Experimental Demonstration of the Time Reversal Aharonov-Casher Effect

Abstract

We demonstrate the time reversal Aharonov-Casher (AC) effect in small arrays of mesoscopic semiconductor rings. By using an electrostatic gate we can control the spin precession rate and follow the AC phase over several interference periods. We show that we control the precession rate in two different gate voltage ranges; in the lower range the gate voltage dependence is strong and linear and in the higher range the dependence in almost an order of magnitude weaker. We also see the second harmonic of the AC interference, oscillating with half the period. We finally map the AC phase to the spin-orbit interaction parameter α and find it is consistent with Shubnikov-de Haas analysis.PACS numbers: 85.35. Ds,71.70.Ej Spintronics is the art of generating, manipulating and detecting the spin of electrons in solid state electronic devices. While this has traditionally involved ferromagnetic materials and external magnetic fields, we can also manipulate spins with purely electric fields via the spin-orbit interaction (SOI) between a moving spin particle and an electric field. In particular, we can design a semiconductor heterostructure with a two dimensional electron gas (2DEG) which has an internal electric field perpendicular to the 2DEG due to an asymmetric quantum well. We will then have SOI even without external electric fields. This is called the Rashba effect [1,2].The SOI is a relativistic effect on a particle with spin which is moving through an electric field. In the particle's frame of reference there will be a magnetic field perpendicular to the electric field and the direction of movement. The spin direction will precess around the axis parallel to this magnetic field and the precession rate depends on the spin-orbit interaction strength α, and the value of α can be controlled by a gate voltage [3]. This allows us to control the spin precession rate with an electrostatic gate on top of the heterostructure.In this letter we present evidence of quantum interference effects due to spin precession in small arrays of mesoscopic 2DEG rings. This interference is an AharonovCasher (AC) effect [4] of time reversal symmetric paths and is the electromagnetic dual [5] to the Al'tshulerAronov-Spivak (AAS) effect [6]. As the AAS effect and the related Aharonov-Bohm (AB) effect have proven to be important tools in research, we can expect that the AC effect will be a powerful tool for understanding quantum interactions and material properties. We further show that we can control the spin precession rate with an electrostatic gate and modulate the interference pattern over several periods. Earlier experiments on square loop arrays yielded similar results, but only for up to one interference period [7]. We also see the second order AC effect where the oscillation period is half the period of the first order effect and the oscillations correspond to up to 26π spin precession angle. Second and third order harmonics have also recently been observed in square loop arrays [8]. We map the interference pattern to changes in α and...

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