Twisted charged particles in the uniform magnetic field with broken symmetry

We present a theoretical description of charged particles with nonzero projection of the orbital angular momentum (OAM) in a uniform magnetic field with broken symmetry of the vector potential. The wave functions we find naturally account for the asymmetry through the continuous gauge parameter and are a generalization of the commonly used Laguerre-Gauss states. We analyze the asymmetric Hamiltonian from an algebraic point of view and show how the OAM projection of the twisted state is modified by symmetry breaking. We provide analytical frameworks for properties of the asymmetric states, such as energy, RMS size, and Cazimir invariant, and discuss advantages of the proposed description.