PHYSICAL REVIEW B 104, 035131 (2021)
Intrinsic nature of chiral charge order in the kagome superconductor RbV
3
Sb
5
Nana Shumiya,
1,*
Md. Shafayat Hossain ,
1,*
Jia-Xin Yin ,
1,*,†
Yu-Xiao Jiang,
1,*
Brenden R. Ortiz,
2
Hongxiong Liu,
3,4
Youguo Shi,
3,4
Qiangwei Yin,
5
Hechang Lei,
5
Songtian S. Zhang ,
1
Guoqing Chang ,
6
Qi Zhang,
1
Tyler A. Cochran,
1
Daniel Multer,
1
Maksim Litskevich ,
1
Zi-Jia Cheng,
1
Xian P. Yang,
1
Zurab Guguchia,
7
Stephen D. Wilson,
2
and M. Zahid Hasan
1,8,9,10,‡
1
Laboratory for Topological Quantum Matter and Advanced Spectroscopy (B7), Department of Physics, Princeton University,
Princeton, New Jersey 08544, USA
2
Materials Department and California Nanosystems Institute, University of California Santa Barbara, Santa Barbara, California 93106, USA
3
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
4
University of Chinese Academy of Sciences, Beijing 100049, China
5
Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of
China, Beijing 100872, China
6
Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University,
Singapore 637371, Singapore
7
Laboratory for Muon Spin Spectroscopy, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
8
Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA
9
Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
10
Quantum Science Center, Oak Ridge, Tennessee 37831, USA
(Received 2 May 2021; accepted 6 July 2021; published 15 July 2021)
Superconductors with kagome lattices have been identified for over 40 years, with a superconducting transition
temperature T
c
up to 7 K. Recently, certain kagome superconductors have been found to exhibit an exotic charge
order, which intertwines with superconductivity and persists to a temperature being one order of magnitude
higher than T
c
. In this work, we use scanning tunneling microscopy to study the charge order in kagome
superconductor RbV
3
Sb
5
. We observe both a 2 × 2 chiral charge order and nematic surface superlattices
(predominantly 1 × 4). We find that the 2 × 2 charge order exhibits intrinsic chirality with magnetic field
tunability. Defects can scatter electrons to introduce standing waves, which couple with the charge order to
cause extrinsic effects. While the chiral charge order resembles that discovered in KV
3
Sb
5
, it further interacts
with the nematic surface superlattices that are absent in KV
3
Sb
5
but exist in CsV
3
Sb
5
.
DOI: 10.1103/PhysRevB.104.035131
Kagome lattices [1], made of corner sharing triangles,
are tantalizing quantum platforms for studying the interplay
between geometry, topology, and correlation. For instance, in-
sulating kagome magnets have been investigated for decades
in the hopes of realizing quantum spin liquids [2]. Re-
cently, focused STM research on correlated kagome magnets
has revealed many topological and many-body phenomena
[3], including Chern gapped phases [4,5], tunable electronic
nematicity [4], orbital magnetism [6–8], and many-body in-
terplay [9,10]. These observations are all closely related to the
emergent physics arising from the fundamental kagome band
structure, which includes Dirac cones, flat bands, and Van
Hove singularities. Notably, the many-body fermion-boson
interplay [10] observed in certain kagome paramagnets leads
us to conjecture from the spectroscopic point of view that
there can be superconductivity instability that competes with
magnetism. Then, we realize that kagome superconductors
*
These authors contributed equally to this work.
†
Corresponding author: jiaxiny@princeton.edu
‡
Corresponding author: mzhasan@princeton.edu
with competing magnetism have been identified for at least
over 40 years [11], such as LaRu
3
Si
2
with T
c
of 7 K and a
fundamental kagome band structure [12]. Recently, another
layered kagome superconductor, AV
3
Sb
5
(A = K, Rb, Cs),
was discovered [13–15], providing research opportunities,
particularly for STM studies [16–21]. While RbV
3
Sb
5
has
been studied by several experimental techniques [15,22,23], it
has not yet been studied with scanning tunneling microscopy
(STM). In our earlier studies [16], we have reported the chiral
2 × 2 charge order in KV
3
Sb
5
, which displays robust chirality
with magnetic field tunability on the defect-free region. Now,
we find that RbV
3
Sb
5
also features 2 × 2 charge order with
additional nematic superlattices. It is crucial to reconfirm the
chiral charge order in this material and test its robustness
against the surface superlattices.
