<p>We theoretically study the quantum confinement effects and transport prop- erties of quantum ring (QR) systems. In particular, we investigate QRs made out of the following materials: single-layer graphene (SLG), single- layer transition-metal dichalcogenides (TMDs) and narrow-gap semiconduc- tor quantum wells (SQWs). Via perturbation theory and assuming that the ring aspect ratio is small, the general subband dispersion relations of these hard-wall ring confined systems are determined. These dispersion results agree with and extend on previous works. We discover the necessity of including both a size-quantisation energy and an angular momentum dependent energy shift to the dispersion equation due to their sizeable impact on the conductance of the system. The topological properties of these QR systems is also investigated. We find that QR confinement of materials may destroy the topologically non-trivial properties of states. The topological phase can be recovered when the band structure is inverted and the confined material parameters satisfy certain critical widths and gap limits. An analytical expression of the conductance for QRs (with symmetrically- arranged leads), in the presence of the perpendicular magnetic field piercing the centre of the ring, is derived. We study the geometric (i.e. Berry) and dynamic phases of the system that arise from the interference of partial waves in the ring branches. We discover that the Berry phase is modified by a correction term that arises purely from the quantum confinement of the materials. This has generally not been taken into account by previous studies. The explicit analytical expressions of the phase correction term are derived and shown to be proportional to the angular momentum dependent energy shift, present in the dispersion relations, for lead injection energies close to the subband energy. Overall, this study finds that the material-dependent phase plays a significant role in both the dispersion relation and the conductance of QRs and thus provides a useful insight for future experimental efforts with regards to transport in QR systems.</p>
Higher Order Pancharatnam-Berry Phase and the Angular Momentum of Light
