# Time-reversal symmetry breaking in charge density wave of CsV3Sb5 detected
by polar Kerr effect

Yajian Hu1∗ Soichiro Yamane1 Giordano Mattoni1,2 Kanae Yada1 Keito Obata1
Yongkai Li3,4,5 Yugui Yao3,4 Zhiwei Wang3,4,5 Jingyuan Wang6 Camron Farhang6
Jing Xia6 Yoshiteru Maeno1,2 Shingo Yonezawa1†

###### Abstract

The Kagome lattice exhibits rich quantum phenomena owing to its unique
geometric properties. Appealing realizations are the Kagome metals AV3Sb5 (A =
K, Rb, Cs), where unconventional charge density wave (CDW) is intertwined with
superconductivity and non-trivial band topology. Several experiments suggest
that this CDW is a rare occurrence of chiral CDW characterized by orbital loop
current. However, key evidences of loop current, spontaneous time-reversal
symmetry-breaking (TRSB) and the coupling of its order parameter with the
magnetic field remain elusive. Here, we investigate the CDW in CsV3Sb5 by
magneto-optic polar Kerr effect with sub-microradian resolution. Under
magnetic field, we observed a jump of the Kerr angle at the CDW transition.
This jump is magnetic-field switchable and scales with field, indicating
magneto–chirality coupling related to non-trivial band topology. At zero
field, we found non-zero and field-trainable Kerr angle below $T_{\rm CDW}$,
signaling spontaneous TRSB. Our results provide a crucial step to unveil
quantum phenomena in correlated Kagome materials.

Department of Physics, Graduate School of Science, Kyoto University, Kyoto
606-8502, Japan

Toyota Riken-Kyoto University Research Center (TRiKUC), Kyoto University,
Kyoto 606-8501, Japan

Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum
Architecture and Measurement (MOE), School of Physics, Beijing Institute of
Technology, Beijing 100081, P. R. China

Beijing Key Lab of Nanophotonics and Ultrafine Optoelectronic Systems, Beijing
Institute of Technology, Beijing 100081, P. R. China

Material Science Center, Yangtze Delta Region Academy of Beijing Institute of
Technology, Jiaxing 314011, P. R. China

Department of Physics and Astronomy, University of California, Irvine,
California 92697, USA

∗e-mail<EMAIL_ADDRESS>†e-mail<EMAIL_ADDRESS>
Dated:

The Kagome lattice has gained the spotlight over decades because of its rich
ground states owing to its intriguing band structure. The nearest-neighbor
tight-binding model of a two-dimensional (2D) Kagome net depicts presence of a
flat band, Dirac cones, and van Hove singularities (vHSs). The flat band with
localized electrons gives rise to strongly correlated phenomena, while the
Dirac cones assist systems to become topological insulators or Weyl semimetals
1, 2. The vHSs, showing divergent density of states, can lead to electronic
instability such as spin-density wave and charge-density wave (CDW).

The Kagome metals AV3Sb5 (A = K, Rb, Cs) have attracted tremendous interest
recently 3. Crystallographically, vanadium atoms form an ideal 2D Kagome net
at ambient temperature (Fig. 1a, b). In the band structure, traces of the flat
band, Dirac cones, and vHSs expected for a 2D Kagome net all appear 4. Both
the Dirac cone and vHSs are located close to the Fermi level, promoting the
topological and strongly correlated phenomena. AV3Sb5 compounds display CDW
order and superconductivity 3, 4, 5, 6. Moreover, giant anomalous Hall effect
(AHE) is reported to occur concurrently with the CDW transition in KV3Sb5 7
and CsV3Sb5 8. Angle-resolved photoemission spectroscopy (ARPES) 9, 10, 11, 12
and X-ray scattering 13 experiments show a strongly momentum-dependent CDW gap
and indicate that the CDW transition is triggered by Fermi surface nesting
dominated by vHSs. In the context of lattice distortions in the CDW state, the
acoustic phonon anomaly is absent 13 while the hardening of an optical phonon
mode is reported 14. These results establish the unconventional nature of the
CDW in the normal-state and it can profoundly influence the superconducting
state, which also exhibits intriguing features 15, 16, 17, 18, 19, 20. Thus,
AV3Sb5 provide a versatile platform to investigate the interplay between novel
band topology, CDW and superconductivity in the Kagome lattice.

A critical issue of the CDW in AV3Sb5 concerns the accompanied symmetry
breakings. In scanning tunnelling microscopy (STM) studies, three-dimensional
$2\times 2\times 2$ or $2\times 2\times 4$ charge modulations have been mapped
out 19, 21. Interestingly, clockwise or counterclockwise intensity modulation
of putatively identical superlattice peaks exist and can be flipped by
magnetic field, as reported for all members of the AV3Sb5 family 22, 23, 24.
These results raise the possibility of time-reversal symmetry breaking (TRSB)
although the long-range magnetic order is absent 3. Zero-field muon spin
relaxation ($\mu$SR) on KV3Sb5 and CsV3Sb5 show enhanced relaxation rates in
the CDW states, supporting the TRSB 18, 25, 26. On the other hand, an
additional $C_{6}$ rotation symmetry breaking is found at a lower temperature
in the CDW state and the electronic ground state is proposed to be nematic 27,
22, 28, 29, 24, 30, 31. Theoretically, the TRSB and rotation symmetry breaking
can be well-explained by orbital loop currents and chiral flux induced as a
consequence of order parameters with non-zero imaginary component. Such an
unconventional CDW state is now called chiral CDW. 32, 33, 34, 35. However,
several experiments report the absence of TRSB in the CDW phase 36, 37, 38,
27, and theories propose the charge bond order with real order parameters 39,
40. We comment that the charge distribution in the CDW state can have a
structural chirality 40, which should not be confused with the chirality and
TRSB due to loop current. For a thorough understanding of the CDW in AV3Sb5,
new probes of TRSB are crucial.

