g. s. diniz and s. e. ulloa spin-orbit coupling and electronic transport in carbon nanotubes in...
TRANSCRIPT
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