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RESEARCH ARTICLE
|
OCTOBER 23 2023
Spin and valley-polarized multiple Fermi surfaces of
α
-
RuCl
3
/bilayer graphene heterostructure
Soyun Kim
;
Jeonghoon Hong
;
Kenji W
atanabe
;
Takashi T
aniguchi
;
Joseph Falson
;
Jeongwoo Kim
;
Youngwook Kim
Appl. Phys. Lett.
123, 173101 (2023)
https://doi.org/10.1063/5.0170810
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Spin and valley-polarized multiple Fermi surfaces
of
a
-RuCl
3
/bilayer graphene heterostructure
Cite as: Appl. Phys. Lett.
123
, 173101 (2023);
doi: 10.1063/5.0170810
Submitted: 4 August 2023
.
Accepted: 11 October 2023
.
Published Online: 23 October 2023
Soyun
Kim,
1
Jeonghoon
Hong,
2,3
Kenji
Watanabe,
4
Takashi
Taniguchi,
5
Joseph
Falson,
6
Jeongwoo
Kim,
2,a)
and Youngwook
Kim
1,a)
AFFILIATIONS
1
Department of Physics and Chemistry, Daegu Gyeongbuk Institute of Science and Technology (DGIST), Daegu 42988,
Republic of Korea
2
Department of Physics, Incheon National University, Incheon 22012, Republic of Korea
3
Department of Physics, Indiana University, Bloomington, Indiana 47405, USA
4
Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba 305-0044, Japan
5
International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba 305-0044, Japan
6
Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, California 91125, USA
a)
Authors to whom correspondence should be addressed:
kjwlou@inu.ac.kr
and
y.kim@dgist.ac.kr
ABSTRACT
We report the transport properties of
a
-RuCl
3
/bilayer graphene heterostructures, where carrier doping is induced by a work function
difference, resulting in distinct electron and hole populations in
a
-RuCl
3
and bilayer graphene, respectively. Through a comprehensive
analysis of multi-channel transport signatures, including Hall measurements and quantum oscillation, we unveil significant band modifica-
tions within the system. In particular, we observe the emergence of spin and valley-polarized multiple hole-type Fermi pockets, originating
from the spin-selective band hybridization between
a
-RuCl
3
and bilayer graphene, breaking the spin degree of freedom. Unlike the
a
-RuCl
3
/
monolayer graphene system, the presence of different hybridization strengths between
a
-RuCl
3
and the top and bottom graphene layers leads
to an asymmetric behavior of the two layers, confirmed by effective mass experiments, resulting in the manifestation of valley-polarized
Fermi pockets. These compelling findings establish
a
-RuCl
3
proximitized to bilayer graphene as an outstanding platform for engineering its
unique low-energy band structure.
Published under an exclusive license by AIP Publishing.
https://doi.org/10.1063/5.0170810
The assembly of different materials has emerged as a promising
strategy for modifying the low-energy band structure through the
proximity effect.
1
–
3
Creating heterostructures has been a well-
established approach in the thin-film epitaxy community. However,
the combination of arbitrary materials has been significantly limited
due to considerations of lattice mismatch between the materials and
substrates. In contrast, within the van der Waals community, the
stacking of different 2D materials allows for desired modifications to
the band structure without geometric constraints.
4
–
7
For example, by
bringing graphene into proximity with materials possessing a large
spin
–
orbit coupling, such as WSe
2
,thespin
–
orbit coupling of gra-
phene can be significantly enhanced.
8
–
14
Moreover, twisting has
emerged as a highly effective technique that utilizes interlayer coupling
between similar materials to alter the low-energy band structure, cre-
ates a flatband near the Fermi level,
15
–
22
and induces a reconstructed
lattice in twisted WTe
2
and
a
-MoO
3
.
23
–
25
In particular, exploring the proximity effect between magnetic
and non-magnetic van der Waals materials presents fascinating possi-
bilities for band engineering. It enables the opening of a bandgap in
bilayer graphene when in proximity to magnetic 2D materials like
chromium trihalides.
26
An interfacial interaction between graphene
and CrOCl gives rise to a SiC-graphene type quantum Hall phase up
to 80 K.
27,28
Similar non-monotonic gate dependences have also been
observed in the graphene/CrI
3
,
29
further demonstrating the potential
for band engineering and interfacial effects. Furthermore, the magnetic
proximity effect allows for the hybridization of spin-polarized materi-
als with non-magnetic materials, leading to the emergence of a spin-
split band structure within the non-magnetic materials.
30,31
However,
this intriguing property in the vicinity of the Fermi level is exclusively
observed in specific material combinations, as it is significantly affected
by the difference in work function between them. As a result, capturing
a spin-selective conduction channel remains a challenging task.
