Aharonov-Casher effect in a two-dimensional hole ring with spin-orbit interaction

We study the quantum interference effects induced by the Aharonov-Casher phase in a ring structure in a two-dimensional heavy-hole (HH) system with spin-orbit interaction realizable in narrow asymmetric quantum wells. The influence of the spin-orbit interaction strength on the transport is analytically investigated. These analytical results allow us to explain the interference effects as a signature of the Aharonov-Casher Berry phases. Unlike previous studies on electron two-dimensional Rashba systems, we find that the frequency of conductance modulations as a function of the spin-orbit strength is not constant but increases for larger spin-orbit splittings. In the limit of thin channel rings (width smaller than Fermi wavelength), we find that the spin-orbit splitting can be greatly increased due to the quantization in the radial direction. We also study the influence of a magnetic field considering both the limits of small and large Zeeman splittings.

Figure 1

(Color online) One channel ring of radius $r_0$ subject to spin-orbit coupling in the presence of an additional magnetic field ${\mathbf{B}}_0$. An electron (hole) spin traveling around the ring acquires phase due to the applied out-of-plane magnetic field (gray arrow) and the spin-orbit in-plane magnetic field (momentum dependent, green solid-line arrows for holes and dashed-line arrows for electrons) caused by the spin-orbit interaction. The spin-orbit in-pane magnetic field is different for holes and electrons.

Figure 2

Conductance-modulations in a 1D ring as a function of the dimensionless spin-orbit strength $Q{k}_F{r}_0$ (note that state-of-the-art experimental systems are in a regime where $Q{k}_F{r}_0\lesssim 0.1$): (a) thin heavy-hole ring (solid line) is compared to the Rashba ring (dashed line), ${\left(k_{F}w\right)}^2=1∕2$; (b) and (c) thick heavy-hole ring (solid line) is compared to the Rashba ring (dashed line).

Figure 3

Conductance-modulations in a 1D ring as a function of magnetic field and dimensionless spin-orbit strength (gate voltage). Left plot corresponds to heavy hole spin-orbit interaction, and right plot corresponds to Rashba spin-orbit interaction: $r_0=1\mu \mathrm{m}$, $1∕k_F\sim 4\mathrm{nm}$, $g=20$, and $m^{*}=0.031m$. Parameters of the left plot correspond to the experimental setup in Ref. 15.

Figure 4

Conductance modulations in a 1D ring as a function of magnetic field and dimensionless spin-orbit strength (gate voltage) with enhanced Zeeman splitting (multiplied by ${10}^3$). Left plot corresponds to heavy hole spin-orbit interaction, and right plot corresponds to Rashba spin-orbit interaction: $r_0=1\mu \mathrm{m}$, $1∕k_F\sim 4\mathrm{nm}$, $g=20$, and $m^{*}=0.031m$. Parameters of the left plot could correspond to the experimental setup in Ref. 15 with the magnetic field (range $1–10\mathrm{T}$) applied under some small angle.