  We study analytically and numerically dynamics and eigenstates of two
electrons with Coulomb repulsion on a tight-binding lattice in one and two
dimensions. The total energy and momentum of electrons are conserved and we
show that for a certain momentum range the dynamics is exactly reduced to an
evolution in an effective narrow energy band where the energy conservation
forces the two electrons to propagate together through the whole system at
moderate or even weak repulsion strength. We argue that such a mechanism of
electron pair formation by the repulsive Coulomb interaction is rather generic
and that it can be at the origin of unconventional superconductivity in twisted
bilayer graphene.