RbV
3
Sb
5
has a layered structure with the stacking of Rb
1
hexagonal lattice, Sb
2
honeycomb lattice, V
3
Sb
1
kagome lat-
tice, and Sb
2
honeycomb lattice shown in Figs. 1(a)–1(c).
Owing to the bonding length and geometry, the V and Sb
layers have a stronger chemical bonding, and the material
tends to cleave between Rb and Sb layers. The Sb surface
is most interesting, as it is strongly bonded to the V kagome
2469-9950/2021/104(3)/035131(6) 035131-1 ©2021 American Physical Society
NANA SHUMIYA et al. PHYSICAL REVIEW B 104, 035131 (2021)
FIG. 1. (a)–(c) Crystal structure of kagome superconductor
RbV
3
Sb
5
from three-dimensional view, top view, and side view,
respectively. (d) Topographic image of a clean Sb surface (V =
− 100 mV, I = 0.5nA). (e) Fourier transform of the topography
showing Bragg peaks and charge ordering vector peaks. The 2 × 2
charge order vector peaks are highlighted by the shaded red ring,
which includes pairs of Q
1
, Q
2
,andQ
3
.
lattice. Previous STM studies have unambiguously resolved
Sb honeycomb surfaces in KV
3
Sb
5
and CsV
3
Sb
5
[16–21], and
studied the charge order and surface superlattices. We study
RbV
3
Sb
5
with STM at 4.2 K. Through cryogenic cleaving,
we have also obtained large clean Sb surfaces in RbV
3
Sb
5
,
as shown in Fig. 1(d). The Fourier transform of the to-
pography reveals a 2 × 2 charge order as marked by the
shaded red region in Fig. 1(e). Such 2 × 2 charge order has
been consistently observed in KV
3
Sb
5
and CsV
3
Sb
5
by both
STM [15–19,21] and bulk [13,16] x-ray measurements. In
addition, there are also nematic superlattice modulations (pre-
dominantly 1 × 4) along the Q
1
direction, and other weaker
superlattice signals along this direction. A similar superlat-
tice signal is also observed in the Sb surface in CsV
3
Sb
5
[17–19,21]. However, such a signal has not been detected in
K/Cs/Rb surfaces (or in the bulk x-ray data), while a bulk
modulation will project and appear on all surfaces. Therefore,
while the nematicity may be a bulk phenomenon, the specific
1 × 4 modulation is more likely to be a surface phenomenon.
KV
3
Sb
5
does not exhibit a 1 × 4 superlattice for Sb surface
[16], and because CsV
3
Sb
5
has a factor of 3 higher T
c
than
that of KV
3
Sb
5
, previous STM observations in CsV
3
Sb
5
con-
jectured a close relationship between the 1 × 4 superlattices
and higher T
c
[19]. Our observation in RbV
3
Sb
5
, which has a
T
c
similar to KV
3
Sb
5
, makes such a scenario unlikely.
Now we focus on the intrinsic anisotropy of the 2 × 2
charge order on a large defect-free region in Fig. 2. We per-
form spectroscopic dI/dV maps at the same region with a
magnetic field perpendicular to the surface. The maps taken at
FIG. 2. (a)–(c) dI/dV maps taken at the same clean Sb surface with B = 0T,−3T,+3 T, respectively. The magnetic field is applied along
the c axis. The maps are all taken at E = 30 meV with V =−100 mV and I = 0.5 nA. (d)–(f) Spectroscopic 2 × 2 vector peaks taken at
B = 0T, −3T,+3 T, respectively. The images are Fourier transforms of spectroscopic maps. A circular region of the full Fourier-transformed
image is shown for clarity, highlighting the six 2 × 2 vector peaks. The height of the three pairs of vector peaks is marked with arbitrary units
for each data. The chirality can be defined as the counting direction (clockwise or anticlockwise) from the lowest to highest pair vector peaks
as marked by the rotating arrows.
