Ring structures fabricated from HgTe/HgCdTe quantum wells have been used to study AharonovBohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe non-monotonic 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 magneto-conductance for a multichannel ring structure within the Landauer-Büttiker formalism. In the early 1980s it was shown that a quantum mechanical system acquires a geometric phase for a cyclic motion in parameter space. This geometric phase under adiabatic motion is called Berry phase [1], while its later generalization to include non-adiabatic motion is known as Aharonov-Anandan phase [2]. A manifestation of the Berry phase is the well known AharonovBohm (AB) phase [3] of an electrical charge which cycles around a magnetic flux. Aside from the AB effect, the first experimental observation of the Berry phase was reported in 1986 for photons in a wound optical fiber [4]. Another important Berry phase effect is the AharonovCasher (AC) effect [5], which has been proposed to occur when an electron propagates in a ring structure in an external magnetic field perpendicular to the ring plane in the presence of SO interaction [6].This AC effect can be seen when two partial waves move around the ring in different directions. They will acquire a phase difference which depends on the spin orientation with respect to the total magnetic field B tot = B ext + B ef f and the path of each partial wave. B ef f is the effective field induced by the SO interaction. The phase difference is approximately [6] where s =↑ and ↓ denote parallel and anti-parallel orientation to B tot , b = +1 for s =↑ and b = −1 for s =↓, and the superscript −(+) denotes a clockwise (counterclockwise) evolution, respectively. In the above equations, α is the SO parameter, r the ring radius, m * the effective electron mass and θ the angle between the external ( B ext ) and the total magnetic field B tot . For both equations, the first term on the right hand side can be identified with the AB phase and the second term of Eq. (1) with the geometric Berry or Aharonov-Anandan phase. The second term in Eq. (2) represents the dynamic part of the AC phase, i.e. the phase of a particle with a magnetic moment that moves around an electric field. From the expressions above, it can be seen that an increase of the AC phase will lead to a phase change that increases continuously with α, whereas the contribution due to the geometric phase results in a phase shift limited to ∆ϕ geom ≤ π.Both the AC phase [7] and the geometric phase [8, 9] depend on the SO interaction. As a result, one expects a complicated non-monotonic interference pattern as a function of magnetic field and SO interaction strength. So far, to our knowledge, apart from the AB effect no direct observation of phase related effects in solid state systems has been reported. Rec...

The transport properties of a magnetic two dimensional electron gas consisting of a modulation doped n type Hg0.98Mn0.02Te /Hg0.3Cd0.7Te quantum well, QW, have been investigated. By analyzing the Shubnikov-de Haas oscillations and the node positions of their beating patterns, we have been able to separate the gate voltage dependent Rashba spin-orbit splitting from the temperature dependent giant Zeeman splitting. It has been experimentally demonstrated that the Rashba spinorbit splitting is larger than or comparable to the sp − d exchange interaction induced giant Zeeman splitting in this magnetic 2DEG even at moderately high magnetic fields.

The transport properties of micrometer scale structures fabricated from high-mobility HgTe quantum-wells have been investigated. A special photoresist and Ti masks were used, which allow for the fabrication of devices with characteristic dimensions down to 0.45 µm. Evidence that the transport properties are dominated by ballistic effects in these structures is presented. Monte Carlo simulations of semi-classical electron trajectories show good agreement with the experiment.

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