The University of Manchester Research
Edge currents shunt the insulating bulk in gapped
graphene
DOI:
10.1038/ncomms14552
Document Version
Final published version
Link to publication record in Manchester Research Explorer
Citation for published version (APA):
Zhu, M. J., Kretinin, A., Thompson, M. D., Bandurin, D., Hu, S., Yu, G. L., Birkbeck, J., Mishchenko, A., Vera-
Marun, I. J., Watanabe, K., Taniguchi, T., Polini, M., Prance, J. R., Novoselov, K., Geim, A., & Ben Shalom, M.
(2017). Edge currents shunt the insulating bulk in gapped graphene. Nature Communications, 8, [14552].
https://doi.org/10.1038/ncomms14552
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Download date:26. Aug. 2022
ARTICLE
Received 26 Jun 2016
| Accepted 11 Jan 2017 | Published 17 Feb 2017
Edge currents shunt the insulating bulk in gapped
graphene
M.J. Zhu
1
, A.V. Kretinin
2,3
, M.D. Thompson
4
, D.A. Bandurin
1
,S.Hu
1
, G.L. Yu
1
, J. Birkbeck
1,2
, A. Mishchenko
1
,
I.J. Vera-Marun
1
, K. Watanabe
5
, T. Taniguchi
5
, M. Polini
6
, J.R. Prance
4
, K.S. Novoselov
1,2
, A.K. Geim
1,2
& M. Ben Shalom
1,2
An energy gap can be opened in the spectrum of graphene reaching values as large as 0.2 eV
in the case of bilayers. However, such gaps rarely lead to the highly insulating state expected
at low temperatures. This long-standing puzzle is usually explained by charge inhomogeneity.
Here we revisit the issue by investigating proximity-induced superconductivity in gapped
graphene and comparing normal-state measurements in the Hall bar and Corbino geometries.
We find that the supercurrent at the charge neutrality point in gapped graphene propagates
along narrow channels near the edges. This observation is corroborated by using the edgeless
Corbino geometry in which case resistivity at the neutrality point increases exponentially with
increasing the gap, as expected for an ordinary semiconductor. In contrast, resistivity in the
Hall bar geometry saturates to values of about a few resistance quanta. We attribute the
metallic-like edge conductance to a nontrivial topology of gapped Dirac spectra.
DOI: 10.1038/ncomms14552
OPEN
1
School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, UK.
2
National Graphene Institute, The University of Manchester,
Booth St E, Manchester M13 9PL, UK.
3
School of Materials, The University of Manchester, Manchester M13 9PL, UK.
4
Department of Physics, University of
Lancaster, Lancaster LA1 4YW, UK.
5
National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.
6
Istituto Italiano di Tecnologia,
Graphene Labs, Via Morego 30I-16163, Italy. Correspondence and requests for materials should be addressed to A.K.G. (email: geim@manchester.ac.uk) or to
M.B.S. (email: moshe.benshalom@manchester.ac.uk).
NATURE COMMUNICATIONS | 8:14552 | DOI: 10.1038/ncomms14552 | www.nature.com/naturecommunications 1
T
he gapless spectra of mono- and bilayer graphene (MLG
and BLG, respectively) are protected by symmetry of their
crystal lattices. If the symmetry is broken by interaction
with a substrate
1,2
or by applying an electric field
3,4
, an energy
gap opens in the spectrum. In BLG, its size E
gap
can be controlled
by the displacement field D applied between the two graphene
layers. Large gaps were found using optical methods
5
and
extracted from temperature (T) dependences of resistivity r at
sufficiently high T (refs 6–10). Their values are in good agreement
with theory. On the other hand, at low T (typically, below 50 K),
r at the charge neutrality point (CNP) in gapped graphene is
often found to saturate to relatively low values that are
incompatible with large E
gap
(refs 6–11). This disagreement is
attributed to remnant charge inhomogeneity
6,8,10
that results in
hopping conductivity and, therefore, weakens T dependences.
