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Spin filtering in mesoscopic systems

Spin filtering in mesoscopic systems. Shlomi Matityahu, Amnon Aharony , Ora Entin-Wohlman Ben-Gurion University of the Negev Shingo Katsumoto University of Tokyo. Spintronics (spin electronics). Spintronics – Study of spin degrees of freedom in condensed matter systems

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Spin filtering in mesoscopic systems

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  1. Spin filtering in mesoscopic systems Shlomi Matityahu, AmnonAharony, OraEntin-Wohlman Ben-Gurion University of the Negev Shingo Katsumoto University of Tokyo

  2. Spintronics (spin electronics) • Spintronics – Study of spin degrees of freedom in condensed matter systems • Typical questions – • How to polarize and manipulate effectively a spin system? • How long is the system able to remember its spin orientation? • How can spin be detected? • Potential applications – • Giant magnetoresistance (GMR) Disk read/write head • Quantum computer??

  3. Spin filtering • Generate spin-polarized current out of an unpolarized source • Can we find a system which generates a full polarization in a tunable direction? Spin filter Unpolarized beam Polarized beam

  4. The Aharonov-Bohm (AB) effect • An electron travelling from point A to point B in a region with zero magnetic field, but non-zero vector potential , acquires a phase • The phase acquired in a close loop is - The magnetic flux through the surface enclosed by the loop - Flux quantum

  5. Spin-Orbit interaction (SOI) • Non-relativistic limit of the Dirac equation • Rashba SOI - In a 2DEG confined to a plane by an asymmetric potential along • This is equivalent to an effective (momentum-dependent) magnetic field • The strength of the Rashba term can be tuned by a gate voltage!

  6. The Aharonov-Casher (AC) effect • Magnetic moment in an electric field also acquires a quantum mechanical phase • In contrast to the AB phase, the AC phase is given by an SU(2) rotation matrix

  7. Quantum networks – Tight-binding approach • Discrete Schrödinger equation tight-binding Hamiltonian - 2-component spinor at site m - site energy - hopping amplitude (a scalar) - unitary matrix representing AB and AC phases

  8. Our spin filter – A simple exercise in quantum mechanics

  9. Derivation of spin filtering • In general, one has to solve for the transmission matrix of the quantum network and then look for the filtering conditions • The main conclusion – we can achieve full spin filtering in a tunable direction provided we use both SOI and AB.

  10. Additional conclusions • The main conclusion – we can achieve full spin filtering in a tunable direction provided we use both SOI and AB • The spin filter can also serve as a spin reader • Spin filtering is robust against current leakage Thankyou!

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