We study longitudinal conductivity in a semi-infinite two-dimensional layer of the molecular Dirac electron system α-(BEDT-TTF)₂I₃, especially regarding an edge state and a bound one on a domain wall with different types of charge order. We investigate the extended Hubbard model, and show that the conductive edge state and the domain wall arise under a specific boundary condition. While the bound state on the domain wall remains metallic even as the charge order increases, the metallic edge state exists only near the phase transition point between the charge order and the massless Dirac fermion phases. The stability of the domain wall is also clarified. Since the actual crystal of α-(BEDT-TTF)₂I₃ consists of many layers, these theoretical results can describe recent transport experiments, which suggest that some metallic channels exist in the charge-ordered phase near the phase boundary.

The nontrivial properties of interband spin fluctuations are studied by the random phase approximation in a Hubbard model describing the molecular conductor α-(BEDT-TTF)₂I₃, where wave functions are based on the four sublattices named A, A′, B, and C in a two-dimensional BEDT-TTF molecular plane. It is found that the ferrimagnetic polarization observed by a recent NMR measurement emerges only if there exist cross terms among intra- and inter-band irreducible susceptibility matrix elements in the presence of the on-site Coulomb interaction U. It is also found that the nontrivial sign of the interband components of the spin susceptibility, being negative only for the B sublattice, is closely related to the characteristic phase structure of wave functions in the Dirac fermion system with multisublattices. The negative value of the spin susceptibility on the B sublattice observed in the experiment is associated with this negative interband susceptibility, which comes from the excitations in the gentle-slope region of the energy dispersion connecting the Dirac points with saddle points in the first Brillouin zone.

The dynamical property of electrons with the tilted Dirac cone was examined using the tilted Weyl equation. The polarization function exhibits cusps and nonmonotonic structures by varying both the frequency and the momentum. A pair of tilted Dirac cones exhibits a new plasmon for the intermediate magnitude of momentum owing to the combined effects of two tilted cones. Dirac electrons with the zero-gap state (ZGS) in organic conductor α-(BEDT-TTF)₂I₃ are examined by calculating the Berry curvature, which displays the peak structure for a pair of Dirac particles between the conduction band and the valence band. The ZGS is theoretically predicted for α-(BEDT-TTF)₂NH₄Hg(SCN)₄ under uniaxial pressure. Examining the band structure of the stripe charge ordered state of α-(BEDT-TTF)₂I₃ under pressure, we have found a topological transition from a conventional insulator to a new phase of a pair of Dirac electrons with a finite mass. Further, investigating the zero-energy (N = 0) Landau level under a strong magnetic field, we propose ferromagnetism breaking the SU(2) valley-pseudo-spin symmetry, and the phase fluctuations of the order parameters leading to Kosterlitz-Thouless transition at lower temperatures.

The optical conductivity in the charge order phase is calculated in the two-dimensional extended Hubbard model describing an organic Dirac electron system $\alpha$ -(BEDT-TTF) ${}_2$ I ${}_3$ using the mean field theory and the Nakano-Kubo formula. Because the interband excitation is characteristic in a two-dimensional Dirac electron system, a peak structure is found above the charge order gap. It is shown that the peak structure originates from the Van Hove singularities of the conduction and valence bands, where those singularities are located at a saddle point between two Dirac cones in momentum space. The frequency of the peak structure exhibits drastic change in the vicinity of the charge order transition.