Alternative models to explain the subgap conductivity were
proposed, too. They rely on the nontrivial topology of Dirac
bands in gapped MLG and BLG
12–15
, which gives rise to
valley-polarized currents
13–15
. Large nonlocal resistances were
reported for both graphene systems at the CNP and explained
by valley currents propagating through the charge-neutral
bulk
16–18
. Graphene edges
12,15
, p–n junctions
19
and stacking
boundaries
20
can also support topological currents. These
conductive channels were suggested to shunt the insulating
bulk, leading to a finite r. Experimentally, the situation is even
more complicated because additional conductivity may appear for
trivial reasons such as charge inhomogeneity induced by chemical
or electrostatic doping
21–23
. Here we show that highly conductive
channels appear near edges of charge-neutral graphene if an
energy gap is opened in its spectrum. We tentatively attribute the
edge channels to the presence of such unavoidable defects as,
for example, short zigzag-edge segments
12
. Their wavefunctions
extend deep into the insulating bulk where they sufficiently
overlap to create a quasi-one-dimensional impurity band with
little intervalley scattering and high conductivity. We believe that,
in certain graphene devices, the localization length can be very
long, comparable to typical distances between electric contacts,
which effectively results in shunting the gapped bulk.
Results
Josephson current distributions. We start with discussing
behaviour observed for superconductor-graphene-superconductor
(SGS) Josephson junctions. Our devices were short and
wide graphene crystals that connected superconducting Nb
electrodes
24
(Fig. 1). Each device contained several such SGS
junctions with the length L varying from 300 to 500 nm and the
width W from 3 to 5 mm. To ensure highest possible quality
24
,
graphene was encapsulated between hexagonal boron nitride
(hBN) crystals with the upper hBN serving as a top gate dielectric
and the Si/SiO
2
substrate as a bottom gate (Fig. 1b). For details of
device fabrication and characterization, we refer to ‘Methods’
section and Supplementary Note 1 and Supplementary Fig. 1. By
measuring the critical current I
c
as a function of perpendicular
magnetic field B, the local density J
s
(x) in the x direction
perpendicular to the supercurrent flow can be deduced
25
,
as illustrated in Fig. 1c,d. This technique is well established and
was previously used to examine, for example, edge states in
topological insulators
26
and wave-guided states in graphene
22
.
In our report, we exploit the electrostatic control of the BLG
spectrum to examine how J
s
(x) changes with opening the gap.
By varying the top and bottom gate voltages (V
tg
and V
bg
,
respectively), it is possible to keep BLG charge neutral while
doping the two graphene layers with carriers of the opposite sign
(see Fig. 2a). This results in the displacement field D(V
tg
,V
bg
) that
translates directly into the spectral gap
3–6
. Its size E
gap
(D) can be
deduced not only theoretically but also measured experimentally, as
discussed in section 1 of Supplementary Information Note 1. To
quantify proximity superconductivity in our devices, we define their
critical current I
c
as the current at which the differential resistance
dV/dI deviates from zero above our noise level
24
. With reference to
Fig. 2b, I
c
corresponds to the edge of the dark area outlined by
bright contours. At high doping (Fermi energy 4E
gap
) and low T,
I
c
is found to depend weakly on D, reaching values of a few
mA mm
1
, in agreement with the previous reports
22,24,27
.The
supercurrent generally decreases with increasing junction’s
resistance and becomes small at the CNP. Its value depends on
E
gap
(Fig. 2b). Accordingly, the largest I
c
in the neutral state is
found for zero D (no gap) reaching E300 nA for the junction
shown in Fig. 2. The value drops to 2 nA at D ¼
±
0.07V nm
1
,
which correspo nds to E
gap
E7 meV. For larger gaps, I
c
becomes
smaller than 1 nA and could no longer be resolved because of a
finite temperature (down to 10 mK) and background noise
24
.
