Polar coherent states in bilayer graphene under a constant uniform magnetic field

In this work, the interaction of the electrons in bilayer graphene with a constant, homogeneous magnetic field perpendicular to its surface is analyzed. A symmetric gauge is used for the electromagnetic vector potential, which leads to the use of polar coordinates. The symmetries associated with the Hamiltonian that describes this system are applied to explain some fundamental properties, such as the spectrum and the integer pseudo-spin character of the eigenfunctions. The current densities associated with the bilayer Hamiltonian have been calculated in both Cartesian and polar coordinates showing that they are gauge invariant. Additionally, the appropriate coherent states of this system have been derived as eigenstates of a suitable annihilation operator with complex eigenvalues. The local current densities of these coherent states have been calculated, revealing a type of radial component interference effect that has been overlooked until now. Some of these newly presented results are illustrated graphically.