Magnetization and magnetic susceptibility of InAs nano-rings

In this work, we investigate theoretically the magnetic susceptibility of the three-dimensional cut-torus-shaped quantum rings. The calculations are carried out for the realistic three-dimensional model of InAs/GaAs nano-rings with the hard-wall confinement potential, three-dimensional effective one-electronic-band Hamiltonian with position and energy-dependent effective mass, and Ben Daniel–Duke boundary conditions. This allows us to describe the penetration of the magnetic field into the torus region. At zero temperature, the ringʹs differential susceptibility demonstrates delta-like paramagnetic peaks, which are generated by aperiodic oscillations of magnetization. With increasing temperature, the peaks gradually transform into Lorenz-shaped peaks and then disappear. As opposed to meso-scopic quantum rings we found a dependence of the peakʹs amplitude on the dimensions of the rings.