035131-2
INTRINSIC NATURE OF CHIRAL CHARGE ORDER IN THE … PHYSICAL REVIEW B 104, 035131 (2021)
FIG. 3. (a),(b) Real space image of the 2 × 2 chiral charge or-
der taken at B =−3T and B =+3T, respectively. The data are
produced by the inverse Fourier transform of the 2 × 2 vector peaks
in Fig. 2(e) and 2(f), respectively. (c),(d) Line-cut profile for along
three directions marked in (a) and (b), respectively. The modulations
along the three directions are different in both cases, defining a
chirality. Magnetic field switch induces a switch of the strengths of
two stronger modulations.
30 meV with B = 0T, −3T,+3 T are displayed in Figs. 2(a)–
2(c), respectively. We find that the +3 T map is different
from the others. To better visualize the difference, we perform
Fourier transform analysis of these maps. Particularly, we
extract the six 2 × 2 vector peaks as shown in Figs. 2(d)–
2(f), which reveals pronounced intensity anisotropy along
with different directions for all cases. This corresponds to
the fact that the amplitudes of the 2 × 2 modulation in real
space along three directions are different from each other. The
observed anisotropy can be due to a chiral charge order as
initially discussed in certain transition-metal dichalcogenides
and high-temperature superconductors [24,25]. The chirality
can be defined as the counting direction (clockwise or anti-
clockwise) from the lowest to highest vector peaks. We find
the chirality at the same atomic area can be switched by the
magnetic field applied along the c axis for opposite directions.
A real space elaboration of the chirality switch is further
shown in Fig. 3, demonstrating that the strength of 2 × 2
modulation is switched by the magnetic field. Figure 4 further
shows the energy-resolved vector peak intensity for different
magnetic fields. The vector peaks have weak intensity for
negative energies, hindering the identification of chirality. For
higher positive energies where the intensities are strong, we
observe strong anisotropy. The intensity of Q
1
is always the
strongest, and we note that this direction is the same as that of
the nematic superlattices. Moreover, the intensities between
Q
2
and Q
3
are different, from which we can determine chiral-
ity. The reversal of their intensities between −3 T and +3T
then demonstrates a chirality switch.
FIG. 4. Magnetic field tunability of the chiral charge order at a
defect-free region. Comparison of intensities of three 2 × 2 vector
peaks as a function of energy for the same defect-free region for
B = 0T, −3T,+3 T, respectively. The vector peaks have weak in-
tensities at negative energies, and the magnetic field induced chirality
switching effects are primarily observed at higher positive energies.
As a comparison, we also perform experiments around the
defect-rich region in Fig. 5. Defects can backscatter electrons
to induce standing waves. Figure 4(a) shows rich standing
waves in the dI/dV map of this region. The Fourier trans-
form of this map shows clear ringlike signals just within
the 2 × 2 charge order vector peaks. A detailed plot of the
energy-resolved vector peak intensity at B = 0T, −3T,+3T
is displayed in Fig. 4(b). Different from the defect-free case
in Figs. 2–4, Q
2
and Q
3
basically have similar intensities over
all measured energies, suggesting a diminishing of chirality.
Moreover, there is no strong magnetic field response. All these
observations are again consistent with our reports for KV
3
Sb
5
[16]. We believe, because the standing wave signals in the q
space are close to the 2 × 2 charge order peaks, there exists
a defect-pinning effect [26], which is an extrinsic property of
the charge order. The interplay between the charge order and
defects can be studied by the Bogoliubov–de Gennes method
in future.
