Very large magnetoresistance in graphene

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.
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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.
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19
,
835 (1969).

5.

Martin, I.
& Blanter, Y. M. Transport in disordered graphene nanoribbons.
Phys.
Rev. B
79
, 235132 (2009).

6.

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18
,
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