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Quantum Resistance Standard Based on Epitaxial Graphene

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Abstract

The quantum Hall effect allows the international standard for resistance to be defined in terms of the electron charge and Planck's constant alone. The effect comprises the quantization of the Hall resistance in two-dimensional electron systems in rational fractions of R(K) = h/e(2) = 25,812.807557(18) Omega, the resistance quantum. Despite 30 years of research into the quantum Hall effect, the level of precision necessary for metrology--a few parts per billion--has been achieved only in silicon and iii-v heterostructure devices. Graphene should, in principle, be an ideal material for a quantum resistance standard, because it is inherently two-dimensional and its discrete electron energy levels in a magnetic field (the Landau levels) are widely spaced. However, the precisions demonstrated so far have been lower than one part per million. Here, we report a quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene at 300 mK, four orders of magnitude better than previously reported. Moreover, by demonstrating the structural integrity and uniformity of graphene over hundreds of micrometres, as well as reproducible mobility and carrier concentrations across a half-centimetre wafer, these results boost the prospects of using epitaxial graphene in applications beyond quantum metrology.
Towards a quantum resistance standard based on
epitaxial graphene
Alexander Tzalenchuk
1
*
, Samuel Lara-Avila
2
, Alexei Kalaboukhov
2
, Sara Paolillo
3
, Mikael Syva
¨
ja
¨
rvi
4
,
Rositza Yakimova
4
, Olga Kazakova
1
,T.J.B.M.Janssen
1
, Vladimir Fal’ko
5
and Sergey Kubatkin
2
The quantum Hall effect
1
allows the international standard for
resistance to be defined in terms of the electron charge and
Planck’s constant alone. The effect comprises the quantization
of the Hall resistance in two-dimensional electron systems in
rational fractions of R
K
5 h/e
2
5 25 812.807 557(18) V, the
resistance quantum
2
. Despite 30 years of research into the
quantum Hall effect, the level of precision necessary for
metrology—a few parts per billion—has been achieved only in
silicon and
IIIV heterostructure devices
3–5
. Graphene should,
in principle, be an ideal material for a quantum resistance stan-
dard
6
, because it is inherently two-dimensional and its discrete
electron energy levels in a magnetic field (the Landau levels
7
)
are widely spaced. However, the precisions demonstrated
so far have been lower than one part per million
8
. Here, we
report a quantum Hall resistance quantization accuracy of
three parts per billion in monolayer epitaxial graphene at
300 mK, four orders of magnitude better than previously
reported. Moreover, by demonstrating the structural integrity
and uniformity of graphene over hundreds of micrometres, as
well as reproducible mobility and carrier concentrations
across a half-centimetre wafer, these results boost the pro-
spects of using epitaxial graphene in applications beyond
quantum metrology.
Graphene—a single layer of graphite—is a truly two-dimensional
gapless semiconductor, with electrons mimicking the behaviour of
relativistic (Dirac) electrons
9
. This last feature of charge carriers in
graphene is manifested most spectacularly through an unusual
sequence of the quantum Hall effect (QHE) plateaux
10
. The QHE
is a result of the Landau level quantization of the energy spectrum
of two-dimensional electrons. In the quantum Hall regime the
current is carried by a quantum state, spreading through the whole
sample, and the sequence of plateaux in the transverse resistance
R
xy
is determined by the topological (Berry) phase acquired by the
charge moving in the magnetic field. This phase is zero in conven-
tional materials, where R
xy
¼+h/ne
2
(n-integer 1); it is equal to
2p in bilayer graphene
11,12
, leading to a sequence of QHE plateaux
at R
xy
¼+(h/4e
2
)/(n þ 1) (n 0), and it is p in the monolayers
13
,
which determines the QHE sequence R
xy
¼+(h/4e
2
)/(n þ 1/2)
(n 0), currently regarded as a smoking gun for the sample to
contain monolayer graphene
10
. The spacing between the n ¼ 0 and
n ¼ 1 Landau levels in graphene, DE
graphene
01
p
(B[T]) 36 meV
is large in comparison with conventional materials such as GaAs.
For example, at 15 T, DE
graphene
01
/DE
GaAs
5.4.
In reality, an impressive range of unconventional transport prop-
erties of electrons in graphene
14
, including QHE, have been seen
almost exclusively in flakes mechanically exfoliated from bulk
graphite. Quantum Hall plateaux have been observed in such
material even at room temperature, albeit with an accuracy of
0.2% (ref. 15), while the highest experimentally achieved accuracy
8
of QHE measurements at 300 mK in exfoliated flakes was 15 parts
in a million—still modest by metrological standards.
An alternative approach to producing graphene is to grow it epi-
taxially on silicon carbide (SiC)
16
. Although angle-resolved photoe-
mission studies of epitaxial graphene
17
have revealed an almost
linear dispersion of carriers around the corners of a hexagonal
Brillouin zone and scanning tunnelling microscopy (STM)
showed the sequence of Landau levels typical for graphene
18
, Hall
resistance quantization has not been observed in epitaxial graphene,
in contrast to the exfoliated material, despite numerous attempts.
