Berry Curvature of the Dirac Particle in $α$-(BEDT-TTF)$_2$I$_3$

Abstract: We examine several properties of the Berry curvature for the organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ consisting of four bands, which exhibits a zero-gap state with Dirac cones. By adding a small potential acting on two molecular sites, which breaks the inversion symmetry, it is shown that the curvature for the Dirac particles displays a pair of peaks with opposite signs and that each peak increases with decreasing potential. The Berry curvature originating from the property of the wave function is analyzed using a reduced Hamiltonian with a 2x2 matrix based on the Luttinger-Kohn representation, which describes a pair of Dirac particles between the conduction band and the valence band. Two types of velocity fields in the reduced Hamiltonian, whose vector product gives the Berry curvature, rotate around the Dirac point as a vortex. It is also shown that the other bands exhibit another pair of peaks of Dirac particles with a tendency toward merging.