Appl. Phys. Lett.
123
, 173101 (2023); doi: 10.1063/5.0170810
123
, 173101-1
Published under an exclusive license by AIP Publishing
Applied Physics Letters
ARTICLE
pubs.aip.org/aip/apl
26 October 2023 18:32:43
a
-RuCl
3
/graphene heterostructure is a promising candidate for
exploring the magnetic proximity effect in 2D materials. Spin-
polarized bands originating from the zig-zag type antiferromagnetic
a
-RuCl
3
are hybridized with the Dirac bands of graphene at the Fermi
level, giving rise to a spin-split Fermi surface.
32
–
37
The quantum oscil-
lations with extraordinary temperature dependence and thermal sig-
nals suggest the presence of spin fractionalization and the potential
existence of Majorana fermions in
a
-RuCl
3
.
38
–
40
However, despite the
fascinating quantum phenomena of
a
-RuCl
3
, the exploration of
hybridization between
a
-RuCl
3
and other two-dimensional materials
of high quality is still lacking, which could offer further possibilities for
exploitable band engineering and strong magnetic proximity coupling.
Furthermore, while spin-splitting can be controlled through proximity
coupling, manipulating the valley degree of freedom remains a signifi-
cant challenge. The valley degree of freedom can only be manipulated
in graphene when it is aligned with the hBN structure.
5
–
7,41
The detec-
tion of a valley-polarized Fermi pocket has not yet been achieved, pre-
senting an ongoing hurdle in this field of research.
In order to identify the potential of band engineering and investi-
gate the proximity effect, we study the transport properties of
a
-RuCl
3
/
bilayer graphene heterostructures. First, we have observed that the
work function difference between
a
-RuCl
3
and bilayer graphene leads
to heavy hole doping in the bilayer graphene. Additionally, the interac-
tion between antiferromagnetic band of
a
-RuCl
3
and bilayer graphene
induces spin-selective band hybridization, breaking the spin degree of
freedom within the bilayer graphene system. In contrast to previous
studies on
a
-RuCl
3
/monolayer graphene, our analysis of effective mass
has confirmed a strong hybridization between the
a
-RuCl
3
band and
the top layer of graphene, while the hybridization with the bottom
layer is comparatively weaker. This interplay between the layer and
valley indices in bilayer graphene results in the lifting of the valley
degree of freedom, allowing us to identify the presence of spin-
polarized and valley-polarized Fermi pockets within the system.
Additionally, we explored the effective mass in higher energy bands of
bilayer graphene, which had remained unexplored until now.
Moreover, we discovered that the band structure of
a
-RuCl3/bilayer
FIG. 1.
(a) Longitudinal resistance as a function of the magnetic field at
T
¼
2 K and
V
g
¼
0 V for bilayer graphene/RuCl
3
. (b) Same as (a) but for the Hall resistivity. Inset dis-
plays a magnified view of the original
R
xy
data, highlighting the nonlinear
R
xy
curve. The red dotted line represents the linear fitting curve of
R
xy
. (c)
D
R
xx
as a function of the
inverse magnetic field. Different colors indicate different gate voltages at
T
¼
2 K. The inset shows schematic of device. (d) FFT spectra of Shubnikov-de Haas oscillations of
(c). Triangles mark six frequency peaks. The inserted graphs with circles represent magnified data of yellow triangle-marked peaks multiplied ten t
imes for each dataset. (e)
Gate voltage-dependent peak sets represented in (d). The color codes are the same as the color of the triangles in (d).
Applied Physics Letters
ARTICLE
pubs.aip.org/aip/apl
Appl. Phys. Lett.
123
, 173101 (2023); doi: 10.1063/5.0170810
123
, 173101-2
Published under an exclusive license by AIP Publishing
26 October 2023 18:32:43
graphene exhibits a highly sensitive response to an applied electric
field, resulting in a phenomenon known as magnetic breakdown. This
phenomenon, specific to bilayer systems, represents a truly unique
aspect when compared to monolayer systems.
a
-RuCl
3
differs from conventional 2D materials, as it is sensitive
to acetone exposure, making traditional lithography and metallization
methods unlikely to succeed.
34,42
To prevent the degradation of
a
-RuCl
3
, we modified the fabrication procedure by first preparing the
bottom electrodes and subsequently transferring the heterostructure
onto them. (The details are available in the Methods section of supple-
mentary material and other relevant Refs.
34
and
42
.) Here, we focus
on our highest quality device, although data from other devices are
available in the supplementary material.