The difficulty was related to the lack of atomically accurate thickness
control during film growth on the C-terminated facet, and also a
strong variation of carrier density (doping) across the layers
grown on the silicon-terminated facet
19
.
Here, we demonstrate the viability of a quantum Hall resistance
standard based on large-area epitaxial graphene synthesized on the
silicon-terminated face of silicon carbide by observation of Hall
resistance quantization accurate to a few parts in a billion at
300 mK and a few tens in a billion at 4.2 K. The samples (Fig. 1)
studied in our experiments were produced on the silicon-terminated
face of a 4H-SiC(0001) substrate (Cree Inc.) using the protocol
described in the Methods. We concentrate on the transport charac-
teristics of the smallest and largest of the fabricated devices ident-
ified by circles in Fig. 1c. Figure 2a shows the longitudinal
(dissipative) R
xx
and transverse (Hall) R
xy
resistance of a
11.6 mm 2 mm Hall bar at 4.2 K and 214 T , B , 14 T. The
absence of positive classical magnetoresistance at magnetic fields
jBj , 2 T indicates that carrier density in this material is quite
homogeneous over the length of at least several micrometres.
However, it was noticed that the magnetoresistance was slightly
asymmetric with respect to the reversal of the magnetic field direc-
tion, which made it difficult to determine the carrier density using
the Hall coefficient (although the symmetry was preserved when the
voltage leads were swapped with the current leads as the field was
reversed). In intermediate magnetic fields we observe Shubnikov–
de Haas (SdH) oscillations (as well as a weak localization peak at
jBj , 0.1 T characteristic of phase coherence electrons in disordered
graphene
20
). The analysis of SdH oscillations enabled us to deter-
mine the carrier density in this device n
s
¼ 6.5 10
11
cm
22
.
Using the density obtained from the SdH oscillations, we estimate
that the magnetic field (B
n
¼ hn
s
/en) needed to reach the exact filling
factor n ¼ 2 in this device is 13.5 T (unfortunately we had no
means of controlling the carrier density in these experiments).
Two Hall resistance plateaux are clearly visible in Fig. 2a, at R
xy
(0)
¼
R
K
/2(n ¼ 0) and R
xy
(1)
¼ R
K
/6(n ¼ 1), corresponding to the filling
1
National Physical Laboratory, TW11 0LW Teddington, UK,
2
Department of Microtechnology and Nanoscience, Chalmers University of Technology, S-412 96
Go
¨
teborg, Sweden,
3
Department of Physics, Politecnico di Milano, 20133 Milano, Italy,
4
Department of Physics, Chemistry and Biology (IFM), Linko
¨
ping
University, S-581 83 Linko
¨
ping, Sweden,
5
Physics Department, Lancaster University, Lancaster LA1 4YB, UK.
*
e-mail: alexander.tzalenchuk@npl.co.uk
LETTERS
PUBLISHED ONLINE: 17 JANUARY 2010 | DOI: 10.1038/NNANO.2009.474
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factors v ¼ 2 and v ¼ 6, respectively. In graphene v ¼ 2 corresponds
to the fully occupied zero-energy Landau level characterized by the
largest separation v
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2h
eB=c
p
from other Landau levels in the spec-
trum, so that the Hall resistance quantization at R
xy
(0)
¼ R
K
/2 is par-
ticularly robust. This plateau appears already at jBj10 T and is
accompanied by a vanishing R
xx
. The n ¼ 1 plateau at v ¼ 6 is not
so flat, with only a weak minimum in R
xx
, and there is also a
visible trace of a structure corresponding to v ¼ 10. Their presence
confirms that the studied material is indeed monolayer graphene.
The magneto-transport measurements on a much bigger,
160 mm 35 mm Hall bar device (Fig. 1c) are presented in
Fig. 2b. A substantial positive magnetoresistance at low fields,
which was absent in the smaller sample, indicates that the carrier
concentration varies along the larger sample. Because of this, the
v ¼ 6 feature in R
xx
in the bigger sample is less prominent.
Nevertheless, despite the inhomogeneity of the carrier density, the
Hall resistance plateau at R
xy
(0)
¼ R
K
/2(n ¼ 0) is robust and is
accompanied by vanishing longitudinal resistance R
xx
.
Importantly, the large-area device has a low resistance R
c
1.5 V
of contacts to the graphene layer (determined at the plateau,
Fig. 2c) and, when compared to smaller devices, can sustain a
much higher current before QHE breaks down, as shown in the
I(V) characteristics in Fig. 2d. Because larger breakdown current
affords higher-precision measurements in the QHE regime, we
chose to perform such measurements in the larger sample. The
choice of the field, 14 T, where the most accurate measurements
were performed, was determined simply by the limitation of
our superconducting magnet. This limit is below B ¼ 17.5 T,
where the filling factor would be exactly v ¼ 2 for this sample
(with n
s
¼ 8.5 10
11
cm
22
calculated from SdH oscillations).
