Interaction mediated electron transport within the many-body tunnelling Hamiltonian

For a non-superconducting system and in the spirit of the transfer or tunnelling Hamiltonian formalism, an expression for the electronic tunnelling current through an insulating barrier is calculated, explicitly taking into account the effects of electron-electron interactions that can persist across the barrier. In the presence of a single tunnelling barrier, the exact Hamiltonian is projected onto the subspaces of the ‘left’ and ‘right’ conducting leads. In the weak-tunnelling limit, the well-known tunnelling Hamiltonian is recovered, along with an additional term. This additional term originates from the projection of the electron-electron interaction onto each subspace and corresponds to a correlated or interaction-mediated tunnelling. It is shown that the tunnelling current in this approximation is related to—in addition to the single-particle density of states—the two-particle spin-spin and density-density susceptibilities. The signatures of these terms have been observed in scanning tunnelling microscope experiments on atomic spin chains.