Existence and merging of Dirac points in $\alpha$-(BEDT-TTF)$_2$I$_3$ organic conductor

We reexamine the existence and stability conditions of Dirac points between valence and conduction bands of 3/4 filled $\alpha$-(BEDT-TTF)$_2$I$_3$ conducting plane. We consider the usual nearest neigbhor tight binding model with the seven transfer energies that depend on the applied pressure. Owing to the four distinct molecules (A, A', B, C) per unit cell of the Bravais lattice, the corresponding Bloch Hamiltonian is a $4\times4$ matrix ${\cal H}({\bm k})$ for each wave vector $\mathbf{k}$ of the Brillouin zone. In most previous works the study of Dirac points was achieved through direct numerical diagonalization of matrix ${\cal H}({\bm k})$. In this work we develop a novel analytical approach which allows to analyze the existence and stability conditions of Dirac points from the knowledge of their merging properties at time reversal points. Within this approach we can discuss thoroughly the role of each transfer integrals and demonstrate that inversion symmetry is convenient but not necessary.