Abstract
We study the algebraic structure of the Dirac fermion state in the organic conductor, \alpha-(BDET-TTF)_2I_3. We find a pair of generators for the Hamiltonian of \alpha-(BDET-TTF)_2I_3 that describes the chirality of Dirac fermions. The phase parameters associated with those generators have an intimate and simple relationship with the positions of the Dirac points in the Brillouin zone. By making use of the form of the generators, a reduced form of the Hamiltonian is constructed that shares some characteristic features of the Dirac fermions with \alpha-(BDET-TTF)_2I_3. For the reduced Hamiltonian we present the analytic expression for the Dirac point position that sits at arbitrary point in the Brillouin zone determined by the hopping parameters.
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