Now we discuss the implications of our experiments. The
observations not only reconfirm the ubiquitous chiral charge
order in AV
3
Sb
5
, but also suggest that the chirality and field
switching are both robust against nematic superlattices. The
2 × 2 charge order has been proposed by pioneering theories
of kagome lattices [27–29] at Van Hove singularity filling. Re-
cently, several theoretical works focused on AV
3
Sb
5
[16,30–
36] have confirmed 2 × 2 charge order with unconventional
features, including time-reversal symmetry breaking, chiral-
ity, nematicity, and topology. The unconventional features
arise from the interferences of three kagome sublattices with
extended Coulomb interactions, and they can further interact
with the topologically nontrivial band structure in these mate-
rials. While the nematicity of the charge order observed here
can be consistent with the surface manifestation of the 2 ×
2 × 2 charge order [37], the chirality ubiquitously observed in
KV
3
Sb
5
[16], RbV
3
Sb
5
(this work), and CsV
3
Sb
5
[38] cannot
be explained by the conventional 2 × 2 × 2 charge order. As
the chirality can be switched by a magnetic field that explicitly
breaks time-reversal symmetry, it implies a complex set of
order parameters of the charge order, which contain relative
035131-3
NANA SHUMIYA et al. PHYSICAL REVIEW B 104, 035131 (2021)
FIG. 5. Absence of chirality and magnetic tunability at standing-
waves-rich region. (a) dI/dV map data taken at a defect-rich Sb
surface. The maps are all taken at E = 0meV with V =−100mV
and I = 0.5nA. This region hosts numerous defect-induced standing
waves. The inset shows the Fourier transform of the map data, which
exhibits additional ringlike signals within the 2 × 2 vector peaks.
(b) Comparison of intensities of three 2 × 2 vector peaks for this
defect-rich region as a function of energy for B = 0T, −3T,+3T,
respectively. In this region, there is no apparent chirality of the charge
order, and we do not observe a strong magnetic field response of the
vector peaks.
phase differences. The phase difference of three sets of the
2 × 2 order parameter, if not 0 or π , breaks time-reversal
symmetry. Recently, more direct evidence of the time-reversal
symmetry breaking comes from muon spin spectroscopy by
observation of a concurrent emergence of an internal magnetic
field with the charge order phase transition [39]. Theoreti-
cally, a broken time-reversal symmetry charge order is also
suggested to be energetically favorable in the kagome lattice
at Van Hove filling and with extended Coulomb interactions
[16,30,32,33,36], which features orbital currents running in
the kagome lattice. Originally, charge order with broken time-
reversal symmetry was proposed as the Haldane model for
achieving quantum anomalous Hall effect [40] and orbital
currents [41,42] for modeling pseudogap phase of cuprates. Its
tantalizing visualization in kagome superconductors comes as
an experimental surprise. Since there has not yet been anoma-
lous Hall measurements for RbV
3
Sb
5
, whether our observed
intrinsic and extrinsic behavior of the chiral charge order can
be related with the intrinsic and extrinsic anomalous Hall
effects [43,44] deserves future attention. It is also crucial to
probe the magnetic field switching effect more systematically
in the future by varying the magnetic field strength, which can
help to determine the critical switching field and to further
compare with anomalous Hall measurements.
Experimental and theoretical work at Princeton University
was supported by the Gordon and Betty Moore Founda-
tion [Grants No. GBMF4547 and No. GBMF9461 (M.Z.H.)].
The material characterization is supported by the United
States Department of Energy (U.S. DOE) under the Basic
Energy Sciences program (Grant No. DOE/BES DE-FG-
02-05ER46200). S.D.W. and B.R.O. acknowledge support
from the University of California Santa Barbara Quantum
Foundry, funded by the National Science Foundation (Grant
No. NSF DMR-1906325). Research reported here also made
use of shared facilities of the UCSB MRSEC (Grant No.