Here, we performed high resolution magneto-optic Kerr effect (MOKE)
measurements to investigate the CDW in CsV3Sb5, a canonical member of the
AV3Sb5 family. We measured the polar Kerr effect (PKE) using a zero-loop
Sagnac interferometer. Different from the ordinary optical setup, PKE measured
with our setup is only sensitive to TRSB of the system 41. This technique has
been used for studying novel TRSB phases in quantum materials, for instance,
the chiral SC of Sr2RuO4 42 and uranium-based superconductors 43, and the
chiral charge order in the high-$T_{\rm{c}}$ cuprates 44. Using a newly-built
all-fiber Sagnac interferometer, we measured polar Kerr angle $\theta_{\rm K}$
at low temperature with sub-microradian resolution, with and without magnetic
field. Under magnetic field, the polar Kerr angle jump $\Delta\theta_{\rm K}$
at the CDW transition is almost linear in field and changes sign with opposite
field direction. We demonstrate that this strong coupling to magnetic field is
related to non-trivial band topology. At zero field, non-zero $\theta_{\rm K}$
has been detected below $T_{\rm CDW}$. This spontaneous $\theta_{\rm K}$ is
switchable by out-of-plane magnetic fields applied while cooling across the
CDW transition, implying spontaneous TRSB in CsV3Sb5. Our results can be well-
interpreted by a magnetic-field switchable loop-current order in the chiral
CDW.

## Results

Crystal characterization and CDW transition in reflectivity. Before optical
measurements, the samples were characterized by Laue diffraction and magnetic
susceptibility. The Laue diffraction image shown in Fig. 1c displays clear
spots, consistent with the hexagonal ($P6/mmm$) crystal structure at room
temperature and indicating high crystal quality without significant stacking
faults. The magnetic susceptibility shows sharp transitions at $\sim 94$ K and
$\sim 2.9$ K, corresponding to the CDW and the superconducting transitions,
respectively (see Supplementary Fig. S1). These data are consistent with
previous reports 3, 4 and demonstrate that the samples are well single-
crystalline.

In our PKE experiments, we used a broadband light source with center
wavelength of $\sim 1550$ nm, and the phase of the light is modulated by the
phase modulator with the frequency $\omega/2\pi\sim 3.848$ MHz. We detect the
first and second harmonic components of the reflected signal from a photo
detector 42. The second harmonic signal $V_{2\omega}$ is proportional to the
reflectivity of the sample, while the ratio between the first harmonic signal
$V_{1\omega}$ to $V_{2\omega}$ gives the polar Kerr angle $\theta_{\rm K}$
$\approx 0.271V_{1\omega}/V_{2\omega}$ (See Methods). Figure 1d displays the
temperature dependence of $V_{2\omega}$ for several selected magnetic fields
between 0 T and 10 T. Upon cooling, the reflectivity jumps and increases below
$\sim 93$ K. Because of the gap opening at the CDW transition, the spectral
weight of low-energy optical conductivity shifts to higher energy ranges. This
leads to the increase in the reflectivity at our wavelength, $\sim 1550$ nm
(0.8 eV), as observed by the optical spectroscopy 45, 46. From the temperature
derivative of $V_{2\omega}$ 47, we extract the transition temperature $T_{\rm
CDW}$ at different magnetic fields and plot it in the inset of Fig. 1d. Among
the three samples that we have measured, $T_{\rm CDW}$ is located within the
range $93\pm 0.5$ K, and remains independent of the external field up to 10 T.

Polar Kerr angle measurements under magnetic field. We first present the polar
Kerr angle $\theta_{\rm K}$ under magnetic field. Because of the Faraday
effect of the lens, there is a background signal contributing to the measured
$\theta_{\rm K}$. In order to examine the signal from the sample across
$T_{\rm CDW}$, we use the measured $\theta_{\rm K}$ of a Nb metal sheet to
subtract the background signal $\theta_{\rm K}^{\rm bg}$ (see Supplementary
Fig. S2). Figure 2a shows extracted sample signal $\theta_{\rm K}^{\rm
sample}=\theta_{\rm K}-\theta_{\rm K}^{\rm bg}$ divided by magnetic field. At
$T_{\rm CDW}$, $\theta_{\rm K}^{\rm sample}$ jumps and gradually increases
with decreasing temperature, consistent with a first-order transition as
previously reported 4. Moreover, with opposite magnetic field, $\theta_{\rm
K}^{\rm sample}$ changes its sign to negative. The fact that $\theta_{\rm
K}^{\rm sample}$ rises concurrently with the CDW transition, and reverses its
sign with opposite magnetic field direction is in agreement with the
intensity-modulation reversal observed in STM spectroscopy 23 and the AHE 8,
which are interpreted in terms of TRSB and large Berry phase in the CDW state
of CsV3Sb5.