We analyse changes in the interference pattern, I
c
(B), with
increasing D (that is, increasing E
gap
). At zero D, we observe the
standard Fraunhofer pattern at the CNP, which is basically
similar to that measured at high doping (cf. two top panels
of Fig. 2c). Only absolute values of I
c
are different because of
different r, as expected
24
. The Fraunhofer pattern corresponds to
a uniform current flow (Fig. 1c,d). In contrast, the interference
pattern measured at the CNP for a finite gap is qualitatively
different (see Fig. 2c; D ¼ 0.055 V nm
1
). The phase of the
–4 –3 –2 –1
–W/2
I
c
(B) =
J
s
(x)e
2πiBx / Φ
0
dx
01
Φ/Φ
0
234
cd
ab
hBN
hBN
SiO
2
Si (bottom gate)
Nb
V
tg
V
bg
BLG
Au (top gate)
Nb
SourceDrain
Au
Nb
x–W/2 W/2
J
s
(x)
I
c
(B)
1 μm
W/2
Figure 1 | Gated Josephson junctions and spatial distribution of
supercurrents. (a) Electron micrograph of our typical device (in false
colour). Nb leads (green) are connected to bilayer graphene (its edges are
indicated by red dashes). The top gate is shown in yellow. (b) Schematics of
such junctions. (c) Illustration of uniform and edge-dominant current flow
through Josephson junctions (top and bottom panels, respectively). (d)The
corresponding behaviour of the critical current I
c
as a function of B. I
c
(B)is
related to J
s
(x) by the equation shown in d. For a uniform current flow, I
c
should exhibit a Fraunhofer-like pattern (top panel) such that the
supercurrent goes to zero each time an integer number N of magnetic flux
quanta F
0
thread through the junction. Maxima in I
c
between zeros also
become smaller with increasing N. For the flow along edges (bottom panel),
I
c
is minimal for half-integer flux values F ¼ (N þ 1/2)F
0
, and maxima in I
c
are independent of B. The spatial distribution J
s
(x) can be found
24,25
from
I
c
(B) using the inverse FFT. Due to a finite interval of F over which the
interference pattern is usually observed experimentally, J
s
(x) obtained
from the FFT analysis are usually smeared over the x axis as shown
schematically in c.
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14552
2 NATURE COMMUNICATIONS | 8:14552 | DOI: 10.1038/ncomms14552 | www.nature.com/naturecommunications
oscillations changes by 90° and the central lobe becomes twice
narrower. In addition, the side lobes no longer decay with
increasing B but exhibit nearly the same amplitude (additional
example in Supplementary Note 2 and Fig. 2). Such a pattern
resembles the one shown schematically in Fig. 1d for the case of
the supercurrent flowing along edges. The only difference with
Fig. 1d is that in our case the central lobe remains higher than the
others. For quantitative analysis, we calculated the inverse
fast Fourier transform (FFT) of I
c
(B), which yielded
26
the
current distributions J
s
(x) shown in Fig. 2d. The supercurrent is
progressively pushed towards device edges with increasing
the gap. This is already visible for D ¼ 0.025 V nm
1
but
further increase in D suppresses the bulk current to practically
zero, within the experimental accuracy of our FFT analysis
(Fig. 2d and Supplementary Fig. 3). The accuracy is limited by a
finite range of B in which the interference pattern could be
detected (Supplementary Note 3).
For completeness, we have also studied SGS junctions that were
fabricated using monolayer graphene placed on top of hBN and
aligned along its crystallographic axes. Such alignment (within
1–2°) results in opening of a gap of E30 meV at the main
CNP
1,2
, and secondary CNPs appear for high electron and hole
doping
1,2,16
. Unlike for the case of BLG, E
gap
cannot be changed
in situ in MLG devices, but one can still compare interference
patterns for neutral and doped states of the same SGS junction
and, also, use nonaligned junctions as a reference. Figure 3a,b
shows typical behaviour of I
c
as a function of carrier concentration
n for SGS devices made from gapped (aligned) and gapless
(nonaligned) MLG. In the gapped device, the supercurrent is
suppressed not only at the main CNP but also at secondary CNPs.
