Motivated by the insulating behavior of $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TSeF}\right)}_2{\mathrm{I}}_3$ at low temperatures ($T$'s), we first performed first-principles calculations based on the crystal structural data at 30 K under ambient pressure, and we constructed a two-dimensional effective model using maximally localized Wannier functions. As possible causes of the insulating behavior, we studied the effects of the on-site Coulomb interaction $U$ and spin-orbit interaction (SOI) by investigating the electronic state and the transport coefficient using the Hartree approximation and the $T$-matrix approximation. The calculations at a finite $T$ demonstrated that a spin-ordered massive Dirac electron (SMD) appeared due to the on-site Coulomb interaction. We had an interest in the anomalous competitive effect with $U$ and SOI when the SMD phase is present in $\alpha \text{−}{\left(\mathrm{BETS}\right)}_2{\mathrm{I}}_3$, and we investigated these contributions to the electronic state and conductivity. The SMD is not a conventional spin order, but it exhibits the spin-valley Hall effect. Direct current resistivity in the presence of a spin order gap increased divergently and exhibited negative magnetoresistance in the low $T$ region with decreasing $T$. The charge density hardly changed below and above the $T$ at which this insulating behavior appeared. However, when considering the SOI alone, the state changed to a topological insulator phase, and the electrical resistivity is saturated by edge conduction at quite low $T$. When considering both the SMD and the SOI, the spin order gap was suppressed by the SOI, and gaps with different sizes opened in the left and right Dirac cones. This phase transition leads to distinct changes in microwave conductivity, such as a discontinuous jump and a peak structure.

The Coulomb interaction among massless chiral particles harbors unusual emergent phenomena in solids beyond the conventional realm of correlated electron physics. An example of such an effect is excitonic condensation of interacting massless Dirac fermions, which drives spontaneous mass acquisition and whose exact nature remains actively debated. Its precursor fluctuations growing prior to the condensate have been suggested by a recent nuclear magnetic resonance study in an organic material, hosting a pair of two-dimensional (2D) tilted Dirac cones at charge neutrality. Here, we theoretically study the excitonic transition in 2D tilted cones to understand the electron-hole pairing instability as functions of temperature ($T$), chemical potential ($\mu$), and in-plane magnetic field ($H$). By solving a gap equation within a weak-coupling treatment and incorporating self-energy effects due to the Coulomb interaction through a renormalization-group technique, we calculate excitonic instability in a $T\text{−}\mu \text{−}H$ parameter space, and find that the pairing is promoted as $H$ is increased but suppressed as $\mu$ moves away from the charge-neutrality point. We show that these findings are explained by enhanced or degraded Fermi-surface nesting between the Zeeman-induced pockets connecting the two tilted cones. Furthermore, to evaluate the precursor excitonic fluctuations in relation to this diagram, we consider the Coulomb interaction via a ladder-type approximation and calculate the nuclear spin-lattice relaxation rate, which provides rational ways to understand otherwise puzzling experimental results in the organic material by the μ and $H$ dependence of the instability.

Focusing on the recently-discovered candidate topological insulator $\alpha \text{−}{\text{(BEDT-TSeF)}}_2{\mathrm{I}}_3$—having two-dimensional charge-neutral Dirac cones in a low symmetry lattice—we combine ab initio and extended-Hubbard model calculations to deal with spin-orbit and nonlocal repulsive interactions, and find a realization of an interaction-induced quantum spin Hall (QSH) insulator, similar to the one proposed in the honeycomb lattice under next-nearest-neighbor repulsions. In the absence of repulsive interactions, a topological insulator appears by the spin-orbit coupling and is characterized by a nonzero spin Chern number. By considering up to next-nearest-neighbor repulsions at Hartree-Fock level, the intrinsic spin-orbit gap is found to grow by orders of magnitude and a QSH insulating phase appears that has both a finite spin Chern number and order parameter. Transport coefficients and spin susceptibility are calculated and found to consistently account for most of the experimental findings, including the metal-to-insulator crossover occurring at $\sim 50\mathrm{K}$ as well as the Berry phase change from 0 to $\pi$ under hydrostatic pressure. We argue that such a QSH insulating phase does not necessitate a sizable spin-orbit interaction to generate a large insulating gap, which is highly advantageous for the search of novel topological phases in generic materials having low symmetry lattice and/or small spin-orbit coupling.

Motivated by the results of recent transport and optical conductivity studies, we propose a semi-infinite two-dimensional lattice model for interacting massive Dirac electrons in the pressurized organic conductor $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2{\mathrm{I}}_3$, and address the problem of domain wall conductivity in a charge-ordered insulating phase under realistic experimental conditions. Using the extended Hubbard model at a mean field level, we present results of extensive numerical studies around the critical region of the model, reporting on the resistivity and optical conductivity calculated by means of the Nakano-Kubo formula. We find that the activation gap extracted from the resistivity data can be much smaller than the optical gap in the critical region, which is induced by metallic conduction along a one-dimensional domain wall emerging at the border of two charge-ordered ferroelectric regions with opposite polarizations. The data are consistent with the observed transport gap in real $\alpha \text{−}{\left(\mathrm{BEDT}\text{−}\mathrm{TTF}\right)}_2{\mathrm{I}}_3$ samples that is reduced remarkably faster than the optical gap upon suppressing charge order with pressure. Our optical conductivity also reveals an additional shoulderlike structure at low energy inside the gap, which is argued to be directly relevant to the metallic bound states residing on the domain wall.

The origin of charge order melting is identified by using the real space dependent mean-field theory in the extended Hubbard model describing an organic Dirac electron system α-(BEDT-TTF)₂I₃. In this model, the width of a domain wall which arises between different types of the charge ordered phase exhibits a divergent increase with decreasing the strength of electron–electron correlations. By analyzing the finite-size effect carefully, it is shown that the divergence coincides with a topological transition where a pair of Dirac cones merges in keeping with a finite gap. It is also clarified that the gap opening point and the topological transition point are different, which leads to the existence of an exotic massive Dirac electron phase with melted-type domain wall and gapless edge states. The present result also indicated that multiple metastable states are emerged in massive Dirac Electron phase. In the trivial charge ordered phase, the gapless domain-wall bound state takes place instead of the gapless edge states, accompanying with a form change of the domain wall from melted-type into hyperbolic-tangent-type.

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.