Precision measurements of R
xy
were performed in the conditions
where R
xx
is very accurately zero: at B ¼ 14 T, I
sd
¼ 2.3 mA for 4.2 K
and I
sd
¼ 11.6 mA for 300 mK (see Supplementary Information).
Note that a higher probe current enables a higher precision of R
xy
measurements to be achieved, so we performed these studies at
300 mK. The accuracy of Hall resistance quantization in graphene
was established in measurements traceable to the GaAs quantum
Hall resistance standard using a cryogenic current comparator
bridge
21
. Figure 3a shows how the mean relative deviation of R
xy
(0)
from R
K
/2 depends on the measurement current through the gra-
phene device. The quantization accuracy þ0.4+3 parts in 10
9
(mean relative deviation of 129 measurements+standard error of
the mean) inferred from our measurements at 11.6 mA and
300 mK is a four orders of magnitude improvement on the previous
best result in exfoliated graphene. This readily puts epitaxial gra-
phene devices in the same league as their semiconductor counter-
parts. Note that our result was obtained on a sample that is
substantially smaller than the semiconductor devices used for cali-
bration and without any optimization. From Fig. 3a it can be seen
that graphene is still accurately quantized at 4.2 K; however, at
this temperature, the measurement current has to be reduced to
2.3 mA, which increases the uncertainty of the data accumulated
over a comparable time interval.
To demonstrate convergence of the measurement process and to
see what kind of noise limits the precision of our measurements, in
Fig. 3b we plot the Allan deviation
22
of R
xy
(0)
from R
K
/2 against the
measurement time
t
. These data follow a 1/
t
1/2
dependence—
behaviour typical of the predominantly white (uncorrelated
random) noise. This justifies the use of the standard measures of
uncertainty and suggests that these (already very accurate) results
can be further improved if one is prepared to measure for longer
and at several smaller values of the filling factor within the R
xy
¼
R
K
/2 plateau. Further development should include methods to
control the carrier density either chemically or by electrostatic
y = 15 μm
z
= 14.2 nm
a
c
b
(μm)
(μm)
0 nm
8
nm
4
nm
0
0
5
5
10
10
Graphene
V
2
V
2
+
V
1
+
V
1
7 mm
I
source
I
drain
L
W
Graphene
SiC
I
drain
I
source
x = 15 μm
V
1
V
2
V
3
V
1
+ V
2
+
V
2
+
V
3
+
V
1
+
V
1
V
2
V
3
V
3
+
Figure 1 | Sample morphology and layout. a, AFM images of the sample: large flat terraces on the surface of the Si-face of a 4H-SiC(0001) substrate with
graphene after high-temperatur e annealing in an argon atmospher e. b, Gr aphene patterned in the nominally 2-mm-wide Hall bar configuration on top of the
terraced substrate. c, Lay out of a 7 7mm
2
wafer with 20 patterned devices. Encircled are two devices with dimensions L ¼ 11.6
m
mandW ¼ 2
m
m (wire
bonded) and L ¼ 160
m
mandW ¼ 35
m
m, for which the QHE data are pr esented in Fig. 2. The contact configuration for the smaller device is shown in the
enlarged image. To visualize the Hall bar this optical micrograph was tak en after oxygen plasma trea tment, which formed the graphene pattern, but before
the removal of resist.
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© 2010 Macmillan Publishers Limited. All rights reserved.
gating, although we believe that the fastest route towards the
implementation of graphene in quantum metrology lies in increas-
ing the breakdown current by taking advantage of the flexibility of
device design offered by the large area of graphene on a SiC
wafer: the optimization of contacts geometry and use of multiple
parallel Hall bar devices.
−15
−15
−10
−5
R
xy
(kΩ)
R
xx
(kΩ)
0
5
10
15
a
b
c
d
0
−13.0 −12.8 −12.6 −12.4 −12.2 −12.0 −11.8 −11.6 −11.4 −11.2 −11.0
2
Resistance (Ω)
4
6
8
10
–4
–2
Voltage (μV)
0
Magnetic flux density (T)
2
4
300 mK
4.2 K
−15
−10
−5
R
xy
(kΩ)
0
5
10
15
−10 −5
R
1
R
xx
R
xx
+
R
l
+
R
c
0
Magnetic flux density (T)
51015
−15 −10 −5 0
Magnetic flux density (T)
51015
−20 −10 0
Current (mA)
10 20
R
xx
R
xx
R
xy
R
xy
R
xy
(1)
R
xy
(1)
R
xy
(0)
R
xy
(0)
20
16
12
8
4
0
R
xx
(kΩ)
20
16
12
8
4
0
Figure 2 | Quantum Hall effect in epitaxial graphene. a,Transverse(R
xy
) and longitudinal (R
xx
) resistance of the 11.6
m
m 2
m
mdevicemeasuredatT ¼ 4.2 K
with 1
m
Acurrent.R
xy
(0)
and R
xy
(1)
repr esent Hall resistance plateaux at filling factors n ¼ 2andn ¼ 6 respectively. The carrier density n
s
¼ 6.5 10
11
cm
22
was
obtained from SdH oscillations. b,Transverse(R
xy
) and longitudinal (R
xx
) resistance of the 160
m
m 35
m
m device measured at T ¼ 4.2 K with 1
m
Acurrent.
