**1. Introduction**

The electron correlation effects in two-dimensional Dirac electron systems have attracted much attention [1–5]. In the Dirac electron system of organic conductor *α*-(BEDT-TTF)2I3 [6–13], it was shown that the electron correlation effects become a key factor to understanding electronic properties [14–22], since the Coulomb interaction is comparable with the band width. Moreover, the Fermi energy almost coincides with the Dirac point in *α*-(BEDT-TTF)2I3; thus, any other energy bands do not overlap with Fermi energy [23,24]. *α*-(BEDT-TTF)2I3 has a clean Dirac electron system, since the density of impurity is estimated to the ppm order [23,24]. These features are also advantageous to developing the physics of the correlated Dirac electron system.

The layered structure of *α*-(BEDT-TTF)2I3 enables interlayer magnetoresistance measurements, which revealed the anomalous electronic properties of two-dimensional Dirac electron systems connected by weak interlayer tunneling [25–30]. In the magnetic field normal to the conductive layer, the energy of Landau levels in a massless Dirac electron system is expressed as *EN* = ±-2*ehv*¯ 2F|*N*|*<sup>B</sup>*, where *h*¯, *v*F, *N*, and *B* denote the Planck constant, the Fermi velocity of the Dirac cone, the Landau index, and the magnetic-field strength, respectively. One of the characteristic features in these systems is the appearance of *N* = 0 Landau levels at the Dirac points. This effect was detected in interlayer magnetoresistance under a transverse magnetic field [25,26]. Interlayer magnetoresistance primarily depends on the interlayer tunneling of the Landau carriers, where Landau carriers indicate the carriers belonging to Landau levels that contribute to electric current. Note that in each Landau levels there are states with density proportional to *B*. Thus, the magnetic field creates mobile *N* = 0 Landau level carriers. The effect of the magnetic field appears only through the change of the *N* = 0 Landau level carrier density at the vicinity of the Dirac points. Thus, negative interlayer magnetoresistance due to the increase of the degeneracy of the *N* = 0 Landau levels was observed [25,26]. It was also shown that interlayer resistance has a minimum for *gμ*B*B*0/2 ∼= *h*¯ /*τ*˜ due to the Zeeman splitting of the *N* = 0 Landau levels, where *g*, *μ*B, and *τ*˜ denote the *g*-factor, the Bohr magneton, and the relaxation time, respectively. If the electron correlation effects in the Landau levels are negligible, *B*0 is independent of the angle of the magnetic field.

The electron correlation effects in the Landau levels, however, have been controversial. Although the possible ordered states due to Coulomb interaction, such as the valley-ordered state [31–33] and the interlayer spin-ordered state [34,35], were proposed, it was suggested that the anomalous increase of the spin lattice relaxation rate at low temperatures [33] can be explained by the spin transverse fluctuation in the absence of ordered states [36].

In the present study, we investigate the effects of the electron correlation between *N* = 0 Landau level carriers on interlayer magnetoresistance as a function of field-angle *θ* from the interlayer axis in collaboration with theory and experiment. The effective *g*-factor, *g*<sup>∗</sup>, is treated using the mean field theory of the Coulomb interaction between the tilted Dirac electrons in the quantum limit. It is numerically shown that effective Coulomb interaction *V*HS, which enhances *g*<sup>∗</sup>, is approximately proportional to (*B* cos *<sup>θ</sup>*)*<sup>γ</sup>*, where *γ* depends on the tilt of the Dirac cone. It is found that a characteristic magnetic field *B*0, at which the interlayer resistance has a minimum, depends on *θ* and temperature *T*, where the inverse of *B*0 is proportional to cos *θ* approximately and the coefficient increases as *T* decreases. These results are in qualitative agreemen<sup>t</sup> with the experiment.