Figure 2b shows the temperature dependence of the measured polar Kerr angle
$\theta_{\rm K}$. With increasing magnetic field, the magnitude of
$\theta_{\rm K}$ and the jump $\Delta\theta_{\rm K}$ at $T_{\rm CDW}$ both
increase. In order to obtain the field dependence of the polar Kerr angle, we
determine $\Delta\theta_{\rm K}$ from the difference between two linear fits
close to $T_{\rm CDW}$ (the inset of Fig. 2c) and plot it as a function of
magnetic field (Fig. 2c). For all three samples, $\Delta\theta_{\rm K}$ is
almost linear in magnetic field in the studied range between -6 T and +10 T,
indicating the polar Kerr angle in the CDW state is strongly coupled to the
magnetic field. Hence, it is natural to compare $\Delta\theta_{\rm K}$,
proportional to the Hall conductivity at the optical frequency, with
magnetization. For the conventional anomalous Hall conductivity, one expects
its magnitude to be proportional to the magnetization. CsV3Sb5 is paramagnetic
and the magnetization decreases below $T_{\rm CDW}$ due to the decreasing
density of states (DOS) (see Supplementary Fig. S1). If $\Delta\theta_{\rm K}$
originates from the change of magnetization, we would expect also $\theta_{\rm
K}$ to decrease at $T_{\rm CDW}$. Our data is opposite to this expectation.
Therefore, the change of Pauli paramagnetic spin susceptibility is not the
main contribution to the polar Kerr angle jump $\Delta\theta_{\rm K}$.
Instead, we expect a new mechanism to be responsible for the observed Kerr
angle data, as we will discuss in the following.

Unusual origin of $\theta_{\rm K}$ in CDW. The different origins of the polar
Kerr angle and the magnetization in CsV3Sb5 is apparent when we compare it
with other materials. Figure 3 shows a log-log plot of the magnitude of polar
Kerr angle versus magnetization for various materials, including ferro- and
ferri-magnets (FM/Ferri) and anti-ferromagnetic (AFM) perovskites with canted
spins 48, 49, 50, 51, 52. Here, the magnetization change associated with the
ordering $\Delta M$ and the polar Kerr angle $\Delta|\theta_{\rm K}|$ in the
saturated states are plotted (details in the inset of Fig. 3). Despite the
relation between $\theta_{\rm K}$ and the magnetization can be complicated
because $\theta_{\rm K}$ is dependent on the light wavelength, the data of
FM/Ferri materials fall into the same area, which is distinct from the AFM
perovskites. For CsV3Sb5, we plot the change of magnetization and polar Kerr
angle jump $\Delta\theta_{\rm K}$ at $T_{\rm CDW}$ (left inset of Fig. 3)
under different magnetic field, where the paramagnetic spins are aligned.
Since the magnetization decreases at $T_{\rm CDW}$, the $\Delta\mu_{0}M$ is
negative. With increasing magnitude of $\Delta\mu_{0}M$, $\Delta\theta_{\rm
K}$ increases. By a linear fitting, we extract the ratio $\Delta|\theta_{\rm
K}|/\Delta\mu_{\rm 0}M=-1.36$ rad/T. The negative sign and the significantly
large magnitude of this ratio indicate the polar Kerr angle in CsV3Sb5 is
decoupled from the paramagnetic spin magnetization. Moreover, we plot
$\Delta\theta_{\rm K}$ and $\Delta M$ for the Kagome magnet Fe3Sn2 53, 54, the
magnetic Weyl semimetals Co3Sn2S2 2, 55 and Mn3Sn 56. These materials show
similarly large $\Delta|\theta_{\rm K}|/\Delta\mu_{\rm 0}M$ ratio, indicating
that the polar Kerr effect does not originate from the ordered magnetism.
Instead, the origin of such Kerr angle is attributed to the Berry curvature.
Interestingly, the CsV3Sb5 displays similar magnitude of $\Delta|\theta_{\rm
K}|/\Delta\mu_{\rm 0}M$ to these materials, but with opposite sign, implying
that the polar Kerr effect in the CDW state is probably related to the
topologically non-trivial band structure.

Spontaneous TRSB in the CDW phase evidenced by zero-field Kerr effect. At
last, we show the presence of non-zero polar Kerr angle at zero field, key
feature of spontaneous TRSB and chiral CDW in CsV3Sb5. Figure 4a shows the
temperature dependence of $\theta_{\rm K}$ collected at zero field, during
both cooling and warming. $\theta_{\rm K}$ fluctuates around zero by $\pm 0.2$
µrad at high temperature and becomes finite below $T_{\rm CDW}$, indicating
the spontaneous TRSB in the CDW state. We observed that the magnitude and the
sign of $\theta_{\rm K}$ vary for each measurement. We repeated this
measurement with different optical power and observed similar behaviour. This
can be well-explained by random formation of TRSB domains after zero-field-
cooling (ZFC). In addition, the magnitude of $\theta_{\rm K}$ tends to grow at
a temperature lower than $T_{\rm CDW}$, probably due to the growth of domain
sizes towards low temperature.

In order to obtain clearer TRSB signal and examine the presence of TRSB
domains, we performed “field training” experiments to align them. We cooled
the sample across $T_{\rm CDW}$ under a perpendicular magnetic field, set the
field to zero at low temperature, and then collected data upon zero-field-
warming (ZFW). Figure 4b displays multiple sets of data after $\pm 1$ T field
training. At $T>T_{\rm CDW}$, the data fluctuate around zero. Below $T_{\rm
CDW}$, the positive-field training yields positive $\theta_{\rm K}$ and vice
versa. Such trends are fully reproducible among all the runs performed. The
successful field training implies that the domains are aligned by the magnetic
field and that a residual moment persists after removing the field. Comparing
Fig. 4a and b, we note that the magnitude of $\theta_{\rm K}$ without training
is in the range $\pm 1$ µrad, while $\theta_{\rm K}$ after field training
reaches $\sim 2$ µrad in some runs at low temperature. This shows how field
training effectively aligns TRSB domains. The non-zero $\theta_{\rm K}$ and
the training effect can be well interpreted as a consequence of TRSB in the
CDW state, possibly with a transition temperature $T_{\rm TRSB}\approx$
$T_{\rm CDW}$.

