New quantum-mechanical phenomenon in a model of electron-electron interaction in graphene

TL;DR

This paper uncovers a novel quantum phenomenon in graphene, revealing new localized states arising from electron interactions, with potential experimental observability due to their finite lifetime.

Contribution

It introduces a previously overlooked set of wave functions in a quantum model of electron interactions in graphene, showing the emergence of localized states at large times.

Findings

Discovery of new wave functions with definite energy

Analytical asymptotics of localized states

Lower bound estimate for state lifetime

Abstract

A quantum mechanical model of two interacting electrons in graphene is considered. We concentrate on the case of zero total momentum of the pair. We show that the dynamics of the system is very unusual. Both stationary and time-dependent problems are considered. It is shown that the complete set of the wave functions with definite energy includes the new functions, previously overlooked. The time evolution of the wave packet, corresponding to the scattering problem setup, leads to the appearance of the localized state at large time. The asymptotics of this state is found analytically. We obtain the lower bound of the life time of this state, which is connected with the breakdown of the continuous model on the lattice scale. The estimate of this bound gives one a hope to observe the localized states in the experiment.