  A continuous deformation of a Hamiltonian possessing at low energy two Dirac
points of opposite chiralities can lead to a gap opening by merging of the two
Dirac points. In two dimensions, the critical Hamiltonian possesses a
semi-Dirac spectrum: linear in one direction but quadratic in the other. We
study the transport properties across such a transition, from a Dirac
semi-metal through a semi-Dirac phase towards a gapped phase. Using both a
Boltzmann approach and a diagrammatic Kubo approach, we describe the
conductivity tensor within the diffusive regime. In particular, we show that
both the anisotropy of the Fermi surface and the Dirac nature of the
eigenstates combine to give rise to anisotropic transport times, manifesting
themselves through an unusual matrix self-energy.
