Readout of CNT Vibrations using Spin-Phonon Coupling

Christoph Ohm (1,4,5), Christoph Stampfer (2,3,5), Janine Splettstoesser (1,5), Maarten R. Wegewijs (1,3,5)

(1) Institut für Theorie der Statistischen Physik, RWTH Aachen University, D-52056 Aachen, Germany
(2) II. Physikalisches Institut B, RWTH Aachen University, D-52056 Aachen, Germany
(3) Peter Grünberg Institut, Forschungszentrum Jülich, D-52425 Jülich, Germany
(4) Institute for Quantum Information, RWTH Aachen University, D-52056 Aachen, German
(5) JARA – Fundamentals of Future Information Technology

We theoretically study a double quantum dot consisting of a carbon nanotube with a suspended and a non-suspended part. We propose a scheme for spin-based detection of the nanotube bending motion in which the high vibrational frequency is down-converted to a lower, more accessible frequency range. We make use of the curvature-induced spin-orbit coupling in the carbon-nanotubes [1,2,3]. In particular, in the presence of vibrations, this yields a weak effective spin-phonon coupling.
Classical vibrations of the carbon nanotubes are shown to induce a time-dependent magnetic field acting on the electrons confined to the suspended dot, thereby generating spin flips. Within a rotating-wave approximation we find that the weakness of the spin-phonon coupling results in an effective down-mixing of the high vibrational frequency to a much lower spin-flip frequency. The latter can be controlled by the strength of an externally applied magnetic field. We propose to read out the vibration-induced spin flips by measuring the leakage current through the double dot tuned to the spin-blockade regime as a function of the external magnetic field. From a master equation we predict that the leakage current shows a pronounced peak, where the position allows to read out the vibrational frequency.

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[3] A. Palyi and G. Burkard. Phys. Rev. Lett. 106, 086801 (2011)