Are there new concepts for the explanation of the wave-particle duality? 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?
 A: The electromagnetic wave is composed by a huge number of photons. Photons are elementary particles, they have zero mass, are point particles and their energy is characterized by the frequency of the classical wave we observe macroscopically, given by



They do not carry explicitly electric or magnetic fields .
Their wave function is the solution of a quantized version of Maxwell's equation,   which has information of the electromagnetic four vector  potential A and thus the continuity between classical and quantum. The square of the wave function gives the probability of finding a photon at (x,y,z,t). The probability has sinusoidal properties of the same frequency as the electromagnetic wave which emerges from zillions of photons. The way this happens is described for the mathematically inclined in this blog entry.
By the way photon photon interactions are very weak, photons do not bunch because they interact, but because they overlap in space time in such a way as to build up the classical field.

We came to QED and work with the quantization of fields but our verbal expression is from 1920.

Our ( physicists) verbal expression is also from the 1650s when we are talking of thermodynamic quantities, and often the  1679's on gravitational  calculations. Physics has continuity. Our knowledge of the fine structure of matter has not destroyed the elegant structure of thermodynamics. The validation of general relativity did not destroy the elegant structure of classical mechanics. When dimensions are large and the quantities entering the Heisenberg Uncertainty Principle are large enough to always satisfy it, quantum mechanical effects are  ignorable, one uses the classical formulations for their elegance and convenience. One can derive thermodynamic variables from quantum statistical mechanics, but the mathematics of QSM would be a huge unnecessary  calculation burden  in designing a car motor.
When classical Maxwell equation solutions are appropriate to a problem , they are much easier to calculate and handle and are used extensively.

Are there new concepts for the explanation of the wave-particle duality?

In my opinion the concepts are there since quantum field theory was used for calculations in the quantum regime. It is just that the language has gotten esoteric, math dependent, and it is easy to make oversimplifications in popularizing modern physics.
If by new you mean the acceptance of the disparate use of the word "particle" and "wave"  in classical and quantum fields , yes, physicists accept that in the quantum regime one should have a name for a quantum mechanical entitity, quarticle maybe  :) , that in some boundary conditions resembles the kinematics of classical point particles, and in some boundary conditions the probability of measurement is periodic with a wave structure .
A: @anna v: It's not an answer but it's to long for comments.
I could not stick together some facts.
1st: "The electromagnetic wave is composed by a huge number of photons." with what I fully agree. But the following sentence "They (photons) do not carry explicitly electric or magnetic fields." I could not stick to the first. Why? How a radio wave could be a EM field without the photons are having a EM field? There is a huge difference between radio waves and photons EM wave. Electrons will be accelerated in the antenna rod and they emit photons. Electrons are doing this more or less synchronous with the AC from the antenna generator. That is the reason of the radio wave with its amplitude (depends only from the rod length) and its frequency (depends from the generator and more or less from the rod length). Some evidence for this is the fact that the receiver not at all needs an antenna with the amplitudes length of the emitter. It's enough to use some tiny piece of conductor that will be hit by a small stream of photons.
2nd: Electrons in the antenna in total are accelerated parallel to the antennas rod. The resulting magnetic field is perpendicular to the rod and the resulting electric field (except the rods end) is again parallel to the rod. This situation changes rapidly. There is some divergence of the radio wave. Does it come it from the interaction of the photons or better to say from the EM fields of the photons?
3rd: What makes the change between the nearfield radio wave with it shift difference of 90° between electric and magnetic component and the farfield without this difference? Are the single photons are responsible for this state?
4th: What about the bouncing (I couldn't find at the moment the right word, it sounds like what I wrote) of photons from far away stars? Two photons are traveling together. How they can do this without interaction of their EM fields?
