1
V
ery large
m
agnetoresistance in
g
raphene
n
anoribbon
s
Jingwei Bai,
1
*
Rui Cheng
,
1*
Faxian Xiu,
2
Lei Liao
3
, Minsheng Wang
2
,
Alexandros
Shailos
4
, Kang L. Wang
2,4
,
Yu Huang
1,
4
& Xiangfeng Duan
3
,
4
*
These authors contribute equally to this work.
Supplementary Inf
ormation
1.
Figure S1
Determin
ation of
the source

drain gap
ΔV
sd
.
2.
Figure S2
Magneto

transport
characteristics
in the electron

transport branch
.
3.
Figure S
3

S5

Additional set
of data show similar
magnetoresistance
in
another
long channel device.
4.
Figure S6
Source

drain
gap evolution in
the
short channel device
.
5.
Figu
re
S
7

Magneto

transport measurement with in

plane magnetic field
.
6.
Figure
S
8

Temperature dependence of the minimum conductance at different
magnetic field
.
1.
Determin
ation
the source

drain gap.
Figure S1

Current as a function of source

drain voltage at
a
fixed gate
voltage
.
The source

drain gap
ΔV
sd
is
defined
by the source

drain voltage region where the
conductance is suppressed.
The source drain gap edge is
determined
by a steep
increase of current in logarithmic scale
1
.
2
2.
Magneto

transport
characteristics
in the electron

transport branch.
Fig
ure S2

Current ratio
I(8T)/I(0T)
as a function of source

drain voltage when gated
at V
g
= 3.0V, 4.7V and 6V
, highlighting that the significant
magnetoresistance (
MR
)
can also be obtained at electron

transport branch
.
3
．
M慧aet潴r慮sp潲t 潦 慮潴her l潮朠cha
nnel
杲慰hene n慮潲ibbon
de癩ce.
Figure
S
3
 Electrical transport measurement of a
graphene nanoribbon
FET
with width of ~25 nm and length of 1 μm. a,
Differential conductance versus gate
voltage with a magnetic field of 0T (black) and 8T (red) normal to
the device plane.
The measurements were carried out at 1.6K.
b

d,
Differential conductance as a
3
function of source

drain bias and back

gate voltage under magnetic field of 0 T (
b
), 2
T (
c
), and 8 T (
d
). These measurements show diamonds of suppressed conduc
tance
shrunk both in source

drain bias and gate voltage direction with increase of the
magnetic field.
The
2D plot
s
have a lower
line resolution than th
ose
in
main text
but
shows that qualitatively similar results
are ob
tained
.
Figure
S
4
 Tunable
magnet
oresistance
in
graphene nanoribbon

FET.
The effect
of magnetic field on current voltage characteristics when the device is gated at V=1.5
V (
a
), 3.5 V (
b
), 5 V (
c
). Each inset shows source

drain gap (
Δ
V
sd
) as a function of
magnetic field. (
d
) Current ratio
I
(8T)/
I
(0T) versus source

drain bias at V
g
=
1.5V,
3.5
V
and 5V
. The middle interval for each plot is in the range of suppressed conductance
which is beyond our equipment detecting limits.
Current ratio:
I
(8T)/
I
(0T) as a function
of source

drain bias and
gate voltage, highlighting huge increase of current under
magnetic field when probing the device close to the diamond of suppressed
conductance. (
e
) Current
I
(M)/
I
(0T) as a function of magnetic field when source

drain
biased at 5.5 mV, 15 mV, 25 mV and 50
mV at V
g
= 3.5 V.
4
Figure
S
5
 Temperature dependence of magneto

transport properties.
(
a
),
Current ratio
I
(8T)/
I
(0T) as a function of source

drain bias at 1.6 K, 4.3 K, 15.6
K,
35.6
K,
77 K and 294 K. The device was gated at 3.5 V. (
b
)
Room temperature (2
94 K)
I