For all electron and hole concentrations away from the CNPs, both
devices exhibit the standard Fraunhofer pattern indi cating a
uniform supercurrent flow (cf. t op panels of Fig. 3c,d). The same
is valid at the CNP in gapless graphene (Fig. 3d,f). In contrast, for
gapped MLG, the interference pattern at the main CNP undergoes
significant changes such that the phase and period of oscillations in
I
c
change (Fig. 3c; bottom panel), so mewhat similar to the
behaviour of gapped BLG at the CNP. Quantitative analysis using
FFT again shows that, in gapped MLG, the supercurrent flows
predominantly along graphene edges for no
±
5 10
10
cm
2
(Fig. 3e). The figure seems to suggest a shift of conductive
channels from edges into the interior. This shift originates from the
increase in the Fraunhofer period at the CNP in Fig. 3c and
corresponds to a decrease in the junction’s effective area. However,
we believe that this shift may arise from non-uniform doping along
the current direction. Our MLG devices do not have a top gate and
this allows doping by metal contacts to extend significantly (tens of
nm) inside the graphene channel
28
, which reduces the effective
length of the junction.
We emphasize that the observed redistribution of super-
currents towards edges is an extremely robust effect observed for
all eight gapped graphene junctions we studied and in none
without a gap (more than 10)
24
. In principle, one can imagine
additional electrostatic and/or chemical doping near graphene
–6 –3 0 3
–4
–2
0
2
R (kΩ)
V
bg
(V)
V
tg
(V)
0.2
2.0
20.0
CNP
D=0
10 K
–0.06 –0.03 0.00 0.03 0.06
–300
0
300
–6 –3 0 3 6
E
gap
(meV)
CNP
I (nA)
2
10 mK, B=0
dV/dI
(kΩ)
D (V nm
–1
)
0.0
2.0
4.0
–60
0
60
CNP 0.025 V nm
–1
I (nA)
0.3
0.8
1.3
–3–2–10123
–5
0
5
CNP 0.055 V nm
–1
B (mT)
I (nA)
0.5
3.5
6.5
–200
0
200
CNP
I (nA)
D=0 V nm
–1
0.1
0.3
0.7
–1
0
1
dV/dI
(kΩ)
n=10
12
cm
–2
I (μA)
0.0
0.1
0.2
10 mK
a
–10 –5 0 5 10
0
50
100
W=3.5 μm
L=0.4 μm
×20
×4
D (V nm
–1
)
0
0.025
0.055
J
s
(nA μm
–1
)
x (μm)
b
c
d
Figure 2 | Redistribution of supercurrent as the gap opens in bilayer graphene. (a) Resistance R of one of our Josephson junctions (3.5 mm wide
and 0.4 mm long) above the critical T as a function of top and bottom gate voltages. The dashed white line indicates equal doping of the two graphene
layers with carriers of the same sign. The dashed green line marks the CNP (maximum R) and indicates equal doping with opposite sign carriers.
(b) Differential resistance dV/dI measured along the green line in a at low T and in zero B. Transition from the dissipationless regime to a finite voltage
drop shows up as a bright curve indicating I
c
. The vertical line marks the superconducting gap of our Nb films. (c) Interference patterns in small B.The
top panel is for the case of high doping [I
c
(B ¼ 0) E10 mA] and indistinguishable from the standard Fraunhofer-like behaviour illustrated in Fig. 1d.
The patterns below correspond to progressively larger E
gap
. Changes in the phase of Fraunhofer oscillations are highlighted by the vertical dashed white
lines. (d) Extracted spatial profiles of the supercurrent density (J
s
) at the CNP for the three values of D in c.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14552 ARTICLE
NATURE COMMUNICATIONS | 8:14552 | DOI: 10.1038/ncomms14552 | www.nature.com/naturecommunications 3
edges
21–23
(Supplementary Note 4), which would enhance their
conductivity and, hence, favour local paths for supercurrent. This
mechanism disagrees with the fact that edge supercurrents
appeared independently of the CNP position as a function of
gate voltage (residual doping in our devices varied from
practically zero to o10
11
cm
2
) and were observed for devices
with the top gate being only a few nm away from the graphene
plane. The latter facilitates a uniform electric field distribution
(Supplementary Fig. 4). Chemical doping at graphene edges was
previously reported in non-encapsulated
21
and, also, encapsulated
but not annealed devices
23
. All our devices were encapsulated and
thoroughly annealed, and some of them had edges that were fully
covered by top hBN rather than exposed to air (Supplementary
Figs 5 and 6). We also note our Josephson experiments yielded
similar supercurrent densities at BLG edges, even in the case
where the two edges were fabricated differently (one is etched as
discussed above and the other cleaved and covered with hBN; see
Fig. 1a). The latter observation in particular indicates little
external doping along the edges. Importantly, we have found no
evidence for enhanced transport along edges of similar but
gapless graphene devices. To this end, we refer, for example,
to Fig. 3e,f. In the gapped MLG device, near-edge J
s
reaches
E100 nA mm
1
. Such supercurrents would certainly be visible in
the distribution profile of the non-gapped graphene at the CNP in
Fig. 3f. All the above observations point at a critical role of the
presence of the gap in creating local edge currents.
