Tuning the RKKY interaction in bilayer graphene: the pivotal role of electron–phonon coupling and external fields

In this work, the effects of electron-phonon coupling are uniquely integrated in a state-of-the-art study of RKKY interaction in simple bilayer graphene. We investigate the Holstein model Hamiltonian using Green's function approaches, taking into account three crucial parameters: an interlayer bias voltage, a perpendicular magnetic field, and a chemical potential to regulate electron density. We provide a detailed perspective of the behavior of the RKKY exchange interaction under different conditions by first calculating the static spin susceptibility and then computing the interaction with great precision. Our new method reveals how important the electron-phonon interaction strength is in forming this magnetic coupling, and the results, which are backed up by a thorough graphical analysis, show how it varies subtly depending on the parameters that are included. These discoveries open the door for creative approaches to the creation of adjustable quantum systems for next-generation technologies and greatly advance our understanding of indirect exchange in two-dimensional materials.