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

Htotal= HL + HLC + HC + HCR + HR

Tight-binding Hamiltonian for the whole System

Theoretical Model: 4-orbitals tight-binding Hamiltonian

The local terms: E-field, B-Field and SOI

',,,,

''†

iiisoSO cSciH

,

2†

0,,

† coscosi

siipii

iiifieldE cceEcceERHr

,,

'† )(

2

1

iiieBzeeman cBScgH

nm

g

meVT

e

B

05.0

14.2

55.1

0

1

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 ConductorHC = Hhop+HE-field+HB-field+HSOI E-Field

B-F

ield

G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

Theoretical Model: 4-orbitals tight-binding Hamiltonian

ssV

spVppV

ppV

Hopping Integrals σ-π hybridizationdue to curvature

nABnAB

jiji

iij

isisishop ccetccH

ij†

,,,,2

†22

0

The Hopping term including curvature

zatRrRd

zatRrRd

zatRrRd

cABAB

cABAB

cABAB

ˆ)6/sin(ˆsinˆ)cos1(

ˆcosˆsinˆ)cos1(

ˆ)6/sin(ˆsinˆ)cos1(

33

22

11

3

2

1

ZθAB1θAB2

θAB3

ZAB1

ZAB2

ZAB3

B2

B3

B1 π/6-θ

d1d

2

d3

t

z

r

Izu

mid

a et

al.

JPS

J 78

,074

707

(200

9).

G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

Theoretical Model: conductance in the central regionGreen’s Function for the Central Conductor

1/ )(

RLC

raC HEG

M. B. Nardelli PRB 60, 7828 (1999).

The Spin-Polarized Conductance @ 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).

aC

RrC

L GGTrGEG ','',0' )(

a

l

r

l

l i

with Self-Energies

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

lCllClHgH †

lgheG

RightLeftl

/

/2

0

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

Tran

sverse E-F

ieldResults: conductance

(6,0)

G. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

Parallel B

-Field

Results: conductance

(6,0)

GGDue 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

',

'(%)

GGGP

Curvature induced gap

Results: polarization

l = 17.052nmG. S. Diniz and S. E. Ulloa Boston, APS March Meeting 2012

10.0

20

VnmE

meVSO

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 = 5.684nml = 11.368nm

l = 17.052nm

)6/cos(

sin

)6/cos(

3

2

1

R

aR

aR

a

cAB

cAB

cAB

)1,0,0(

)0,cos,sin(

)0,sin,(cos

zn

ABABtn

ABABrn

n

n

n

nn

nn