G. S. Diniz 1, A. Latgé 2 and S. E. Ulloa 1 Spin manipulation in carbon nanotubes: All electrical spin filtering through spin-orbit interactions 1 Department of Physics and Astronomy, Ohio University, Athens-OH 2 Instituto de Física, Universidade Federal Fluminense, Niterói-RJ, Brazil Supported by G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011

Motivation & Outline G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011  Spin-orbit effects can play an important effect on electronic structure of CNT, hence its conductance  Fully electrical manipulation of spin dependent transport  Adsorption of molecules on the CNT’s wall  Uniform radial electric field  Uniform transverse electric field  Chiral field through a line of charge: spin- polarization mechanism F. Kummeth et al, Nature, 452, 448 (2008). Gang Lu et al, Nano Letters, 5, 897 (2005). A. N. Enyashin et al, Nanotechnology, 18, (2007). E. J. Mele et al, PRB, 77, (2008).

G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011 Theoretical Model: the system H total = H L + H LC + H C + H CR + H R Sheng et al, PRL 95, (1998). Rashba Term δ1δ1 δ2δ2 δ3δ3 Tight-binding Hamiltonian including spin-orbit effects Kane & Mele, PRL 95, (2005). Intrinsic Term Hamiltonian for the Central Conductor

M. B. Nardelli PRB 60, 7828 (1999). G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011 Green’s Function for the Central Conductor with Self-Energies Green’s function for the left/right leads obtained through an iterative procedure The Spin-Polarized the Central Conductor Using the Landauer’s Formula Where the Couplings are Related to the Self-Energies Theoretical Model: conductance Lopez Sancho et al, J. Phys. F: Met. Phys 14, 1205 (1984).

(9,0) Uniform Radial Field G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011 Numerical Results: SOI manipulation (10,0) Broken charge conjugation symmetry

G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011 Numerical Results: length dependence Uniform Radial Field (9,0) (10,0)

G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011 Tranverse Field (9,0)(10,0) Numerical Results: SOI manipulation atom along CNT’s circumference (n,0) CNT

G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011 Numerical Results: length dependence Transverse Field (9,0) (10,0)

A helical line of charge G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011 Numerical Results: chiral model Chiral FieldBA helical line along 30 degrees: “AAA-type” helical line along 60 degrees: “ABA-type” All results are for (9,0) Image credit: V. I. Puller et al. EPL 77, (2007).

G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011 Numerical Results: chiral field 4 units cell long 5 units cell long

G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011 Along “AAA” Numerical Results: chiral field pitch ≈ nm

G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011 Along “ABA” Numerical Results: chiral field pitch ≈ nm

 Uniform radial and transverse fields in presence of SO interactions do not break TRS  Tube length is quite important when studying SOI  Manipulation of SOR and SOI is reflected in the transmission, providing a way to measure the SOI and SOR parameters as well as controlling the current through the CNTs  Chiral field breaks TRS allowing spin-filtering mechanism through SOI  Possible utilization of CNTs in molecular sensing devices exploring SO effects Thanks for you attention! G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011 Conclusions