See this answeranswer and the comments. There is an explanation how occures fringes due to the EM field from the surface of the slit or wire: https://commons.m.wikimedia.org/wiki/File:Moellenstedt_biprisma_voltage_shadow.JPG It shows the influence of an electrical field to fringes.
https://commons.m.wikimedia.org/wiki/File:Moellenstedt_biprisma_schematic_arrangement.JPG This shows how experiment with electrons was arranged in generally.
As a result you may find out that the potential of the material which forms the slits is responsible for changes in fringes dimensions. Ergo can we say that the potential is responsible for the fringes at all?
And therethere is a relative question too: Whenever we can observe photons immediate, they are particles. That includes that photons have a inner structure with periodically varying electric and magnetic fields. The EM field of a radio antenna exists because this field consists a lot of photons with their periodically changing EM components. Whenever we observe statistical manifestation of interaction between photons and certain physical states (most of them based on diffraction) we interpret the fringes on a screen as waves manifestation of particles. And at the same moment we always emphasize that these states are not observable. It's an interpretation of what we see. To interpret the fringes as a result of the interaction between photons (or electrons, ...) and the EM field of certain physical states is not common but has some charme. No more need in interference of an electron (or photon) with itself in the single particle experiments. No more sentences like "we can mathematically write down but not describe what happens".
Yes we always describe that photons interfer EM fields (static between condenser plates or in interaction with other particles or especially with other photons (photon bunching)) but we don't articulate that. We repeat what physicists understood 90 years ago. We came to QED and work with the quantization of fields but our verbal expression is from 1920.
Are there new concepts for the explanation of the wave-particle duality?