Non-perturbative macroscopic theory of interfaces with discontinuous dielectric constant

Discontinuity of dielectric constants at interfaces and surfaces is a common feature of nanostructures and semiconductor heterostructures. Near such interfaces, a charged particle experiences a singular self-interaction potential, which can be interpreted as interaction with fictitious mirror charges. The singularity of this interaction at the interface presents an obstruction to a perturbative approach.  We develop a non-perturbative theory that provides a self-consistent description of carrier propagation across an interface with dielectric discontinuity. The approach is based on current-density conservation at the interface and formulated in terms of general boundary conditions (GBC) for the wave function, characterized by a single phenomenological parameter W.[1]. Using these results, we describe the photo effect at the semiconductor/vacuum interface and the energy spectrum of quantum wells (QWs) at the interface with the vacuum or a high-k dielectric. For a surface of liquid helium, we estimate the parameter W, and match the resulting electron spectrum with the existing experimental data and theoretical analysis.

[1] Y. M. Beltukov , A. V. Rodina  , A. Alekseev   and  Al. L. Efros  ^“submitted, http://arxiv.org/abs/2507.15580