The carrier density n
s
¼ 8.5 10
11
cm
22
was obtained from SdH oscillations. c, Measur ements of the longitudinal resistance R
xx
performed in a four-point
configuration (filled red circles), which excludes contact resistances, and in a three-point configuration (open blue circles), which, as well as R
xx
, includes the
contact resistance R
c
and the resistance of the leads from room-tempera tur e electronics down to the sample R
l
¼ 2.5 V. On the plateau, R
xx
is very nearly
zero and R
c
is 1.5 V for all measured contacts. These measurements wer e performed while sweeping the magnetic field; hence there is a relativ ely large
spread. d, Determination of the breakdo wn current I
max
of non-dissipativ e transport from measurement of the current–voltag e chara cteristic in the
longitudinal direction at 14 T: I
max
13
m
A at 300 mK and I
max
5
m
A at 4.2 K. The residual longitudinal resistance was confirmed as R
xx
, 0.2 mV at
300 mK measured with I
sd
¼ 12
m
A, and R
xx
, 2.4 mV at 4.2 K measured with I
sd
¼ 2.5
m
A.
0
−60
−40
−20
0
20
2(R
xy
R
K
/2)/R
K
(ppb)
2R
xx
/R
K
(ppb)
2,000
4,000
6,000
a
b
−60
−40
−20
0
20
Allan deviation
2,000
4,000
6,000
τ
–1/2
10
−7
10
−8
10
−9
2 4 6 8 10 12 14
Current (μA)
16 18 20 22 24
0.01 0.1 1 10
Time interval (h)
Figure 3 | Determination of Hall resistance quantization accuracy. a, Mean relative deviation of R
xy
(0)
from R
K
/2 at different bias currents (ppb, parts per
billion). The value at the smallest current was measured at 4.2 K (open blue squares), and all other values at 300 mK (filled red squares). The most accurate
measurement with an 11.6
m
A source–drain current at 14 T and 300 mK was performed over 11 h. The value of R
xx
/R
K
determined in the same conditions is
also shown (black star) together with the measurement uncertainty. b, Allan deviation of R
xy
(0)
from R
K
/2 versus measurement time
t
. The square root
dependence indicates purely white noise.
LETTERS
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To summarize, we report quantum Hall resistance quantization
accurate to a few parts in a billion at 300 mK in a large-area epitaxial
graphene sample. Several more devices have been studied at 4.2 K,
demonstrating quantization within an accuracy of some tens in
10
9
, confirming the robustness of the QHE in graphene synthesized
on the silicon-terminated face of SiC. This remarkable precision
constitutes an improvement of four orders of magnitude over the
best previous results obtained in exfoliated graphene, and is similar
to the accuracy achieved in the established semiconductor resistance
standards. In the future, improvements in measurement precision
may advance the understanding of the QHE effect itself, by deter-
mining whether there exist systematic deviations of the quantized
Hall resistance in graphene from the fundamental values at the
rational fractions of h/e
2
. Even more importantly, the experiments
have demonstrated structural integrity over hundreds of micro-
metres and revealed relative uniformity of epitaxial graphene
across a half-centimetre SiC wafer (as well as from wafer to wafer).
This supports the potential of SiC technology for microelectronics
applications possibly extending far beyond quantum metrology.
Methods
The material used in the reported experiments was produced on the Si-face of SiC;
the reaction kinetics is slower there than on the C-face because of the higher surface
energy. This aids in the well-controlled formation of homogeneous graphene
23
.
Graphene was grown at 2,000 8C and 1 atm argon gas pressure, resulting in
monolayers of graphene atomically uniform over more than 50 mm
2
, as confirmed
by low-energy electron microscopy. Twenty Hall bar devices of different sizes, from
160 mm 35 mm down to 11.6 mm 2 mm were produced on two 0.5-cm
2
wafers
using standard electron-beam lithography and oxygen plasma etching (Fig. 1c).
