G. S. Diniz1, A. Latgé2 and S. E. Ulloa1

Spin manipulation in carbon nanotubes: All electrical spin

filtering through spin-orbit interactions

1 Department of Physics and Astronomy, Ohio University, Athens-OH2 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, 245702 (2007).E. J. Mele et al, PRB, 77, 085429 (2008).

G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011

Theoretical Model: the system

Htotal= HL + HLC + HC + HCR + HR

Sheng et al, PRL 95, 136602 (1998).

Rashba Term

δ1 δ2

δ3

Tight-binding Hamiltonian including spin-orbit effects

Kane & Mele, PRL 95, 146802 (2005).

Intrinsic Term

soiV

soiV

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

Ga=rC = ¡! ¨ ¡ HC ¡ § L ¡ § R

¢¡ 1Green’s Function for the Central Conductor

§ a=rL =R = H y

(L =R )C ga=rL =R H(L =R )C

with Self-Energies

ga=rL =R

Green’s function for the left/right leads obtained through an iterative procedure

G¾¾0 = G0Tr £¡ L¾Gr

¾¾0¡ R¾0Ga

¾0¾¤

The Spin-Polarized Conductance @ the Central Conductor Using the Landauer’s Formula

¡ (L =R ) = ih§ r

(L =R ) ¡ § a(L =R )

iWhere 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

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 modelC

hiral Field

BA

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, 27006 (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≈ 3.907 nm

G. S. Diniz, A. Latgé and S. E. Ulloa Dallas, APS March Meeting 2011

Along “ABA”

Numerical Results: chiral field

pitch≈ 1.345 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