Off-axis magneto-donor impurity in a non-uniform height quantum ribbon

•We report the off-axis donor eigenenergies in a non-uniform height quantum ribbon.•The height dependence with polar angle is modeled trough a two-parametric function.•The energy structure is obtained via matrix diagonalization scheme.•The energy structure is very sensitive to the number and depth of the protuberances.•The number of protuberances defines the degeneration degree of vibrational states in the Aharonov–Bohm pattern.

Single electron and off-axis neutral donor in non-uniform height quantum ribbon under threading external magnetic field is analyzed. The quantum ribbon height dependence with polar angle is modeled trough the two-parametric function. One of these parameters define the number of protuberances and the other one allows us to exert control on the structural deformation depth. By considering quantum ribbons with very small height-to-base aspect ratio, it was possible to obtain the energy structure through the adiabatic procedure. The corresponding angular dependent Schrödinger equation can be solved in the framework of the exact diagonalization method. The results of calculation show that the Aharanov–Bohm oscillation patterns are very sensitive against changes of the quantum ribbon structural parameters.