NSF DMR-1720256). B.R.O. also acknowledges support
from the California NanoSystems Institute through the Elings
fellowship program. T.A.C. was supported by the National
Science Foundation Graduate Research Fellowship Program
under Grant No. DGE-1656466. H.C.L. was supported by
National Natural Science Foundation of China (Grants No.
11822412 and No. 11774423), Ministry of Science and Tech-
nology of China (Grants No. 2018YFE0202600 and No.
2016YFA0300504), and Beijing Natural Science Foundation
(Grant No. Z200005). Y.S. was supported by the National
Natural Science Foundation of China (Grant No. U2032204),
and the K. C. Wong Education Foundation (Grant No. GJTD-
2018-01). G.C. would like to acknowledge the support of the
National Research Foundation, Singapore under its NRF Fel-
lowship Award (Award No. NRF-NRFF13-2021-0010) and
the Nanyang Assistant Professorship grant from Nanyang
Technological University.
[1] M. Mekata, Kagome: The story of the basketweave lattice,
Phys. Today 56(2), 12 (2003).
[2] Y. Zhou, K. Kanoda, and T.-K. Ng, Quantum spin liquid states,
Rev. Mod. Phys. 89, 025003 (2017).
[3] J.-X. Yin, S. H. Pan, and M. Z. Hasan, Probing topological
quantum matter with scanning tunnelling microscopy, Nat. Rev.
Phys. 3, 249 (2021).
[4] J.-X. Yin, S. S. Zhang, H. Li, K. Jiang, G. Chang, B.
Zhang, B. Lian, C. Xiang, I. Belopolski, H. Zheng, T.
A. Cochran, S.-Y. Xu, G. Bian, K. Liu, T.-R. Chang,
H. Lin, Z.-Y. Lu, Z. Wang, S. Jia, W. Wang, and M.
Zahid Hasan, Giant and anisotropic spin–orbit tunability in a
strongly correlated kagome magnet, Nature (London) 562,91
(2018).
035131-4
INTRINSIC NATURE OF CHIRAL CHARGE ORDER IN THE … PHYSICAL REVIEW B 104, 035131 (2021)
[5] J.-X. Yin, W. Ma, T. A. Cochran, X. Xu, S. S. Zhang, H.-J.
Tien, N. Shumiya, G. Cheng, K. Jiang, B. Lian, Z. Song, G.
Chang, I. Belopolski, D. Multer, M. Litskevich, Z.-J. Cheng,
X. P. Yang, B. Swidler, H. Zhou, H. Lin et al., Quantum-limit
Chern topological magnetism in TbMn
6
Sn
6
, Nature (London)
583, 533 (2020).
[6] J.-X. Yin, S. S. Zhang, G. Chang, Q. Wang, S. Tsirkin,
Z. Guguchia, B. Lian, H. Zhou, K. Jiang, I. Belopolski, N.
Shumiya, D. Multer, M. Litskevich, T. A. Cochran, H. Lin, Z.
Wang, T. Neupert, S. Jia, H. Lei, and M. Zahid Hasan, Negative
flat band magnetism in a spin–orbit-coupled correlated kagome
magnet, Nat. Phys. 15, 443 (2019).
[7] J.-X. Yin, N. Shumiya, Y. Jiang, H. Zhou, G. Macam, H. O. M.
Sura, S. S. Zhang, Z. Cheng, Z. Guguchia, Y. Li, Q. Wang, M.
Litskevich, I. Belopolski, X. Yang, T. A. Cochran, G. Chang,
Q. Zhang, Z.-Q. Huang, F.-C. Chuang, H. Lin et al., Spin-orbit
quantum impurity in a topological magnet, Nat. Commun. 11,
4415 (2020).
[8] Y. Xing, J. Shen, H. Chen, L. Huang, Y. Gao, Q. Zheng, Y.-Y.
Zhang, G. Li, B. Hu, G. Qian, L. Cao, X. Zhang, P. Fan, R. Ma,
Q. Wang, Q. Yin, H. Lei, W. Ji, S. Du, H. Yang et al., Localized
spin-orbit polaron in magnetic Weyl semimetal Co
3
Sn
2
S
2
, Nat.