Figure 1(a)
shows
R
xx
plotted
against the magnetic field at a
V
g
¼
0V and
T
¼
2 K. The quantum
oscillations exhibit two characteristics. First, we found rapid oscilla-
tions that exhibit a beating mode, which is attributed to two or more
comparable oscillation frequencies. The second feature is an oscillation
with a slower frequency. These findings demonstrate the emergence of
at least two similar-sized Fermi surfaces and a smaller Fermi surface
than the former pockets. In addition to multiple quantum oscillations,
the Hall resistance exhibits a nonlinear curve in the inset of
Fig. 1(b)
,
suggesting that multiple charge carriers are involved in the transport
measurements.
34
To perform an accurate analysis, we subtracted the background
oscillations and plotted
D
R
xx
as a function of 1/
B
in
Fig. 1(c)
.We
noticed two changes with adjusting the backgate voltage from 60 to
60 V: (i) the number of nodes for slow oscillations increased and (ii)
the intensity of fast oscillations decreased. FFT analysis facilitated a
simpler comparison, as shown in
Fig. 1(d)
. In the low-frequency range,
two dominant peaks are observed below 100 T, for example, at 16 and
30T for
V
g
¼
60V. These peaks gradually shift toward higher frequen-
cies until reaching 65 and 81T at
V
g
¼
60V, indicating two hole-
type Fermi pockets. While extra peaks were observe, such as 12 and
24T at
V
g
¼
0, they do not consistently depend on gate voltage in the
left panel of
Fig. 1(c)
, which may be attributed to low-frequency back-
ground noise. The high-frequency peaks exhibit a similar trend to the
low-frequency region but have four peaks: two prominent peaks (blue
and green triangles) and two minor peaks (purple and yellow trian-
gles). These peaks shifted to higher frequencies as the gate voltage
decreased. Additional peaks were discovered in the high-frequency
range, as marked by gray triangles, but they appeared when the back
gate voltage was negative, and the resulting oscillations were very
weak. In contrast to the six peaks depicted in
Fig. 1(e)
, these particular
peaks do not demonstrate any discernible systematic dependence on
the gate voltage. Therefore, it was challenging to determine the origin
of the three bluish FFT outputs shown in
Fig. 1(d)
. However, we
noticed significant FFT peaks at 60V, which were associated with
strong oscillations and could not be ignored.
To elucidate the origin of the FFT peaks, we investigated the elec-
tronic structure of the
a
-RuCl
3
/bilayer graphene heterostructure as
shown in
Fig. 2(a)
. We reproduced the observed charge transfer from
graphene to
a
-RuCl
3
. The hole-doped bilayer graphene states were
observed at the K point, exhibiting weak hybridization with the flat
bands originating from
a
-RuCl
3
.Incontrastto
a
-RuCl
3
/monolayer
FIG. 2.
(a) Calculated band structure of
a
-RuCl
3
/bilayer graphene heterostructure along the high symmetry line, as indicated in the inset. The Fermi level set to zero. (b)
Atomically projected band structure of the heterostructure near the Fermi level, with blue and red dots representing the atomic contribution from bi
layer graphene (BLG) and
a
-RuCl
3
, respectively. (c) Calculated band structures for the heterostructure, shown with graphene layer resolution (upper). Green and orange dots repres
ent the top layer gra-
phene adjacent to
a
-RuCl
3
(Gra1) and the bottom layer graphene (Gra2), respectively. (d) Same as (c) but with spin resolution near the Fermi level. Empty and filled dots
denote the spin-up and spin-down components, respectively. (e) Calculated Fermi surface with atomic resolution, where blue and red lines represent
BLG and
a
-RuCl
3
, respec-
tively. Red arrow indicates distorted band at K-point. (f) Calculated Fermi surface with atomic resolution, where green and orange lines represent t
he top graphene layer and
the bottom graphene layer, respectively. (f) Variation in the Fermi surface in an energy range between
0.02 and
þ
0.02 eV. Blue and red lines represent BLG and
a
-RuCl
3
,
respectively.
Applied Physics Letters
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Appl. Phys. Lett.
123
, 173101 (2023); doi: 10.1063/5.0170810
123
, 173101-3
Published under an exclusive license by AIP Publishing
26 October 2023 18:32:43
graphene, the proximity of the
a
-RuCl
3
layer to bilayer graphene
results in the breaking of valley symmetry due to the strong interaction
with the top graphene layer. This leads to distinct band dispersions
along the K
–
M and K
0
–
M lines as exhibited in
Fig. 2(b)
.Notably,
Figs.