Furthermore, we performed field training with magnetic field different from 1T
(data in the Supplementary Fig. S6). Figure 4c shows $\theta_{\rm K}$ at 50 K
plotted against the training field $\mu_{\rm 0}H_{\rm T}$. The data show a
clear trend that after positive (negative) field training, $\theta_{\rm K}$ is
positive (negative). The magnitude of the spontaneous polar Kerr angle does
not significantly depend on the strength of the training field. This fact may
imply that the coercive field of domain alignment across $T_{\rm CDW}$ is much
lower than 1 T. We use a step function $\theta_{\rm K}^{\rm fit}{\rm
sgn}(H_{\rm T})$ to fit the data and get $\theta_{\rm K}^{\rm fit}=0.573\pm
0.123$ µrad. Data from zero-field training (Fig. 4a), also included in this
figure, lie between the two branches of the step function fit.

## Discussion

The non-zero $\theta_{\rm K}$ at zero field arising below $T_{\rm CDW}$ is a
sign of spontaneous TRSB in the CDW state. Since long-range magnetic order has
not been detected in CsV3Sb5, the TRSB is not due to magnetism. Our analysis
of the Polar Kerr angle jump $\Delta\theta_{\rm K}$ under magnetic field
displays a behaviour different from the expectation for the conventional
anomalous Hall effect originating from the field-induced polarization of
paramagnetic spins. Instead, we discuss below that the observed TRSB can be
explained in terms of loop-current order in the CDW state.

The CDW in CsV3Sb5 is dominated by Fermi-surface nesting characterized by
wavevectors connecting the vHSs at the M points of the hexagonal Brillouin
zone. The electronic states around the vHS are dominated by vanadium $d$
orbitals. Due to the three sublattices of the Kagome net, the inhomogeneous
DOS at $E_{\rm F}$ promotes nearest-neighbor interaction, thereby resulting in
periodic modulation of the bond strength instead of the onsite charge density.
This corresponds to a charge bond order (CBO). Further Ginzburg–Landau
analysis shows that the three order parameters are imaginary with unequal
phases 32, 33, 34, 35. The imaginary CBO spontaneously induces orbital loop
current in the Kagome lattice and hence breaks time-reversal symmetry, as
sketched in Fig. 4d. The loop currents (gray arrows) generate opposite chiral
flux in hexagons (blue arrow) and triangles (orange arrows). Since both the
bond and on-site charge densities are inhomogeneous, an uncompensated net flux
appears in each unit cell. Different chiral CDW patterns form domains, and
thus, the residue moments over domains are responsible for non-zero polar Kerr
angle at zero field (Fig. 4a, b). These domains can be aligned by a moderate
magnetic field and result in the observed field-training effect.

In addition, the loop-current order can also explain the Kerr angle jump
$\Delta\theta_{\rm K}$ at $T_{\rm CDW}$ under magnetic field shown in Fig. 2.
When a magnetic field is applied, the chiral flux in each hexagon and triangle
tend to be parallel to the external field. However, the energy scale of the
CDW transition ($T_{\rm CDW}$ $\sim 94$ K) is much larger than the magnetic-
energy scale of our experiments. Therefore, the total flux, and hence the
resulting polar Kerr angle, do not reach saturation and are linearly
proportional to the magnetic field.

In AV3Sb5, competing phases have been proposed. The CBO theory with imaginary
order parameters suggests rotational-symmetry breaking without translational-
symmetry breaking, namely electronic nematicity in the CDW phase 32. Such
nematicity may be the reason of the bulk two-fold rotational symmetry observed
in transport measurements 27, 30. The CBO theories for the CDW are based on
the two-dimensional Kagome lattice. Remarkably, the interlayer charge
modulation appears to be important in CsV3Sb5. STM measurement showed that a
$\pi$-phase shift of the charge modulation intensity across single-unit-cell
surface steps has three-dimensional ordering 19. Out-of-plane superlattice
peaks have also been observed in X-ray diffraction 57, 58, 59, 60. Such
interlayer coupling may lead to the emergence of multiple sub-phases in the
CDW. Indeed, high pressure experiments showed suppression of the CDW phase and
unusual two-peak superconducting dome at a moderate pressure 61, 62. In a µSR
study of CsV3Sb5 25, TRSB was observed below 70 K (noticeably lower than
$T_{\rm CDW}$$\sim 94$ K) along with an additional magnetic transition below
30 K. Other µSR studies on CsV3Sb5 and KV3Sb5 report that TRSB occurs just
below $T_{\rm CDW}$ 18, 26. In our data of $\theta_{\rm K}$ measured at zero
field (Fig. 4a and b), we could not resolve clear transitions between multiple
phases, but some datasets exhibit features such as slope or intensity changes
at around 60 K and 80 K. These features may hint at competing phases in CDW
and call for further investigation.

We notice that optical polarization rotation studies on CsV3Sb5 were performed
very recently in zero field using 800 nm light and by ordinary polarizer-based
optical setups, methodologies different from ours 63, 64. Both works show the
emergence of birefringence and isotropic polarization rotation below $T_{\rm
CDW}$. The former indicates the electronic nematicity and the latter may come
from either TRSB or structural chirality. In our study, we use the zero-loop
Sagnac interferometer and the detected polar Kerr angle is solely due to TRSB
41. Furthermore, our optical results under magnetic field and field-training
effect show that the polar Kerr effect in CsV3Sb5 is strongly coupled to
magnetic field.

