One-electron quantum ring of non-uniform thickness in magnetic field

Effect of variation of the central-hole depth and the axial anisotropy on the AB oscillations in a wide nanoring

“…However, further numerical analysis of more realistic 3D model of non-uniform crater-like QRs shows that, although the real QR shape differs strongly from an idealized circular-symmetric narrow ring structure, AB-type oscillations in the magnetization survive [8,10]. A 3D exactly solvable model of the crater-like one-electron QR, proposed recently in reference [11,12] provides an explanation of the stability of the AB oscillations with respect to structural nonuniformities. In the presence of the magnetic field applied along the symmetry axis, more probable electron paths in this model are clustered close to the crater's rim being similar to those in quasi-onedimensional quantum rings independently on the crater width.…”

“…It is possible to extend the model considered in reference [11,12] in order to analyse additionally the effect of the variation of the width and the depth of the central-hole on the AB oscillations. In this extended model, proposed in this paper, the crater's height between the central hole and the outer border…”

“…A 3D exactly solvable model of the crater-like one-electron QR, proposed recently in reference [11,12] provides an explanation of the stability of the AB oscillations with respect to structural nonuniformities. In the presence of the magnetic field applied along the symmetry axis, more probable electron paths in this model are clustered close to the crater's rim being similar to those in quasi-onedimensional quantum rings independently on the crater width.…”

“…It is possible to extend the model considered in reference [11,12] in order to analyse additionally the effect of the variation of the width and the depth of the central-hole on the AB oscillations. In this extended model, proposed in this paper, the crater's height between the central hole and the outer border grows linearly with different slopes at different radial directions in the case of non-uniform structure, while the corresponding slopes in the central-hole at all radial directions are zero.…”

“…However, any slight non-uniformity produced by a single radially directed valley or single hill suppresses the oscillations of several lower levels due to the localization of the corresponding rotational states. Nevertheless, when the nonuniformity becomes substantial due to the presence of multiple valleys and hills, the AB oscillations generated by the external magnetic field becomes again possible owing to the electron tunnelling through thin potential barriers.It is possible to extend the model considered in reference [11,12] in order to analyse additionally the effect of the variation of the width and the depth of the central-hole on the AB oscillations. In this extended model, proposed in this paper, the crater's height between the central hole and the outer border…”