2(c)
and
2(d)
demonstrate that the hybridization between the top gra-
phene layer (Gra1) and the adjacent
a
-RuCl
3
layer (gray) induces band
splitting along the K
–
Mline(
a
region) while leaving the K
0
–
M
0
line
unaffected (
d
region). The hybridized bands naturally become spin-
polarized due to the magnetic order of the
a
-RuCl
3
layer, as depicted
in
Figs. 2(d)
and S2(c). This anisotropic graphene band induced by the
hybridization with the
a
-RuCl
3
suggests the presence of different
Fermi wavevectors, potentially correlated with the multiple peaks in
the high-frequency region. Furthermore, the presence of two distinct
low-frequency peaks can be attributed to the spin splitting at the K or
K
0
point, as illustrated in
Figs. 2(d)
and S2(b). Although the bottom
layer (Gra2) is not in direct contact with the
a
-RuCl
3
layer, the gra-
phene bands at the K point primarily originating from it are spin-
polarized. The broken valley symmetry may lead to the emergence of
one or two additional peaks in the low-frequency region, contingent
upon the Fermi level. However, the magnitude of this splitting is mar-
ginal, posing challenges in its experimental identification.
We computed the Fermi surface of the
a
-RuCl
3
/bilayer graphene
heterostructure and investigated its variation with the binding energy.
As exhibited in
Fig. 2(e)
,the
a
-RuCl
3
possesses a lemon-shaped elec-
tron pocket (red line) centered at the
C
point, while the bilayer gra-
phene exhibits inner (small K
f
) and outer (large K
f
) hole pockets (blue
line) located at the corners of the Brillouin zone (K point) [
Fig. 2(f)
].
For pure bilayer graphene, there are spin-degenerate Fermi pockets at
the K point. However, due to the hybridization with
a
-RuCl
3
,oneof
the outer hole pockets from the top graphene layer undergoes slight
distortion, resulting in the formation of a smaller, closely packed
Fermi surface. This can be observed as the red pocket at the K point in
Fig. 2(e)
(indicated by red arrow). The emergence of spin-dependent
red pocket at K indicates the existence of two distinct oscillations in
the high-frequency region. In addition, the broken valley symmetry of
K and K
0
induces a slight variation in the size of the outer pockets
depending on the valley [Fig. S2(c)], thereby leading to the occurrence
of additional oscillation peaks, as observed in
Fig. 1
.
Figure 2(g)
shows
that the Fermi surface driven by the bilayer graphene (blue line) is well
maintained against hole/electron doping, whereas the
a
-RuCl
3
states
(red line) are highly sensitive to the Fermi energy. In the negative bind-
ing energies (or hole doping), two concentric hole pockets monotoni-
cally increase in size, while the electron pocket shrinks to the
C
point,
which is consistent with the trends shown in
Fig. 1
. In the positive
binding energies, the separated electron pockets become connected at
the M point and start to form an open Fermi surface, and the hole
pocket coming from the bottom graphene layer (Gra2) disappears. At
10 meV, the Fermi pockets at the K point and the open Fermi surface
at
C
point are in close proximity, leading to possibility of the formation
of different carrier orbit paths. This phenomenon, known as magnetic
breakdown, is particularly likely to occur and results in the appearance
of additional peaks in the high-frequency region at
V
g
¼
60 V, as illus-
trated in
Fig. 1(d)
.
We analyze the band mass of the inner and outer Fermi surfaces
to identify the valley polarization in the
a
-RuCl
3
/bilayer graphene het-
erostructure. The band mass quantifies the hybridization strength
between the
a
-RuCl
3
layer and each graphene layer. Specifically, the
a
-RuCl
3
band component leads to an increase in the effective mass of
the bilayer graphene band, making it significantly heavier. To deter-
mine the cyclotron, we performed temperature-dependent quantum
oscillations and subtracted the fast and slow background
R
xx
, respec-
tively. We plotted the isolated Shubnikov
–
de Haas oscillations (at
V
g
¼
0 V) for each fast and slow case in
Figs. 3(a)
and
3(b)
, after sub-
tracting the respective backgrounds. The temperature dependence of
the singular peak, denoted by a star, in each panel is presented in
Figs. 3(a)
and
3(b)
(see section 4 of supplementary material for
details).
To evaluate the effective masses, we have fitted the data points
with temperature factor (
R
T
)ofLifshitz
–
Kosevich formula,
R
T
¼
a
p
l
T
=
B
sinh
a
p
l
T
=
B
ðÞ
with
a
¼
2
p
2
m
e
k
B
=
eh
14
:
69
ð
T
=
K
Þ
,where
p
is harmonics,
h
is the
Planck constant,
m
e
is the free electron mass,
k
B
is the Boltzmann con-
stant, and
e
is the elementary charge. The
l
represents the ratio of
cyclotron mass to the free electron mass,
m
/
m
e
,where
m
denotes the
cyclotron mass. We have found that the value of
m
/
m
e
for fast
FIG. 3.