In conclusion, we have studied the TRSB in CDW state of CsV3Sb5 via polar Kerr
effect. Under magnetic field, the Kerr-angle jump at the CDW transition
$\Delta\theta_{\rm K}$ is proportional to the magnetic field and its sign is
field-switchable. Our analysis reveals that $\Delta\theta_{\rm K}$ increase
does not originate from the decreasing magnetization at the CDW transition,
indicating that the Kerr effect cannot be ascribed to conventional anomalous
Hall effect. At zero field, non-zero $\theta_{\rm K}$ arises in the CDW state
and can be effectively trained by magnetic field. These results point toward
spontaneous TRSB in the CDW states, which can be explained by the loop-current
order theory. Our polar Kerr effect results elucidate the central issue of the
symmetry breaking in the CDW of CsV3Sb5, motivating further experimental and
theoretical research on these Kagome metals. Our study demonstrates that the
high-resolution MOKE experiment under low temperature and high magnetic field
condition is a powerful tool for exploring non-trivial symmetry breakings,
which is crucially important for exploring exotic quantum materials.

High-quality single crystals of CsV3Sb5 were grown by a self-flux method with
Cs-Sb binary eutectic mixture (Cs0.4Sb0.6) as flux 23. The typical lateral
size of the obtained crystal is $\sim 3$ mm. The crystal structure were
examined by Laue diffraction at room temperature. The magnetization was
measured by a SQUID magnetometer (MPMS, Quantum Design). Polar Kerr angle was
measured using an all-fiber zero-loop Sagnac interferometer, constructed based
on Ref. 42. We used a broadband light source with wavelength centered at 1550
nm and a line width of 110 nm. The incident light was split into horizontally
and vertically polarized components of the polarization-maintaining (PM)
fiber, and then phase modulated using an electro-optical modulator (EOM). The
modulation frequency was $\omega/2\pi$ $\sim 3.848$ MHz so that the light
reflected from the sample has a $\pi$ phase shift relative to the incident
light. The maximum incident optical power is 200 $\mu$W and the spot size is
$\sim 4~{}\mu$m. The sample surface was cleaved before optical measurements,
with typical thickness after cleavage of $\sim 100~{}\mu$m. The low-
temperature measurements were performed in a 4He refrigerator with a base
temperature of about 1.9 K . The magnetic field was applied by a 11 T
superconducting magnet along the c axis. In the field training measurements, a
Hall sensor was used to determine the zero-field with an error within 5 Oe.

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## Data Availability

All the data that support the findings of this paper are available from the
corresponding authors upon reasonable request.

## Acknowledgments

We acknowledge M. Cuoco, A. Kapitulnik, Y. Yanase, and J. Goryo, for fruitful
discussion. This work was supported by Grant-in-Aids for Scientific Research
on Innovative Areas “Quantum Liquid Crystals” (KAKENHI Grant Nos. 20H05158,
22H04473) from the Japan Society for the Promotion of Science (JSPS), a Grant-
in-Aid for JSPS Fellows (KAKENHI Grant No. 20F20020) from JSPS, Grant-in-Aids
for Scientific Research (KAKENHI Grant Nos. 17H06136, 22H01168) from JSPS, by
Core-to-Core Program (No. JPJSCCA20170002) from JSPS, by a research support
funding from The Kyoto University Foundation, and by ISHIZUE 2020 of Kyoto
University Research Development Program. G. Mattoni acknowledges the support
from the Dutch Research Council (NWO) through Rubicon Grant No. 019.183EN.031.
The work at Beijing was supported by the Natural Science Foundation of China
(Grant No. 92065109), the National Key R$\&$D Program of China (Grant No.
2020YFA0308800), the Beijing Natural Science Foundation (Grant No. Z210006).
Z. Wang thanks the Analysis$\&$Testing Center at BIT for assistance in
facility support. The work at UCI is funded by the Gordon and Betty Moore
Foundation through Grant GBMF10276 to Jing Xia.

## Author contributions

This study was designed by S. Yonezawa and Y. Maeno. Y. Hu and S. Yamane
performed polar Kerr effect measurements and analyses, with assistance from G.
Mattoni, K. Yada, J. Wang, C. Farhang, J. Xia, S. Yonezawa, and Y. Maeno. Y.
Hu, S. Yamane, and K. Obata performed the magnetization measurements. K. Obata
took Laue diffraction images. Z. Wang, Y. Li, and Y. Yao grew single
crystalline samples and characterized them. The manuscript was mainly written
by Y. Hu and S. Yonezawa, based on discussion among all authors.

## Competing financial interests

All authors declare there is no competing interests regarding this work.

Figure 1:  Crystal structure of CsV3Sb5 and CDW transition detected by
reflectivity. a. Room-temperature crystal structure of CsV3Sb5. b. Kagome net
formed by V atoms (red spheres). Sb atoms (blue spheres) are located at the
hexagonal center. The crystal structure is illustrated by using the software
VESTA 65. c. Laue diffraction image taken on sample $\\#$14 along the [001]
direction. d. Temperature dependence of the second-harmonic signal
$V_{2\omega}$, which is proportional to the sample reflectivity, near the CDW
transition measured on sample $\\#$10 at different magnetic fields. The arrow
indicates the CDW transition. The inset shows the magnetic-field dependence of
the transition temperature $T_{\rm CDW}$ of samples $\\#$2, $\\#$10 and
$\\#$14\. $T_{\rm CDW}$ is determined by the peak in the temperature
derivative of $V_{2\omega}$. These data show that $T_{\rm CDW}$ is nearly the
same for all three samples and independent of H.

