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Attractive Coulomb interaction of 2D Rydberg excitons

We analyze theoretically the Coulomb scattering processes of highly excited excitons in the direct bandgap semiconductor quantum wells. We find that contrary to the interaction of ground state excitons the electron and hole exchange interaction between excited excitons has an attractive character both for $s$- and $p$-type 2D excitons. Moreover, we show that similarly to the three-dimensional (3D) highly excited excitons, the direct interaction of 2D Rydberg excitons exhibits van der Waals type long-range interaction. The results predict the linear growth of the absolute value of exchange interaction strength with an exciton principal quantum number, and point the way towards enhancement of optical nonlinearity in 2D excitonic systems.