Tunable Aharonov-Anandan phase in transport through mesoscopic hole rings

We present a theoretical study of spin-3/2 hole transport through mesoscopic rings that is based on the spherical Luttinger model. A quasi-one-dimensional ring is created in a symmetric two-dimensional quantum well by a singular-oscillator potential for the radial in-plane coordinate. The quantum-interference contribution to the two-terminal ring conductance exhibits an energy-dependent Aharonov-Anandan phase, even though Rashba and Dresselhaus spin splittings are absent. Instead, confinement-induced heavy-hole–light-hole mixing is found to be the origin of this phase, which has ramifications for magnetotransport measurements in gated hole rings.

Figure 1

(Color online) The lowest hole-ring subbands (solid curves) arising from the in-plane ring-potential bound-state level with $n=0$, calculated for $\overline{\gamma }=0.37$, ${\lambda }_d=0.5$, and ${\lambda }_R=10$. The dashed curves are obtained when HH-LH splitting is included but HH-LH mixing is neglected.

Figure 2

(Color online) Two-terminal transport. The holes in scattering states $|\nu ⟩$ are injected via a lead attached at $\phi =0$. Eigenmodes with angular momenta $m_{s\sigma }$ provide propagation channels in the ring. Upon reaching the point $\phi =\pi$, interference and coupling into outgoing scattering states $|\mu ⟩$ occurs.

Figure 3

(Color online) Solid curve: Anomalous component ${\Phi }_G$ of the AA phase appearing in the two-terminal hole-ring transmission. The parameters used in the calculation are the same as in Fig. 1. Dashed curve: Corresponding result obtained when HH-LH mixing is neglected.