G. S. Diniz and S. E. Ulloa Spin-orbit coupling and electronic transport in carbon nanotubes in external fields Department of Physics and Astronomy, Ohio University, Athens-OH Supported by G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

Motivation & Outline  Spin-orbit effects can play an important effect on electronic structure of CNT, hence its conductance  Fully control of the spin dependent transport  Implementation in spintronic devices  Uniform transverse electric field  Uniform parallel magnetic field  SO interaction (modeled using atomic SOI)  Curvature effects In this presentation… G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

H total = H L + H LC + H C + H CR + H R Tight-binding Hamiltonian for the whole System Theoretical Model: 4-orbitals tight-binding Hamiltonian The local terms: E-field, B-Field and SOI del Valle et al. PRB (2011); Izumida et al. JPSJ (2009); Klinovaja et al. PRL (2011); Klinovaja et al. PRB (2011); Jeong et al. PRB (2009), F. Kuemmeth et al. Nature (2008).. Hamiltonian for the Central Conductor H C = H hop +H E-field +H B-field +H SOI E-Field B-Field G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

Theoretical Model: 4-orbitals tight-binding Hamiltonian Hopping Integrals σ-π hybridization due to curvature The Hopping term including curvature Z θ AB 1 θAB2θAB2 θ AB 3 Z AB 1 Z AB 2 Z AB 3 B2B2 B3B3 B1B1 π/6-θ d1d1 d2d2 d3d3 t z r Izumida et al. JPSJ 78, (2009). G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

Theoretical Model: conductance in the central region Green’s Function for the Central Conductor M. B. Nardelli PRB 60, 7828 (1999). The Spin-Polarized the Central Conductor Using the Landauer’s Formula Where the Couplings are Related to the Self-Energies Lopez Sancho et al, J. Phys. F: Met. Phys 14, 1205 (1984). with Self-Energies Green’s function for the left/right leads obtained through an iterative procedure G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

Results: conductance (9,0) Without: External fields, Curvature and SOI 2 G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

Results: conductance (6,0) G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

Transverse E-Field Results: conductance (6,0) G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

Parallel B-Field Results: conductance (6,0) Due to Zeeman Field: G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

Results: polarization (6,0) G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012 Curvature induced gap

Results: polarization l = nm G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

 Moderate Spin polarization for “low” B-field and dependent on CNT’s radius  Tube length can be quite important!  Manipulation of E-field and B-field is reflected in the transmission, providing a way to control the current through the CNTs  More interesting features in armchair CNTs, results on the way...  Possible utilization of CNTs in spintronic devices exploring SOI effects Thank you! Conclusion G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

l = 2.842nm l = 5.684nm l = nm l = nm