Commun. 11, 5613 (2020).
[9] S. S. Zhang, J.-X. Yin, M. Ikhlas, H.-J. Tien, R. Wang, N.
Shumiya, G. Chang, S. S. Tsirkin, Y. Shi, C. Yi, Z. Guguchia,
H. Li, W. Wang, T.-R. Chang, Z. Wang, Y.-F. Yang, T. Neupert,
S. Nakatsuji, and M. Zahid Hasan, Many-Body Resonance in
a Correlated Topological Kagome Antiferromagnet, Phys. Rev.
Lett. 125, 046401 (2020).
[10] J.-X. Yin, N. Shumiya, S. Mardanya, Q. Wang, S. S. Zhang,
H.-J. Tien, D. Multer, Y. Jiang, G. Cheng, N. Yao, S. Wu, D.
Wu, L. Deng, Z. Ye, R. He, G. Chang, Z. Liu, K. Jiang, Z.
Wang, T. Neupert et al., Fermion–boson many-body interplay
in a frustrated kagome paramagnet, Nat. Commun. 11, 4003
(2020).
[11] H. C. Ku, G. P. Meisner, F. Acker, and D. C. Johnston, Su-
perconducting and magnetic properties of new ternary borides
with the CeCo
3
B
2
-type structure, Solid State Commun. 35,91
(1980).
[12] C. Mielke, III, Y. Qin, J.-X. Yin, H. Nakamura, D. Das, K. Guo,
R. Khasanov, J. Chang, Z. Q. Wang, S. Jia, S. Nakatsuji, A.
Amato, H. Luetkens, G. Xu, M. Z. Hasan, and Z. Guguchia,
Nodeless kagome superconductivity in LaRu
3
Si
2
, Phys. Rev.
Mater. 5, 034803 (2021).
[13] B. R. Ortiz, S. M. L. Teicher, Y. Hu, J. L. Zuo, P. M. Sarte,
E. C. Schueller, A. M. M. Abeykoon, M. J. Krogstad, S.
Rosenkranz, R. Osborn, R. Seshadri, L. Balents, J. He, and S.
D. Wilson, CsV
3
Sb
5
: A Z2 Topological Kagome Metal with a
Superconducting Ground State, Phys. Rev. Lett. 125, 247002
(2020).
[14]B.R.Ortiz,P.M.Sarte,E.M.Kenney,M.J.Graf,S.M.L.
Teicher, R. Seshadri, and S. D. Wilson, Superconductivity in
the Z2 kagome metal KV
3
Sb
5
, Phys. Rev. Mater. 5, 034801
(2021).
[15] Q. Yin, Z. Tu, C. Gong, Y. Fu , S. Yan , and H. Lei,
Superconductivity and normal-state properties of kagome
metal RbV
3
Sb
5
single crystals, Chin. Phys. Lett. 38, 037403
(2021).
[16] Y.-X. Jiang, J.-X. Yin, M. M. Denner, N. Shumiya, B. R. Ortiz,
G. Xu, Z. Guguchia, J. He, M. S. Hossain, X. Liu, J. Ruff,
L. Kautzsch, S. S. Zhang, G. Chang, I. Belopolski, Q. Zhang,
T. A. Cochran, D. Multer, M. Litskevich, Z.-J. Cheng et al.,
Unconventional charge order in kagome superconductor
KV
3
Sb
5
, Nat. Mater. (2021).
[17] H. Zhao, H. Li, B. R. Ortiz, S. M. L. Teicher, T. Park, M. Ye,
Z. Wang, L. Balents, S. D. Wilson, and I. Zeljkovic, Cascade of
correlated electron states in a kagome superconductor CsV
3
Sb
5
,
arXiv:2103.03118.
[18] Z. Liang, X. Hou, F. Zhang, W. Ma, P. Wu, Z. Zhang, F.
