=0 Landau level) that is epected to appear at the contact points of Dirac cones in the magnetic field normal to the two-dimensional plane. The characteristic feature of zero-mode Landau carriers including the Zeeman effect is clearly seen in the interlayer magnetoresistance.

Abstract:
We investigate the effect of the interlayer spin-flip tunneling for the interlayer magnetoresistance under magnetic fields in alpha-(BEDT-TTF)2I3, which is a multilayer massless Dirac fermion system under pressure. The mean field of the spin-flip correlation associated with the interlayer Coulomb interaction enables the interlayer spin-flip tunneling. Assuming the non-vertical interlayer spin-flip tunneling, we calculate the interlayer magnetoresistance using the Kubo formula. The crossover magnetic field, at which the interlayer magnetoresistance changes from positive to negative is shifted by the Zeeman energy and in good agreement with the experiment.

Abstract:
We present a theoretical description of the interlayer magnetoresistance in the layered Dirac fermion system with the application to the organic conductor \alpha-(BEDT-TTF)_2I_3 under pressure. Assuming a non-vertical interlayer tunneling and including higher Landau level effects we calculate the interlayer conductivity using the Kubo formula.We propose a physical picture of the experimentally observed crossover from the negative interlayer magnetoresistance, where the Dirac fermion zero-energy Landau level plays a central role, to the positive interlayer magnetoresistance that is the consequence of the Landau level mixing effect upon non-vertical interlayer hopping. The crossover magnetic field depends on the Landau level broadening factor and can be used to determine the Dirac fermion Landau level energy spectrum.

Abstract:
Graphene and topological insulators (TI) possess two-dimensional Dirac fermions with distinct physical properties. Integrating these two Dirac materials in a single device creates interesting opportunities for exploring new physics of interacting massless Dirac fermions. Here we report on a practical route to experimental fabrication of graphene-Sb2Te3 heterostructure. The graphene-TI heterostructures are prepared by using a dry transfer of chemical-vapor-deposition grown graphene film. ARPES measurements confirm the coexistence of topological surface states of Sb2Te3 and Dirac {\pi} bands of graphene, and identify the twist angle in the graphene-TI heterostructure. The results suggest a potential tunable electronic platform in which two different Dirac low-energy states dominate the transport behavior.