V
characteristic (V
g
=3.5 V) at different magnetic field. In all gate range, the device show
linear transport behavior and similar magnetic field response. Inset is the negative
magnetoresistance
s which linearly increase as a function of magnetic fi
eld.
4.
Source

drain
gap evolution in short channel device
.
Figure
S
6
 Evolution of source

drain gap at selected gate voltages for the short
channel
graphene nanoribbon
FET device shown in Figure 5.
5.
Magneto

transport measurement with in

plane magnetic
field.
5
Figure S
7

Current

voltage characteristic
s
under in

plane magnetic field.
No
obvious conductance change
is observed
with
in

plane
magnetic field up to 8T
, in
contrast to
the case
with perpendicular
magnetic field
described in the main article
.
Th
is observation excludes the
magnetoresistance
originat
ion
from magnetic edge
state
s
which h
ave
small magnetic field angular dependence due to weak spin

orbital
coupling
2,3
.
6.
Temperature dependence of the minimum conductance
at different magnetic
field.
Figure S
8
 Temperature dependence of the minimum conductance at different
magnetic field.
The dash line at high temperature region of each magnetic field is
a
fit to simple thermal activated transport
:
G
min
~exp(

E
a
/2k
B
T)
;
and the dash line at low
temperat
ure region is a fit to variable range hopping
:
G
min
~exp(

(T
0
/T)
γ
with γ = 0.4.
Here we studied the temperature dependen
t
charge transport in the transport gap
region. The minimum conductance (off

resonance differential conductance near the
6
charge neutralit
y point) was plotted with temperature at different magnetic field
1
. The
plot shows that high temperature charge transport follow thermal activated behavior
given by G
min
~exp(

E
a
/2k
B
T). At low temperature region, the transport can be
described by quasi

1D v
ariable hopping behavior with G
min
~exp(

(T
0
/T)
γ
), where γ is a
dimensional factor in the range of 1/2~1/3
4
. The high temperature activation energy E
a
can be obtained by linear fitting of the Arrhenius plot (dash line), and E
a
is 291 KT
(25.1 meV) at 0T for this particular device. Interestingly, the ac
tivation energy
decrease with increasing vertical magnetic field: the value drops to 196 KT (16.9 meV)
at 4T and further reduces to 145 KT (12.5 meV) at 8T. Previous theoretical stud
ies
show that
the
high temperature E
a
contributed by edge roughness and Co
ulomb
interaction can be approximated by (0.2t+t/ε)/W, where confinement gap E
g
~ t/W (t is
the nearest hopping element, ε is the dielectric constant of the
e
mbedded medium
and W represent the width)
5
. Therefore, the decrease of high temperature activation
energy with magnetic field indicates the shrinkage of the confinement gaps by
modifying the hopping matrix with additional magnetic flux
6
.
Reference
1.
Han, M. Y., Brant, J. C. & Kim, P. Electron transport in disordered graphene
nanoribbons.
Phys. Rev. Lett.
104
, 056801 (2010).
2.
Munoz

Rojas, F., Fernandez

Rossier, J. & Palacios, J. J. Giant Magnetoresistance
in Ultrasmall Graphene Based Devices.
Phys. Rev. Lett.
102
, 136810 (2009).
3.
Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K.
The electronic properties of graphene.
Rev. Mod. Phys.
81
, 109

162 (2009)
.
4.
Mott, N. F. Conduction in non

crystalline materials. 3. localized states in a
pseudogap and near extremities
of conduction and valence bands.
Phil. Mag.
19
,
835 (1969).
5.
Martin, I.
& Blanter, Y. M. Transport in disordered graphene nanoribbons.
Phys.
Rev. B
79
, 235132 (2009).
6.
Huang, Y., Chang, C. P. & Lin, M. F. Magnetic and quantum confinement effects
on electronic and optical properties of graphene ribbons.
Nanotechnology
18
,
495401
, (2007).
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