We examine the Dirac point of α type organic conductor described by a tight binding model with a \(4\times 4\) matrix. The Dirac point between a conduction band and a valence band, is calculated without diagonalization of the Hamiltonian, by focusing on α-(BEDT-TTF)2I3 containing four molecules (A, A\('\), B, C) in a unit cell. With varying uniaxial pressure, the Dirac point in the Brillouin zone moves from \(Y\) point to Γ point at which the merging of two Dirac points occurs. The role of the transfer energy \(t_{aj}\) (\(j=1,2,3\)) along the stacking axis is examined by comparing with the simplified case without \(t_{aj}\). The necessary condition to find the Dirac point in the \(4\times 4\) matrix Hamiltonian is discussed in terms of the inversion symmetry between A and A\('\).

The possible quantum Hall ferromagnet at a filling factor $\nu =0$ is investigated for the zero-energy (N=0) Landau level of the two dimensional massless Dirac fermions in $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure with tilted cones and a twofold valley degeneracy resulting from time-reversal symmetry. In the case of the Dirac cones without tilting, the long-range Coulomb interaction in the N=0 Landau level exhibits the SU(2) valley-pseudo-spin symmetry even to the order $O(a/l_{\rm H})$, in contrast to $N \ne 0$ Landau levels, where $a$ and $l_{\rm H}$ represent the lattice constant and the magnetic length, respectively. Such a characteristic comes from a fact that zero-energy states in a particular valley are restricted to only one of the spinor components, whereas the other spinor component is necessarily zero. In the case of the tilted Dirac cones as found in $\alpha$-(BEDT-TTF)$_2$I$_3$, one obtains a non-zero value of the second component and then the ackscattering processes between valleys becomes non-zero. It is shown that this fact can lead to easy-plane pseudospin ferromagnetism (XY-type). In this case, the phase fluctuations of the order parameters can be described by the XY model leading to Kosterlitz-Thouless transition at lower temperature. In view of these theoretical results, experimental findings in resistivity of $\alpha$-(BEDT-TTF)$_2$I$_3$ are discussed.Comment: 15 pages, 4 figure

A role of umklapp scattering has been examined for two-coupled chains with both forward and backward scattering by applying the renormalization group method to the bosonized Hamiltonian. It has been found that a state with relevant interchain hopping changes into a state with irrelevant (confined) one when the magnitude of umklapp scattering becomes larger than that of interchain hopping. The critical value of umklapp scattering for such a confinement-deconfinement transition is calculated as the function of interchain hopping and intrachain interactions. A crossover from one-dimensional regime into that of coupled chains is also shown with decreasing temperature.

In this paper, recent theoretical developments on Anderson localization in one-dimensional electron systems are reviewed. First, the theories for noninteracting systems are summarized together with the various results based on numerical simulation. Special attention will be paid to the dynamical structure of the systems. The second part discussed Anderson localization in interacting electron systems by the phase Hamiltonian, and the close relationship between the localization and the impurity pinning of charge density wave is demonstrated. Results of the numerical simulations by quantum Monte Carlo technique are also presented.