Corbino geometry. While providing important insights about the
current flow, Josephson interference experiments are limited to
small E
gap
such that junction’s resistance remains well below 1
MOhm allowing superconducting proximity. To address the
situation for the larger gaps accessible in BLG devices, we com-
pare their normal transport characteristics in the Corbino and
Hall bar geometries. Because the Corbino geometry does not
involve edges, such a comparison has previously been exploited
to investigate the role of edge transport (for example, in the
quantum Hall effect
29
). A number of dual-gated BLG devices
such as shown in Fig. 4a were fabricated and examined over a
wide range of D and T. Our experiments revealed a striking
difference between r measured in the two geometries. In the
Corbino geometry, r at the CNP rises exponentially with D and
its value is limited only by a finite dielectric strength of
E0.7 V nm
1
achievable for our hBN (Fig. 4b) and, at low T,
by leakage currents. In contrast, in the Hall bar geometry, r at the
–5
0
5
10 mK
dV/dI
n (cm
–2
)
1×10
12
0
40
80
–10 –5 0 5 10
0
50
100
W=5 μm
W=3 μm
L=0.4 μm L=0.35 μm
n (cm
–2
)
3×10
11
3×10
12
2×10
10
CNP
J
s
(nA μm
–1
)
J
s
(nA μm
–1
)
x (μm)
–10 –5 0 5 10
x (μm)
J
s
/10
–2 –3 –2 –1 0 1 2 3–1012
–0.1
0.0
0.1
dV/dI
10 mK
CNP
B (mT)
0.0
1.5
3.0
–3 –2 –1 0 1 2 3
–10
0
10
ab
cd
ef
0.3 K, B=0
n (10
12
cm
–2
)
–3 –2 –1 0 1 2 3
n (10
12
cm
–2
)
I (μA)I (μA)I (μA)
I (μA)I (μA)I (μA)
0
250
500
dV/dI
(Ω)
(Ω)
(KΩ)
(KΩ)
(Ω)
(Ω)
0
200
400
J
s
/10
n (cm
–2
)
CNP
–10
–5
0
5
10
dV/dI
0.3 K, B=0
0
250
500
–10
0.6
0.0
–0.6
–5
0
5
10
0.3 K
n (cm
–2
)
3×10
12
0
40
80
0.0
0.4
0.8
dV/dI
dV/dI
Gapless graphene
0.3 K
hBN/graphene superlattice
CNP
B (mT)
Figure 3 | Interference patterns and supercurrent flow in gapped and non-gapped graphene monolayers. (a) Differential resistance as a function of
carrier concentration n and applied current I for a Nb-MLG-Nb junction (5 mm wide and 0.4 mm long). The gap is induced by alignment with the bottom hBN
crystal. (b) Same for encapsulated but nonaligned monolayer graphene (the junction is 3 mm wide and 0.35 mm long). (c) Interference patterns for gapped
MLG at relatively high doping (top panel) and at the CNP. (d) Same for non-gapped graphene. ( e,f) Corresponding spatial profiles of the supercurrent
density (J
s
). They were calculated using experimental patterns such as shown in c,d. Note that graphene edges in e support fairly high supercurrent at the
CNP, whereas there is no indication of any enhanced current density along edges for the non-gapped case in f.
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14552
4 NATURE COMMUNICATIONS | 8:14552 | DOI: 10.1038/ncomms14552 | www.nature.com/naturecommunications