Strongly anisotropic Rytova-Keldysh interaction and the ground state of 2D excitons

Andrei Galiautdinov

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arXiv · 2606.23033

Strongly anisotropic Rytova-Keldysh interaction and the ground state of 2D excitons

Andrei Galiautdinov

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Abstract

The classic Rytova-Keldysh potential describes the non-local dielectric screening of Coulomb interactions in ultrathin two-dimensional (2D) materials. Recently, the corresponding potential for arbitrary in-plane anisotropy was derived in integral form, with numerical studies suggesting that an effective isotropic approximation remains robust for highly directional systems. In this paper we provide the analytical foundation for these observations by mapping the complete spatial landscape of the strongly anisotropic Rytova-Keldysh interaction. By applying the method of steepest descent and momentum-space coordinate scaling to the exact one-dimensional integral representation, we derive closed-form asymptotic expressions for the potential across all spatial regimes. We find that the intermediate-range screening exhibits a non-trivial amplitude scaling driven by the direction of weakest polarizability, while the short-range limit produces an anisotropic logarithmic well governed by the geometric mean of the principal polarizabilities. Finally, utilizing this short-range confinement, we implement an anisotropic Gaussian variational ansatz to solve the Wannier equation, providing a closed-form analytical expression for the exciton ground-state binding energy that explicitly captures the competition between the effective mass and dielectric tensors.

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Andrei Galiautdinov. 2026-06-22. Strongly anisotropic Rytova-Keldysh interaction and the ground state of 2D excitons. https://arxiv.org/abs/2606.23033

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