Atomic force microscopy (AFM) images reveal that the graphene layer covers the
substrate steps like a carpet, preserving its structural integrity (Fig. 1a). Contacts to
graphene were produced by straightforward deposition of 3 nm of titanium and
100 nm of gold through a lithographically defined mask followed by lift-off, with a
typical area of graphene–metal interface of 1 10
4
mm
2
for each contact. This
process favourably compares with the laborious contact preparation to two-
dimensional electron gas in conventional semiconductor technology. The
manufactured devices were not cleaned in any way before measurements. Using low-
magnetic-field measurements, we established that the manufactured material was
n-doped, owing to charge transfer from SiC, with the measured electron
concentration lying in the range 5 10
11
to 10 10
11
cm
22
, mobility of
2,400 cm
2
V
21
s
21
at room temperature and between 4,000 and
7,500 cm
2
V
21
s
21
at 4.2 K, almost independent of device dimensions and
orientation with respect to the substrate terraces. The scattering mechanisms in the
epitaxial graphene and the role of the substrate need further investigation. As seen in
the AFM images (Fig. 1b), the graphene Hall bars are patterned across many
substrate terraces; however, the measurements of the QHE reveal that the continuity
of graphene is preserved.
Received 14 September 2009; accepted 3 December 2009;
published online 17 January 2010; corrected online 23 F ebruary 2010
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Acknowledgements
The authors would like to thank L. Wallde
´
n, T. Lo¨fwander, F. Lombardi, J. Gallop and
T. Claeson for stimulating discussions and S. Giblin and J. Williams for help with
experiments. We are grateful to the NPL Strategic research programme, Swedish Research
Council and Foundation for Strategic Research, European Union FP7 SINGLE, UK
Engineering and Physical Sciences Research Council grant no. EP/G041954 and the
Science & Innovation Award EP/G014787 for financial support.
Author contributions
S.K., A.T. and V.F. conceived and designed the experiments. A.T., S.L., A.K., S.P., O.K., T.J.
and S.K. performed the experiments. R.Y. and M.S. contributed materials. A.T., V.F. and
S.K. analysed the data and co-wrote the paper. All authors discussed the results and
commented on the manuscript.
Additional information
The authors declare no competing financial interests. Supplementary information
accompanies this paper at www.nature.com/naturenanotechnology.
Reprints and
permission information is available online at http://npg.nature.com/reprintsandpermissions/.
Correspondence and requests for materials should be addressed to A.T.
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... The 2019 redefinition of the International System of Units (SI) has fundamentally changed the world of electrical precision measurements, and the base units are now derived from seven exactly defined fundamental constants 1 , such as Planck's constant h and elementary charge e. The quantum Hall effect (QHE) is one cornerstone in the SI, and epigraphene QHE devices have already revolutionized practical resistance metrology [2][3][4] , becoming the preferred embodiment of primary electrical resistance standards due to their robustness and relatively relaxed measurement conditions. The QHE in epigraphene provides an exact relationship between resistance and fundamental constants R = R K /(4(N + 1/2)), where R K = h/e 2 ≈ 25.8 kΩ (von Klitzing constant) and an integer N ≥ 0. Epigraphene combines large Landau level spacing 5 with high energy loss rates, resulting in larger I C compared to conventional semiconductors 6,7 . ...
... Moreover, the large quantum capacitance of epigraphene leads to a B-dependent charge transfer from the substrate, resulting in the widest resistance plateau observed to date, extending to B>50 T 9,10 . The N = 0 plateau is not only the most robust, but also the most well-quantized and is therefore preferred for precision metrology [2][3][4] . All of these epigraphene-specific virtues translate into highly robust quantization over a wide parameter space 3 and greatly facilitates practical quantum resistance metrology. ...
... Due to their stability, QHAs are also desired for precision measurements of current in general 17 are also useful for practical resistance metrology and will reduce uncertainties in calibrations of a wide range of resistance values since they allow for direct comparison measurement between primary quantum standards and secondary standards, shortening the calibration chain. However, a technological breakthrough is needed to enable the aforementioned applications, since a single graphene Hall bar (HB) can in practice only achieve R = R K /2 and I C~1 00 μA at typical operating conditions [2][3][4]18 . ...
Article
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Graphene quantum Hall effect (QHE) resistance standards have the potential to provide superior realizations of three key units in the new International System of Units (SI): the ohm, the ampere, and the kilogram (Kibble Balance). However, these prospects require different resistance values than practically achievable in single graphene devices (~12.9 kΩ), and they need bias currents two orders of magnitude higher than typical breakdown currents IC ~ 100 μA. Here we present experiments on quantization accuracy of a 236-element quantum Hall array (QHA), demonstrating RK/236 ≈ 109 Ω with 0.2 part-per-billion (nΩ/Ω) accuracy with IC ≥ 5 mA (~1 nΩ/Ω accuracy for IC = 8.5 mA), using epitaxial graphene on silicon carbide (epigraphene). The array accuracy, comparable to the most precise universality tests of QHE, together with the scalability and reliability of this approach, pave the road for wider use of graphene in the new SI and beyond.
