Abstract
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.
Highlights
The interactions of electrons in narrow band structures play an important role in various physical processes
The interest in narrow band structures with strong Coulomb electron-electron interactions has been inspired by the observation of unconventional superconductivity in magic-angle twisted bilayer graphene (MATBG) [4]
The presented analytical and numerical analysis definitely shows that a specific energy dispersion law of free electrons in narrow bands leads to the possibility of pair formation induced by Coulomb repulsion between electrons
Summary
The interactions of electrons in narrow band structures play an important role in various physical processes. Extensive numerical studies by quantum-chemistry methods show the appearance of flat lowest-energy minibands [8,9,10,11] These bands are rather narrow and the Coulomb interactions play an important role as pointed out in early theoretical studies [12]. In the case of long-range Coulomb interactions, this mathematical simplification is not possible and the physical situation, especially in two dimensions with potentially chaotic dynamics in the relative coordinate, is more complicated Our results take these complications into account and show the appearance of pairing of two electrons induced even by a moderate Coulomb repulsion with ballistic pairs propagating over the whole system size. We show that this effect strongly depends on the values of the conserved center of mass momenta
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