Supplementary material
Large room-temperature quantum linear magnetoresistance in
multilayered epitaxial graphene: evidence for two-dimensional
magnetotransport
Ram Sevak Singh,1 Xiao Wang,1,3 Wei Chen,1,2, Ariando,1,3a) Andrew. T. S. Wee 1,a)
1
Department of Physics National University of Singapore, Singapore 117542
2
Department of Chemistry, National university of Singapore, Singapore 117543
3
NUSNNI-Nanocore, National University of Singapore, Singapore 117411
a)
Authors to whom correspondence should be addressed. electronic mail:
ariando@nus.edu.sg, phyweets@nus.edu.sg
1
(a)
Raman intensity (a.u.)
(b)
2600
2700
2800
Wavenumber (cm-1)
(c)
2900
(d)
Multilayer EG on C-face SiC
(FWHM ~ 42 cm-1)
2590
2660
2730
2800
2870
Wavenumber (cm-1)
EG
(e)
(f)
10
Z(nm)
8
6
4
2
0
0
SiC
200
400
600
800
1000
X (nm)
Figure S1. Optical picture of the tested device. (b) Raman spectra acquired from different
locations (> 20 points) within the area (highlighted by white dash rectangular area in (a)). All
the spectra of 2D-band were found to fit with single Lorentzian, showing the electrically
decoupled film grown on C-face SiC. (c-d) Single Lorentzian fitted 2D-band of epitaxial
graphene (EG) on C-face and Si-face SiC respectively, showing an identical width of the 2Dband. For thickness measurement, parts of the EG film were etched using oxygen plasma for
sake of height profile measurement from SiC. (e) A typical atomic force microscopy (AFM)
image showing the EG film and SiC (etched part of EG) region. (f) A line profile taken across
the white dash line indicated in (e). The Average thickness of the EG film was found to be ~
6 nm±1 nm, that corresponds to ~ 20±3 layers in EG.
2
1500
200
200
R∝ln(T)
1000
190
R ()
R ( )
Resistance R ()
195
185
190
180
180
175
2 4 6 8 10121416182022
T (K)
1.0
1.5
2.0 2.5
ln(T)
3.0
500
0
50
100 150 200 250 300
Temperature T (K)
Figure S2. Resistance (R) vs. temperature (T) at zero magnetic field (B). The left inset is the
enlarged data in low temperatures (≤20 K) regime. The right inset showing data of left inset
plotted in appropriate axes for weak localization (WL)-type behaviour [G. Bergmann, Phys.
Rev. B 28, 2914 (1983)].
3
0.035
data
Linear fit
0.030
MR
0.025
0.020
0.015
0.010
0.005
0.000
0.0
0.2
0.6
0.4
B2 (T2)
0.8
1.0
Figure S3. Magnetoresistance (MR) as a function of B2. Under a perpendicular B, the
electron trajectories in a two-dimensional (2D) electron gas system (such as graphene) will be
a set of circles. These electron orbits can be expressed by cyclotron frequency ωc= eB/mc,
where mc is the effective mass of the electrons. For the semi-classical theory, the curving of
electron trajectories usually results in a positive MR (defined as MR = [R(B)−R(0)]/R(0))
with a quadratic B dependence to protect the rotational symmetry [Olsen J. L., Electron
Transport in Metals (Interscience, New York) 1962]:
MR ∝ ωcτ2 = (eBτ/mc)2 = (μB)2
A slope of the above curve gives rise to mobility μ ~ 1862 cm-2V-1s-1.
4
dMR/dB (%/T)
Figure S4 (a-g) Linear fits to linear magnetoresistance (LMR) data in 1 T≤B≤9 T range at
different temperatures: 300, 100, 50, 20, 10, 5 and 2 K. These plots give the slopes
(dMR/dB(%/T)) at different temperatures.
20
7
3
1
1
3
7
20
55
148
403
T (K)
Figure S5. Slope of LMR (dMR/dB(%/T)) vs. temperature T (logarithmic scales).This graph
is plotted from the data obtained in Fig. S4. It is evident that the curve does not follow a
linear relationship, it is just a constant function, which rules out a power law dependency
((dMR/dB)∝T n), which is expected for a classical LMR model.
5