... This section provides security in a quantum environment [35][36][37]. On the basis of the difficulty in some lattices, the security of our proposal is assumed. ...
Article
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Both security and privacy are central issues and need to be properly handled because communications are shared among vehicles in open channel environments of 5G-enabled vehicular networks. Several researchers have proposed authentication schemes to address these issues. Nevertheless, these schemes are not only vulnerable to quantum attacks but also use heavy operations to generate and verify signatures of messages. Additionally, these schemes need an expensive component RoadSide Unit (RSU)-aided scheme during the joining phase. To address these issues, we propose a lightweight quantum-resistant scheme according to the lattice method in 5G-enabled vehicular networks. Our proposal uses matrix multiplication instead of operations-based bilinear pair cryptography or operations-based elliptic curve cryptography to generate and verify signatures of messages shared among vehicles. Our proposal satisfies a significant reduction in performance, which makes it lightweight enough to handle quantum attacks. Our proposal is based on 5G technology without using any RSU-aided scheme. Security analysis showed that our proposal satisfies privacy and security properties as well as resists quantum attacks. Finally, our proposal also shows favorable performance compared to other related work.
... We describe here in brief the sample fabrication procedure; more details can be found in the Materials and Methods section. The decomposition of a 6H-SiC(0001) substrate at high temperature under atmospheric pressure in an argon atmosphere was used to produce a graphene monolayer with high electron mobility [25][26][27][28][29][30][31] (label "Gr" in Fig. 1 refers to graphene). The graphene monolayer was obtained by tuning the annealing temperature of the initial SiC substrate 32 . ...
Article
Nearly localized moiré flat bands in momentum space, arising at particular twist angles, are the key to achieve correlated effects in transition-metal dichalcogenides. Here, we use angle-resolved photoemission spectroscopy (ARPES) to visualize the presence of a flat band near the Fermi level of van der Waals (vdW) WSe2/MoSe2 heterobilayer grown by molecular beam epitaxy. This flat band is localized near the Fermi level and has a width of several hundred meVs. By combining ARPES measurements with density functional theory (DFT) calculations, we confirm the coexistence of different domains, namely the reference 2H stacking without layer misorientation and regions with arbitrary twist angles. For the 2H-stacked heterobilayer, our ARPES results show strong interlayer hybridization effects, further confirmed by complementary micro- Raman spectroscopy measurements. The spin-splitting of the valence band at K is determined to be 470 meV. The valence band maximum (VBM) position of the heterobilayer is located at the Γ point. The energy difference between the VBM at Γ and the K point is of -60 meV, which is a stark difference compared to individual 1L WSe2 and 1L WSe2, showing both a VBM at K.
... Since the redefinition of the International System of Units (SI) took place in 2019, many efforts have focused on the simplification of measurements so that the new SI, based on quantum phenomena, is accessible to sectors beyond government and metrology institutes [1][2][3][4][5][6][7]. For resistance metrology, this handoff manifests as the development of graphene-based quantum Hall effect (QHE) standards, with devices capable of accessing a quantized Hall resistance at higher temperatures and lower magnetic fields than the GaAs-based devices used previously. ...
Article
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Efforts to make the International System of Units (SI) more accessible have been growing since the global redefinition of the SI in 2019. Presently, the ohm is defined through the quantum Hall effect (QHE). However, quantum Hall devices require strong magnetic fields for a robust expression of the QHE. Magnetically doped topological insulators offer an opportunity to circumvent this limitation, as they require no magnetic field to provide a quantized resistance plateau via the quantum anomalous Hall effect (QAHE). Here, we detail experimental methodology and noise-analysis techniques for high-precision measurements of QAHE devices.
... This limits the integration of spinhosting GNRs into spintronic devices. Ballistic transport through metallic GNRs [36][37][38] would ease the implementation by facilitating the read out of the embedded spins. ...
Article
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Spin-hosting graphene nanostructures are promising metal-free systems for elementary quantum spintronic devices. Conventionally, spins are protected from quenching by electronic band gaps, which also hinder electronic access to their quantum state. Here, we present a narrow graphene nanoribbon substitutionally doped with boron heteroatoms that combines a metallic character with the presence of localized spin 1/2 states in its interior. The ribbon was fabricated by on-surface synthesis on a Au(111) substrate. Transport measurements through ribbons suspended between the tip and the sample of a scanning tunneling microscope revealed their ballistic behavior, characteristic of metallic nanowires. Conductance spectra show fingerprints of localized spin states in the form of Kondo resonances and inelastic tunneling excitations. Density functional theory rationalizes the metallic character of the graphene nanoribbon due to the partial depopulation of the valence band induced by the boron atoms. The transferred charge builds localized magnetic moments around the boron atoms. The orthogonal symmetry of the spin-hosting state's and the valence band's wave functions protects them from mixing, maintaining the spin states localized. The combination of ballistic transport and spin localization into a single graphene nanoribbon offers the perspective of electronically addressing and controlling carbon spins in real device architectures.
