Direct Observation of the Aharonov-Casher Phase

Ring structures fabricated from $\mathrm{HgTe}/\mathrm{HgCdTe}$ quantum wells have been used to study Aharonov-Bohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe nonmonotonic phase changes indicating that an additional phase factor modifies the electron wave function. We associate these observations with the Aharonov-Casher effect. This is confirmed by comparison with numerical calculations of the magnetoconductance for a multichannel ring structure within the Landauer-Büttiker formalism.

Figure 1

Microscope image of the sample layout without top gate electrode. The average ring radius is $1\mu \mathrm{m}$ and the width of each arm is 300 nm. Inset (a): the symmetry point is estimated from the subband population differences as a function of the applied gate voltage, i.e., $V_{\mathrm{Gate}}\approx -2.57\mathrm{V}$. Inset (b) shows the conductance oscillations at $V_{\mathrm{Gate}}=-2.57\mathrm{V}$. The period, $\Delta B=1.3\mathrm{mT}$, is consistent with the ring radius.

Figure 2

Color plot of the conductance fluctuations, maxima (yellow) and minima (blue), as a function of magnetic field and gate voltage. The dashed line indicates ${\Delta }_R=0$ which can be located at $V_{\mathrm{Gate}}=-2.568\mathrm{V}$, based on the mirror symmetry of the conductance around this line.

Figure 3

(a) Near the symmetry point ($V_{\mathrm{Gate}}=-2.568\mathrm{V}$) the interference pattern is unperturbed by the SO interaction. (b) The theoretical calculations for a 6-channel ring show consistent results for the corresponding range of ${\Delta }_R$. Yellow and blue correspond to conductance maxima and minima, respectively.

Figure 4

When the SO interaction is modified via the gate voltage, a shift of the conductance maxima (yellow) can be observed due to the Aharonov-Casher phase (a). In (b), the theoretical results for the conductance in a 6-channel ring as a function of the Rashba energy and $B_{\mathrm{ext}}$ are shown. The scaling of the $y$ axis allows a direct comparison of the experimental and theoretical data.