Figure 2:  Temperature and magnetic field dependence of the polar Kerr angle
of CsV3Sb5. a. Temperature dependence of the background-subtracted polar Kerr
angle $\theta_{\rm K}^{\rm sample}=\theta_{\rm K}-\theta_{\rm K}^{\rm bg}$
divided by magnetic field for sample $\\#$2\. The polar Kerr angle
$\theta_{\rm K}$ of a Nb metal sheet obtained by a separated measurement was
used as the background $\theta_{\rm K}^{\rm bg}$ (see Supplementary Fig. S2).
b. Temperature dependence of $\theta_{\rm K}$ for $\\#$14 measured from 1 T
(bottom curve) to 10 T (top curve) upon cooling. c. Polar Kerr angle jump
$\Delta\theta_{\rm K}$ at $T_{\rm CDW}$ as a function of magnetic field for
three samples. $\Delta\theta_{\rm K}$ is determined by the difference at
$T_{\rm CDW}$ between the linear fits below and above $T_{\rm CDW}$, as
examplified in the inset. The shaded region indicates a line with slope
$\Delta\theta_{\rm K}/\mu_{0}H\sim 8.0$ $\mu$rad/T deduced from all the data.

Figure 3:  Relationship between magnetization and the polar Kerr effect for
various materials, including CsV3Sb5. In the right side of the graph, polar
Kerr angle versus magnetization observed in the ordered state is plotted in
log-log scale for various ferromagnetic (FM), ferrimagnetic (Ferri) and anti-
ferromagnetic (AFM) materials, as well as the Kagome magnet Fe3Sn2 and
magnetic Weyl semimetals Co3Sn2S2 and Mn3Sn 48, 49, 50, 51, 52, 53, 54, 2, 55,
56. Here, the horizontal axis indicates the change of the saturated
magnetization due to the ordering $\Delta M$, and the vertical axis is the
change of the Kerr angle in the ordered state, as illustrated in the right
inset. The gray dashed line indicates an empirical linear relationship with
slope 0.0035 rad/T for FM/Ferri materials 56. For CsV3Sb5, the estimated polar
Kerr angle jump $\Delta\theta_{\rm K}$ and change of magnetization at $T_{\rm
CDW}$ at 1 to 7 T obtained for sample $\\#$10 are plotted. The definitions of
plotted values are schematically shown in the left inset. The red solid line
is the linear fit to the CsV3Sb5 data with slope $-1.36$ rad/T, and the red
dashed line is a line with positive slope for comparison purposes.

Figure 4:  Polar Kerr effect at zero field and field training effect to probe
spontaneous TRSB in CsV3Sb5. a. Temperature dependence of the polar Kerr angle
$\theta_{\rm K}$ measured at zero field. The data are obtained at different
incident optical powers of 100 µW, 150 µW and 200 µW. The arrow indicates
$T_{\rm CDW}$ $\sim 94$ K. b. Temperature dependence of $\theta_{\rm K}$
measured during zero-field-warming (ZFW) after cooling from above $T_{\rm
CDW}$ with a training field of $\pm 1$ T. The incident optical power is $\sim
100$ µW. The arrow indicates $T_{\rm CDW}$. The data show systematic positive
(negative) trend with positive (negative) training field. For (a) and (b),
each data point is obtained by averaging the signal for 2 hours. The error bar
is the standard error and is within the size of the markers. c. $\theta_{\rm
K}$ at 50 K versus training field for measurements with $\sim 100$ µW and
$\sim 200$ µW. The blue dashed line is the fitting by a step-function
$\theta_{\rm K}^{\rm fit}{\rm sgn}(H_{\rm T})$, the shaded area indicating the
error bar. The fitted magnitude of Kerr angle $\theta_{\rm K}^{\rm fit}$ is
$0.573\pm 0.123$ µrad. d. Schematic of the real-space loop-current pattern in
the Kagome lattice 35. The grey arrows indicate the orbital current direction.
The associated chiral flux is indicated by the clockwise and counter-clockwise
arrows. Within the unit cell in the CDW state (dashed lines), there are two
triangles and one hexagon with opposite chiral flux. Their incomplete
compensation, predicted by theories, would result in non-zero spontaneous Kerr
effect.

See pages - of CsV3Sb5_cdw_arxiv_supp.pdf


# Crowdsharing Wireless Energy Services

Abdallah Lakhdari  School of Computer Science
The University of Sydney
Sydney, Australia
<EMAIL_ADDRESS>Amani Abusafia  School of Computer Science
The University of Sydney
Sydney, Australia
<EMAIL_ADDRESS>Athman Bouguettaya  School of Computer Science
The University of Sydney
Sydney, Australia
<EMAIL_ADDRESS>
###### Abstract

We propose a novel self-sustained ecosystem for energy sharing in the IoT
environment. We leverage energy harvesting, wireless power transfer, and
crowdsourcing that facilitate the development of an energy crowdsharing
framework to charge IoT devices. The ubiquity of IoT devices coupled with the
potential ability for sharing energy provides new and exciting opportunities
to crowdsource wireless energy, thus enabling a green alternative for powering
IoT devices anytime and anywhere. We discuss the crowdsharing of energy
services, open challenges, and proposed solutions.

###### Index Terms:

IoT, energy, service, crowdsharing, sustainable, green IoT, crowdsourcing

##  I Introduction

The pervasive presence of wireless sensors and embedded systems has enabled
physical devices to connect to the Internet (i.e., Internet of Things (IoT))
[1]. IoT devices’ capabilities are augmented with sensors, computing
resources, and network connectivity. Abstracting the capabilities of IoT
devices using the service paradigm provides novel IoT services [2]. _IoT
services_ are defined by their _functional_ and _non-functional_ properties.
An example of _IoT services_ is sensing health-related information by a
smartwatch. The functionality of the services is sensing bio-signals from the
body. The accuracy of signals and their freshness represent the non-
functional, known as Quality of Service (QoS), properties [3].