... Since a metrological demonstration [8] of Hall quantization with graphene grown on silicon carbide (SiC), epitaxial graphene has been employed to demonstrate a QHR under relaxed experimental conditions with metrological accuracy [9][10][11][12][13]. Additionally, epitaxial graphene on SiC with a small carrier density may provide a scalable platform for quantum resistance metrology [14,15]. ...
Article
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The large Landau energy spacing, stemming from the linear energy-momentum dispersion of quasiparticles in graphene, allows an efficient realization of the quantum Hall effect at a small density of charge carriers. Promising scalable epitaxial graphene on silicon carbide, however, requires molecular doping, which is generally unstable under ambient conditions, to compensate for electron transfer from the silicon carbide substrate. Here, we employed classical glass encapsulation common in organic electronics to passivate molecular doped epitaxial graphene against water and oxygen molecules in air. We have investigated the stability of Hall quantization in a glass-encapsulated device for almost one year. The Hall quantization is maintained above a threshold magnetic field within 2 nΩ/Ω smaller than the measurement uncertainty of 3.5 nΩ/Ω through multiple thermal cycles for almost one year, while the ordinary unencapsulated device in air distinctly shows a relative deviation larger than 0.05% from the nominal quantized Hall resistance in one month.
Article
Selective, sensitive and accurate gas monitoring system can help to control the air pollution, prevent an explosion and injury to industrial workers. Due to very high surface to volume ratio and unique properties, graphene is a highly suitable carbon material to detect toxic gases. As single layer, few layer or multi-layer, graphene either in pure form or after modifications has been studied for the application in gas sensors. Present paper serves as a compendium of research work carried out on graphene and its derivatives in gas sensing applications. Review is mainly concentrated on the sensing of three toxic gases namely nitrogen dioxide (NO 2 ), carbon monoxide (CO) and ammonia (NH 3 ). Special emphasis is done on describing the mechanisms for gas sensing by pristine graphene and after modifications.
Article
The extreme versatility of van der Waals materials originates from their ability to exhibit new electronic properties when assembled in close proximity to dissimilar crystals. For example, although graphene is inherently nonmagnetic, recent work has reported a magnetic proximity effect in graphene interfaced with magnetic substrates, potentially enabling a pathway toward achieving a high-temperature quantum anomalous Hall effect. Here, we investigate heterostructures of graphene and chromium trihalide magnetic insulators (CrI3, CrBr3, and CrCl3). Surprisingly, we are unable to detect a magnetic exchange field in the graphene but instead discover proximity effects featuring unprecedented gate tunability. The graphene becomes highly hole-doped due to charge transfer from the neighboring magnetic insulator and further exhibits a variety of atypical gate-dependent transport features. The charge transfer can additionally be altered upon switching the magnetic states of the nearest CrI3 layers. Our results provide a roadmap for exploiting proximity effects arising in graphene coupled to magnetic insulators.
Article
Using the normal incidence x-ray standing-wave technique as well as low-energy electron microscopy we have investigated the structure of quasifreestanding monolayer graphene (QFMLG) obtained by intercalation of antimony under the (63×63)R30∘ reconstructed graphitized 6H-SiC(0001) surface, also known as zeroth-layer graphene. We found that Sb intercalation decouples the QFMLG well from the substrate. The distance from the QFMLG to the Sb layer almost equals the expected van der Waals bonding distance of C and Sb. The Sb intercalation layer itself is monoatomic, flat, and located much closer to the substrate, at almost the distance of a covalent Sb-Si bond length. All data is consistent with Sb located on top of the uppermost Si atoms of the SiC bulk.
Article
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In this work, the limiting factors for developing metrologically useful arrays from epitaxial graphene on SiC are lifted with a combination of centimeter-scale, high-quality material growth and the implementation of superconducting contacts. Standard devices for metrology have been restricted to having a single quantized value output based on the ν = 2 Landau level. With the demonstrations herein of devices having multiple outputs of quantized values available simultaneously, these versatile devices can be used to disseminate the ohm globally. Such devices are designed to give access to quantized resistance values over the range of three orders of magnitude, starting as low as the standard value of ∼12.9 k[Formula: see text] and reaching as high as 1.29 M[Formula: see text]. Several experimental methods are used to assess the quality and versatility of the devices, including standard lock-in techniques and Raman spectroscopy.
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This paper describes the main tests and precautions necessary for both reproducible and accurate results in the use of the quantum Hall effect as a means to establish a reference standard of dc resistance having a relative uncertainty of a few parts in 109.
