Spintronics in quantum wires Physics Department Korea University Seoul (Korea) Llorenç Serra home institution Physics Department, University of the Balearic Islands UIB and Institute of Interdisciplinary Physics and Complex systems IFISC, CSIC-UIB Palma de Mallorca (Spain)

Where is Mallorca island, Spain ?

The Balearic Islands University students 100 in Physics (5 years) Main campus in Palma, Mallorca island

Outline of the talk  Spintronics: Introduction Giant magnetoresistance in multilayers The spin transistor  Quantum wires with extended Rashba coupling Band structure and conductance modifications Spin textures Evanescent states  Localized coupling: The Fano-Rashba effect Conductance anomalies In-plane magnetic fields

 Spintronics  Novel technology based on the manipulation of the electron spin  Spin is ignored in conventional electronics  Nobel prize in 2007: Albert Fert and Peter A. Grunberg Giant magneto resistance  thin magnetic layers (nm)  antiferromagnetic interlayer exchange coupling  control with an applied magnetic field

 GMR is the basis of the spin valves used in hard discs read heads

 magnetic funnel junctions  spintronics with molecules

Spintronics in semiconductors Multiband k.p Hamiltonians conduction band SO term Kane parameters Similarity to SO in relativistic QM [Winkler] Dirac equation Pauli SO coupling: The Rashba interaction

Spin-orbit coupling (Rashba) Interband couplingSpin precesion Rashba parameter  can be tuned with electric gates Nitta et al. ‘97

The Datta-Das spin transistor advantages?  Faster data manipulation  Lower consumption  Higher integration

the mismatch problem  Difficult injection of spin currents

 Quantum wires with extended Rashba coupling 2d quantum wires without Rashba Landauer’s conductance L. Serra, D. Sánchez, R. López Phys. Rev. B 72, (2005)

With only Rashba “precession term” With “Rashba intersubband coupling” (RIC) Moroz and Barnes, Governale and Zülicke, Valín-Rodríguez et al, …

With in-plane B fields Neglecting RIC Subband maxima and quasi-gaps: Streda and Seba Pershin et al Anomalous conductance steps: Nesteroff et al

No RIC full - structureless without RIC - collapse in odd plateaus RIC is very important even at perpendicular field lengths 

- in-plane spin rotation with k - z-component accumulations - eigenstate at k g first band Spin textures

Evanescent states wavenumber transverse motion Propagating (real k) versus evanescent (complex k) modes Evanescent states are not physically realizable in the entire wire, only in restricted domains L. Serra, D. Sánchez, R. López Phys. Rev. B 76, (2007)

Usual case (separable) transverse modes wire bands

Evanescent modes with Rashba coupling?

The equation to solve Mathematical peculiarities:  E given, not a linear eigenvalue problem  k unknown, nonlinear k-eigenvalue problem  If k complex, non Hermitian  Usual computation strategy invalid if k complex

The evanescent mode dispersion diagrams

Analytic weak  Argument: neglect interband coupling diagonal Hamiltonian Rashba wavenumber Independent of E

An illustrative application: The potential step energy  The wave function  Evanescent modes crucial for matching and flux conservation

 Potential step: distributions  p1  p2 reverts magnetization  maximum density for x>0 (?)

 Evanescent oscillations! Nontrivial k real parts y cut integrated

 Above barrier transmission

 Finite region (double interface) and current-induced spin polarization

Localized Rashba coupling: The Fano-Rashba effect A finite Rashba region Dips in conductance D. Sánchez, L. Serra Phys. Rev. B 74, (2006)

Quasibound states Density distribution (b)(c) Dips with asymmetric Fano profile

Sparse linear system Harwell library routine Schrödinger equation asymptotic equation Grid calculations The quantum transmitting boundary method

Systematics  dip minimum ~ zero  renormalized quasi-bound states  Rashba interaction as a gate voltage gate voltage

Feshbach’s coupled channel model “potential well” “potential mixing”

solution by ansatz bound state outgoing wave retarded Green function asymptotic solution

Generalized Fano lineshape Fano parameter

Generalized Fano lineshape Kobayashi et al. ‘02 Rashba spin-orbit coupling yields complex q ’s without breaking time-reversal symmetry !!

Spin effects  Change quantization axis

With in-plane magnetic fields D. Sánchez, L. Serra, M.-S. Choi Phys. Rev. B 77, (2008)

Summary Spintronics has provided technological breakthrough (GMR) and possibly more will come. Rashba spin-orbit coupling allows spin manipulation with electric fields Peculiar behavior of evanescent states. Conductance resonances with localized Rashba couplings Collaborators Rosa López (Mallorca) David Sánchez (Mallorca) Mahn-Soo Choi (Seoul) Thank you !