Crowdsourcing IoT services creates a self-sustained, fast, and inexpensive IoT
ecosystem [4]. People may exchange a wide range of IoT services using the
augmented capabilities of their IoT devices. For example, a set of co-located
smartphones in a coffee shop may share their idle computing power to any
resource-constrained IoT user in the vicinity [5][6]. Another example is a
smartphone with low battery power which may elect to receive energy from
nearby IoT devices using WiFi [7][8][9]. Our focus is on providing a platform
for crowdsourcing energy services, also known as crowdsharing energy, among
IoT devices, anytime and anywhere.

Crowdsharing energy presents a novel solution to overcome the increasing
demand of energy by IoT devices. Several technologies have been developed over
the time to address the energy constraint in the IoT environment (See Fig.1).
Thus far, IoT devices have depended heavily on the power grid [10]. Recently,
new technologies and solutions have been developed to rely on renewable energy
as an alternative resource of energy [10]. We propose the energy crowdsharing
paradigm as an alternative clean and enhanced source to charge IoT devices.

The energy crowdsharing paradigm leveraging energy harvesting, wireless
charging, and crowdsourcing give rise to the concept of crowdsharing energy
services. We introduce energy service as the wireless exchange of energy among
battery-based IoT devices [11]. Crowdsharing energy refers to
opportunistically crowdsourcing energy services to charge nearby devices. An
_energy provider_ refers to an IoT device that can share energy. An _energy
consumer_ is an IoT device that needs energy. We focus on using wearables and
IoT devices in the energy crowdsharing paradigm. Wearables refer to IoT
devices that can be worn or hand-helds like smart shirts, and smartphones
[12][13]. Wearables have the ability to harvest energy from natural resources,
e.g., body heat or kinetic activity [14]. For instance, Solar Shirt uses
flexible solar panels to harvest solar energy and stores it in a battery [15].
The harvested energy can be shared with nearby IoT devices as an energy
service. Energy services may be achieved with the emergence of new
technologies known as “Over-the-Air wireless charging” [16]. For example,
Energous developed a technology to enable wireless charging up to a distance
of 4.5 meters111www.energous.com.

Figure 1: IoT Energy Sources Timeline Figure 2: Wireless Energy Crowdsharing
Market

The energy crowdsharing paradigm in the IoT environment has a twofold impact
on both IoT users and the environment. (i) The idea of recycling spare energy
promotes a green IoT environment by depending less on the power grid to charge
IoT devices. (ii) Enabling wireless charging between IoT devices provides
convenience to IoT users and less apprehension to charge their devices. The
convenience is a result of allowing IoT users to acquire energy anywhere and
anytime from surrounding devices.

We introduce the concept of crowdsourced IoT energy market where IoT devices
exchange energy services. The market could be created by a group of IoT users
in a microcell (See Fig 2). A microcell is a confined area in a smart city
where people may gather such as coffee shops, restaurants, and museums. The
prospected crowdsourced IoT energy market is a dynamic environment consisting
of providers and consumers that move spatially and temporally across
microcells boundaries. The deployment of this crowdsourced market is strongly
dependent on the participation of IoT devices. Energy consumers may subscribe
to the crowdsharing ecosystem to fulfill their energy requirements. Energy
providers, on the other hand, may share their harvested or spare energy
altruistically to contribute to a green IoT environment. They also may be
motivated by egotistic purposes through a set of incentives [17]. Due to the
limited resources of wearables, a single energy request may not be fulfilled
by one energy service [11]. In such cases, we may need to combine (i.e.
compose) multiple energy services for one request or vise versa. Additionally,
energy service providers and consumers may have different Spatio-temporal
preferences. Therefore, these preferences have to be considered in
advertising, matching, and composing energy services and requests.

This paper maps out a strategy to leverage the emerging technologies of energy
harvesting and wireless power transfer to unlock the full potential of the
energy crowdsharing paradigm. We envision the architecture of a green energy
ecosystem where IoT devices may exchange energy seamlessly. We identify the
major obstacles that hinder the development and potential deployment of the
crowdsourced IoT energy market in the real world. We propose and draw a road
map for future research directions to achieve this novel vision.

The remaining of the paper is organized as follows. Section II presents the
advantages of the energy crowdsharing ecosystem. Section III presents the
architecture of the ecosystem. Section IV discusses in detail the uprising
challenges to implement the envisioned ecosystem. Section V highlights the
future research directions. Section VI concludes the paper.

##  II Crowdsharing energy services

Sharing energy services offer multiple advantages to the environment and IoT
users. In what follows, we discuss each of the advantages in detail.

  * •

Eco-friendly: The global energy consumption of IoT devices is predicated with
a 20% annual increase to reach 46 TWh by 2025. The massive energy consumption
of IoT devices is one of the main contributors to 6% - 8% of the global carbon
footprint caused by information and communication technologies [10].
Crowdsharing energy contributes to reducing the carbon footprint by creating a
self-sustained green IoT environment. The energy services rely on recycling
spare energy or harvesting green energy from renewable resources such as body
heat, solar, or kinetic activity [13].

  * •

Spatial freedom: Crowdsharing energy services provide spatial independence for
IoT users. Energy-constrained IoT devices are regularly required to be
tethered to power outlets or carrying power banks. Both charging-cords and
charging-pads are the last obstacle for IoT devices to achieve their spatial
freedom. The prospected crowdsourced IoT environment is expected to enable
wireless energy delivery up to five meters. This allows the seamless delivery
of energy services.