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The effectively massless, relativistic behaviour of graphene's charge carriers—known as Dirac fermions—is a result of its unique electronic structure, characterized by conical valence and conduction bands that meet at a single point in momentum space (at the Dirac crossing energy). The study of many-body interactions amongst the charge carriers in graphene and related systems such as carbon nanotubes, fullerenes and graphite is of interest owing to their contribution to superconductivity and other exotic ground states in these systems. Here we show, using angle-resolved photoemission spectroscopy, that electron–plasmon coupling plays an unusually strong role in renormalizing the bands around the Dirac crossing energy—analogous to mass renormalization by electron–boson coupling in ordinary metals. Our results show that electron–electron, electron–plasmon and electron–phonon coupling must be considered on an equal footing in attempts to understand the dynamics of quasiparticles in graphene and related systems.
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This paper gives the 2006 self-consistent set of values of the basic constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA) for international use. Further, it describes in detail the adjustment of the values of the constants, including the selection of the final set of input data based on the results of least-squares analyses. The 2006 adjustment takes into account the data considered in the 2002 adjustment as well as the data that became available between 31 December 2002, the closing date of that adjustment, and 31 December 2006, the closing date of the new adjustment. The new data have led to a significant reduction in the uncertainties of many recommended values. The 2006 set replaces the previously recommended 2002 CODATA set and may also be found on the World Wide Web at physics.nist.gov/constants.
Conference Paper
Graphene is the first example of truly two-dimensional crystals - it's just one layer of carbon atoms. It turns out that graphene is a gapless semiconductor with unique electronic properties resulting from the fact that charge carriers in graphene obey linear dispersion relation, thus mimicking massless relativistic particles. This results in the observation of a number of very peculiar electronic properties - from an anomalous quantum Hall effect (QHE) to the absence of localization. It also provides a bridge between condensed matter physics and quantum electrodynamics and opens new perspectives for carbon-based electronics.
Article
Measurements of the Hall voltage of a two-dimensional electron gas, realized with a silicon metal-oxide-semiconductor field-effect transistor, show that the Hall resistance at particular, experimentally well-defined surface carrier concentrations has fixed values which depend only on the fine-structure constant and speed of light, and is insensitive to the geometry of the device. Preliminary data are reported.
Article
Homogeneous large-area graphene monolayers were successfully prepared ex situ on 6H-SiC(0001). The samples have been studied systematically and the results are compared with those from a sample cut from the same wafer and prepared by in situ heating. The formation of smaller graphene flakes was found on the in situ prepared sample, which is in line with earlier observations. Distinctly different results are observed from the ex situ graphene layers of different thicknesses, which are proposed as a guideline for determining graphene growth. Recorded C 1s spectra consisted of three components: bulk SiC, graphene (G), and interface (I), the latter being a 6√3 layer. Extracted intensity ratios of G/I were found to give a good estimate of the thickness of graphene. Differences are also revealed in micro low energy electron diffraction images and electron reflectivity curves. The diffraction patterns were distinctly different from a monolayer thickness up to three layers. At a larger thickness only the graphitelike spot was visible. The electron reflectivity curve showed a nice oscillation behavior with kinetic energy and as a function of the number of graphene layers. The graphene sheets prepared were found to be very inert and the interface between the substrate and the layer(s) was found to be quite abrupt. No free Si could be detected in or on the graphene layers or at the interface.
Article
In this paper, studies of frequency standards, standard-volt cells, and gauge blocks are used as examples of long-term random-correlated time series which indicate behavior that is not 'white' (not random and uncorrelated). A straightforward time-domain statistical approach which for power-law spectra yields an alternative estimation method for most of the important random power-law processes encountered is outlined. Knowing the spectrum provides for clearer uncertainty assessment in the presence of correlated random deviations. The statistical approach outlined also provides a simple test for a white spectrum, thus allowing a metrologist to know whether use of the classical variance is suitable or whether to incorporate better uncertainty assessment procedures.
Article
Measurements of the quantized Hall resistance RH (i) (i = 2 or 4) in 7 different heterostructures (six GaAs based, one InP based) are reported. RH (i) is measured in terms of ΩLCIE by means of a resistance-ratio measurement bridge using a cryogenic current comparator. The peak-to-peak scatter of the results is 8.5 × 10⁻⁸. An estimation of RH (i = 2) in terms of ΩLCIE is given with a 1 σ (one standard deviation) total uncertainty of 2.2 × 10⁻⁸.
Article
The quantum Hall effect (QHE) provides an invariant reference for resistance linked to natural constants. It is used worldwide to maintain and compare the unit of resistance. The reproducibility reached today is almost two orders of magnitude better than the uncertainty of the determination of the ohm in the international system of units SI. In this article, mainly the aspects of the QHE relevant for its metrological application are reviewed. After a short introduction of the theoretical models describing the integer QHE, the properties of the devices used in metrology and the measurement techniques are described. A detailed summary is given on the measurements carried out to demonstrate the universality of the quantized Hall resistance and to assess all the effects leading to deviations of the Hall resistance from the quantized value. In addition, the present and future role of the QHE in the SI and the field of natural constants is discussed.