(a) Fast oscillations isolated from original
D
R
xx
as a function of inverse
magnetic field at
V
g
¼
0 V. Different colors indicate different temperatures from 2 to
50 K. (b) Same with (a) but for slow oscillation. (c)
D
R
xx
normalized by its
R
xx
at
T
¼
2 K and 1/
B
¼
0.078 T
1
as a function of temperature for the fast oscillations.
Dotted line is the fitting curve with Lifshitz
–
Kosevich formula. (d) Same with (c), but
for slow oscillations at 1/
B
¼
0.082 T
1
.
Applied Physics Letters
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Appl. Phys. Lett.
123
, 173101 (2023); doi: 10.1063/5.0170810
123
, 173101-4
Published under an exclusive license by AIP Publishing
26 October 2023 18:32:43
oscillations [
Fig. 3(c)
] is 0.070 56, whereas for slow oscillations
[
Fig. 3(d)
], it is 0.04523. This discrepancy suggests a notable difference
in band hybridization between the inner/outer Fermi surfaces and the
a
-RuCl
3
Fermi surface. These results align with our theoretical calcula-
tions, as depicted in
Figs. 2(c)
and
2(e)
. Note that the slow oscillation
was exclusively observed using the ionic liquid gate technique applied
to bilayer graphene. However, there has been no previous analysis of
band mass in this specific context. The
a
-RuCl
3
/bilayer graphene het-
erostructure presents a unique advantage that underscores its distinc-
tive characteristics.
In conclusion, we demonstrate the magnetic proximity effect in
the
a
-RuCl
3
/bilayer graphene heterostructure through various trans-
port measurements, including Hall measurements and Shubnikov-de
Haas oscillations. The interaction between
a
-RuCl
3
andthetoplayer
of bilayer graphene leads to spin-selective band hybridization, resulting
in the breaking of the spin degree of freedom in bilayer graphene.
Interestingly, we discovered an intrinsic valley-polarized Fermi pocket,
which arises from the stronger hybridization between the top layer of
graphene and the
a
-RuCl
3
band. This observation was further con-
firmed through effective mass analysis and theoretical calculations,
revealing the distinct properties of our heterostructure that sharply
contrast with those of the
a
-RuCl
3
/monolayer graphene heterostruc-
ture. Overall, our findings shed light on the complex interplay between
a
-RuCl
3
and bilayer graphene, encompassing band modifications, and
spin and valley degrees of freedom.
See the supplementary material for the additional magnetotran-
sport data, extra effective mass data, theoretical calculation for break-
ing of the spin and valley symmetry in bilayer graphene, six Fermi
pockets, lithium intercalation data, theoretical calculation for electronic
structure of
a
-RuCl
3
/bilayer graphene heterostructure with Li interca-
lation, and experimental and theoretical methods.
This work was supported by the Basic Science Research
Program NRF-2020R1C1C1006914, the DGIST R&D Program (23-
CoE-NT-01) of the Korean Ministry of Science and ICT, the
DGIST-Caltech collaboration research program (23-KUJoint-01),
and Samsung electronics. K.W. and T.T. acknowledge support from
the JSPS KAKENHI (Grant Nos. 20H00354, 21H05233, and
23H02052) and World Premier International Research Center
Initiative (WPI), MEXT, Japan. J.K. was supported by the National
Research Foundation of Korea funded by the Korea government
(MSIT) (No. NRF-2022R1F1A1059616).
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Soyun Kim and Jeonghoon Hong contributed equally to this
work.
Soyun Kim:
Data curation (lead); Formal analysis (lead); Writing
–
original draft (supporting).
Jeonghoon Hong:
Data curation (equal);
Formal analysis (equal); Methodology (equal); Writing
–
review &
editing (equal).
Kenji Watanabe:
Funding acquisition (supporting);
Resources (supporting).
Takashi Taniguchi:
Funding acquisition (sup-
porting); Resources (supporting).
Joseph Falson:
Formal analysis (sup-
porting); Funding acquisition (supporting); Writing
–
original draft
(supporting).
Jeongwoo Kim:
Data curation (equal); Formal analysis
(equal); Writing
–
original draft (equal).
Youngwook Kim:
Data cura-
tion (equal); Formal analysis (equal); Funding acquisition (equal);
Project administration (equal); Writing
–
original draft (equal).
DATA AVAILABILITY
The data that support the findings of this study are available from
the corresponding authors upon reasonable request.
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