Yu, J.-J. Ying, K. Jiang, L. Shan, Z. Wang, and X.-H. Chen,
Three-dimensional charge density wave and robust zero-bias
conductance peak inside the superconducting vortex core of a
kagome superconductor CsV
3
Sb
5
, arXiv:2103.04760.
[19] H. Chen et al., Roton pair density wave and unconventional
strong-coupling superconductivity in a topological kagome
metal, arXiv:2103.09188.
[20] H. Li, H. Zhao, B. R. Ortiz, T. Park, M. Ye, L. Balents, Z.
Wang, S. D. Wilson, and I. Zeljkovic, Rotation symmetry break-
ing in the normal state of a kagome superconductor KV
3
Sb
5
,
arXiv:2104.08209.
[21]H.-S.Xu,Y.-J.Yan,R.Yin,W.Xia,S.Fang,Z.Chen,Y.Li,
W. Yang, Y. Guo, and D.-L. Feng, Multiband superconductivity
with sign-preserving order parameter in kagome superconduc-
tor CsV
3
Sb
5
, arXiv:2104.08810.
[22] Z. Liu, N. Zhao, Q. Yin, C. Gong, Z. Tu, M. Li, W. Song,
Z. Liu, D. Shen, Y. Huang, K. Liu, H. Lei, and S. Wang,
Temperature-induced band renormalization and Lifshitz transi-
tion in a kagome superconductor RbV
3
Sb
5
, arXiv:2104.01125.
[23] H. X. Li, T. T. Zhang, Y.-Y. Pai, C. Marvinney, A. Said, T.
Yilmaz, Q. Yin, C. Gong, Z. Tu, E. Vescovo, R. G. Moore,
S. Murakami, H. C. Lei, H. N. Lee, B. Lawrie, and H. Miao,
Observation of Unconventional Charge Density Wave with-
out Acoustic Phonon Anomaly in Kagome Superconductors
AV
3
Sb
5
(A = Rb,Cs), arXiv:2103.09769.
[24] J. Ishioka, Y. H. Liu, K. Shimatake, T. Kurosawa, K. Ichimura,
Y. Toda, M. Oda, and S. Tanda, Chiral Charge-Density Waves,
Phys. Rev. Lett. 105, 176401 (2010).
[25] J. Xia, E. Schemm, G. Deutscher, S. A. Kivelson, D. A.
Bonn, W. N. Hardy, R. Liang, W. Siemons, G. Koster, M.
M. Fejer, and A. Kapitulnik, Polar Kerr-Effect Measurements
of the High-Temperature YBa
2
Cu
3
O
6+x
Superconductor: Evi-
dence for Broken Symmetry Near the Pseudogap Temperature,
Phys. Rev. Lett. 100, 127002 (2008).
[26] H. Fukuyama and P. A. Lee, Dynamics of the charge-density
wave. I. Impurity pinning in a single chain, Phys. Rev. B 17,
535 (1978).
[27] S.-L. Yu and J.-X. Li, Chiral superconducting phase and chiral
spin-density-wave phase in a Hubbard model on the kagome
lattice, Phys. Rev. B 85, 144402 (2012).
[28] W.-S. Wang, Z.-Z. Li, Y.-Y. Xiang, and Q.-H. Wang, Competing
electronic orders on kagome lattices at van Hove filling, Phys.
Rev. B 87, 115135 (2013).
[29] M. L. Kiesel, C. Platt, and R. Thomale, Unconventional Fermi
Surface Instabilities in the Kagome Hubbard Model, Phys. Rev.
Lett. 110, 126405 (2013).
[30] X. Feng, K. Jiang, Z. Wang, and J. Hu, Chiral flux phase in the
Kagome superconductor AV
3
Sb
5
, arXiv:2103.07097.
[31] H. Tan, Y. Liu, Z. Wang, and B. Yan, Charge density waves
and electronic properties of superconducting kagome metals,
arXiv:2103.06325.
035131-5
