Electron localization and optical absorption of polygonal quantum rings

Abstract

We investigate theoretically polygonal quantum rings and focus mostly on the triangular geometry where the corner effects are maximal. Such rings can be seen as short core-shell nanowires, a generation of semiconductor heterostructures with multiple applications. We show how the geometry of the sample determines the electronic energy spectrum, and also the localization of electrons, with effects on the optical absorption. In particular, we show that irrespective of the ring shape low-energy electrons are always attracted by corners and are localized in their vicinity. The absorption spectrum in the presence of a magnetic field shows only two peaks within the corner-localized state domain, each associated with different circular polarization. This picture may be changed by an external electric field which allows previously forbidden transitions, and thus enables the number of corners to be determined. We show that polygonal quantum rings allow absorption of waves from distant ranges of the electromagnetic spectrum within one sample.

Conductance oscillations of core-shell nanowires in transversal magnetic fields

“…Note that at a fixed energy, depending on m, k m can be real or imaginary. The real values describe open channels, propagating from one lead to another lead, whereas the imaginary values describe closed (or evanescent) channels which are states bound around the scattering region [17]. Although we are formally treating the leads as semiinfinite extensions of the CSN, with the same circular symmetry, in fact the wave functions (1) are important only at (or close to) the boundaries z l .…”

“…Electrons confined in prismatic CSNs may form conductive channels along the sharp edges [2,[12][13][14][15][16][17]. Rich quantum transport phenomena have been observed in CSNs, e.g., flux periodic, similar to Aharonov-Bohm (AB), magnetoconductance oscillations [6,18], single electron tunneling, or electron interference [6,11].…”

Multi-domain electromagnetic absorption of triangular quantum rings

“…The energy levels of polygonal quantum rings show a unique degeneracy pattern which depends only on the number of corners [20,21]. In the case of symmetric (restricted internally and externally by regular triangles) rings and zero magnetic field the ground state is twofold (spin) degenerate, the second and third levels are fourfold (spin and orbital momentum) degenerate and the fourth level is again twofold degenerate, Fig.…”

“…The triangular samples are achieved by imposing polygonal boundaries within the disk, and excluding from the grid all sites situated outside those boundaries. We have recently used this method to describe various polygonal rings [20]. In the position representation the Hilbert space is spanned by vectors |kjσ , where the indexes k and j correspond to discretized radial r = r k and angular φ = φ j coordinates, separated by intervals δr and δφ, and σ is the spin projection on the z direction.…”

“…In the case of polygonal rings the ground state is also twofold degenerate, but higher levels are either two-or fourfold degenerate and the degeneracy pattern is determined by the number of corners [21]. Depending on the ring shape, corner-localized states may be separated from side-localized ones by an energy gap [20].…”