there is no specific quantum theory that explains the Meissner effect in superconductors analogous to the BCS (Bardeen-Cooper-Schrieffer) theory, which explains conventional superconductivity.
The Meissner effect is a fundamental property of superconductors where they expel magnetic fields from their interior when cooled below a certain critical temperature. This effect arises due to the formation of Cooper pairs, which are pairs of electrons with opposite spins and momenta. The BCS theory successfully explains the formation of these Cooper pairs and the onset of superconductivity in conventional superconductors.
However, the BCS theory does not explicitly address the Meissner effect. Instead, the Meissner effect is commonly understood in terms of the Ginzburg-Landau theory, which provides a phenomenological description of superconductivity. This theory incorporates the concept of an order parameter, which characterizes the transition from a normal to a superconducting state.
In the Ginzburg-Landau theory, the Meissner effect arises from the spontaneous symmetry breaking of the electromagnetic gauge symmetry in the superconducting state. This symmetry breaking leads to the expulsion of magnetic fields and the formation of a superconducting current on the surface of the material.
It is worth noting that there are other types of superconductors, such as high-temperature superconductors, where the BCS theory is not applicable. The mechanisms underlying superconductivity in these materials are still an active area of research, and a comprehensive theory that explains both the formation of Cooper pairs and the Meissner effect in these unconventional superconductors is yet to be fully established.
However, it is important to keep in mind that scientific knowledge is continually advancing, and there may have been developments since I'm not interested in that topic as much as i used to and my answer might be a bit outdated that could provide new insights or theories explaining the Meissner effect in superconductors. It is advisable to consult recent scientific literature and research for the most up-to-date information on this topic.