  * •

Flexibility:  Crowdshared energy services are typically represented by time
intervals. In this environment, consumers and providers may invoke or offer
services for the full-time interval or only partially according to their
preferences [11][17], i.e., they do not have any lock-in contracts like
traditional services. In addition, providers and consumers may extend their
stay-time to offer or receive an energy service [18]. These features offer
flexible charging services in the crowdsharing environment.

  * •

Energy on demand:  The miniaturization of IoT devices restricts the size of
their batteries[19]. The small size of the battery results in a limited energy
storage capacity. This limitation restrains the capabilities of the IoT
devices. Energy consumption optimization has been extensively researched to
enable long-lasting working-time on a single charge. However, there is still a
gap for further energy optimizations. Hence, crowdsharing energy presents a
simple and yet effective solution to charge IoT devices and extend their
working-time [20].

  * •

Convenience: Crowdsharing energy services present a convenient alternative to
charge IoT devices as it allows them to be charged wirelessly anywhere and
anytime. This ubiquity of wireless charging facilitates access to energy for
IoT users. In addition, the flexibility in advertising and requesting energy
services, as previously discussed, emphasizes the convenience for IoT users.
IoT users might subscribe to crowdsharing energy without any lock-in contract.
They can also move freely while providing or acquiring energy [21]. This
convenience promises a wide spread of the crowdsharing ecosystem.

  * •

Growth of the Market: The concept of wireless crowdcharging has recently
gained increasing interest in industry [22]. The market for wireless charging
has an annual growth rate of 23.4 % and is predicted to reach $50 billion
dollars in 2027 [23]. This recent trend of adopting the wireless charging
technology in the industry and the ubiquity of IoT promises the spread and
accessibility of crowdsharing energy services [22].

##  III Proposed crowdsharing ecosystem architecture

The architecture of the system shall include the setup of four pillar
components to implement an energy crowdsharing ecosystem. These components
comprise the context of the environment, in-development technology, energy
services management system, and market design. In what follows, we discuss
these components in detail.

  * •

Environment: We envision a scenario where a number of people gather in
different places within the downtown of any major smart city (See Fig.2A). The
city residents will use their wearables to harvest energy [7]. The smart
buildings in the city such as a smart mall are split into geographical
$microcells$ where a microcell is a confined area such as cafes, movie
theaters, etc. (see Fig.2B). There are several IoT devices and wearables in
every microcell (see Fig.2C). The devices are assumed to be equipped with
wireless energy transmitters and receivers. The IoT users might share their
spare harvested energy to fulfill the requirements of nearby IoT devices. We
identify four components in the crowdsharing environment: energy service,
energy request, energy provider, and energy consumers. An energy service
refers to the wireless transfer of energy among IoT devices. An energy request
is an inquiry to receive an amount of energy through wireless means. An
_energy provider_ refers to an IoT device that may share energy. An _energy
consumer_ refers to an IoT device that requires energy.

  * •

Wireless energy transfer technology: Two energy technologies are required to
implement the crowdsharing ecosystem, namely, energy harvesting and Over-the-
Air wireless charging. Energy harvesters may be any wearable IoT device such
as smart clothes, smart shirts, smart glasses, smartwatches, and smartphones.
Energy harvesters have the ability to generate energy from natural resources
such as body heat, solar, or kinetic activity [13]. Existing wearable
technology allows for the harvesting of several microwatts to a few watts
[24]. For instance, Solar Shirt uses flexible solar panels to harvest solar
energy and stores it in a battery [15]. Another example, PowerWalk kinetic
energy harvester produces 10-12 watts on-the-move power [13]. PowerWalk
harvester can generate enough energy to charge up to four smartphones from an
hour walk at a comfortable speed by its user [25]. Over-the-Air wireless
charging technologies are the wireless energy transmitters and receivers that
enable the wireless transfer of energy[16]. For example, “Energous” created a
technology to enable wireless charging up to a distance of 4.5
meters222www.energous.com. IoT devices need to be equipped with both,
harvesting and wireless transmitting, energy technologies to be able to
crowdshare energy services.

Figure 3:  Energy Services Management System Figure 4:  Open Challenges in
Energy Crowdsharing Ecosystem

  * •

Energy services management system The energy service management system is
responsible to manage the received energy services and requests. An energy
service is defined by spatio-temporal preferences, the amount of available
energy, the usage behavior, and the mobility model of the IoT owner (See
Fig.3). Similarly, an energy request is defined by spatio-temporal
preferences, the amount of requested energy, the usage behavior, and the
mobility model of the IoT owner. A single energy request may not be fulfilled
by one energy service due to the limited resources of IoT devices [11]. In
such cases, the system may compose multiple nearby energy services to one
request or vise versa. Additionally, energy service providers and consumers
may have different Spatio-temporal preferences. Therefore, the system should
consider these preferences in matching and composing energy services and
requests.

  * •

Edge-based crowdsharing market The crowdsharing market consists of energy
providers and consumers in a microcell exchanging energy services (see Fig.2
C). Typically, an energy provider advertises their services to the energy
services management system. Similarly, an energy consumer submits their energy
request to the system. All local energy requests and advertisements are
handled in the energy services management system at the edge e.g., a router
associated with the microcell. Presumably, the management system sets a limit
on the amount of requested energy by a consumer and uses a reward system to
encourage providers to share energy. Rewards come in the form of stored
credits to providers. The collected credits may be used later by the provider
to increase the limit on the amount of requested energy when they are in the
consumer role. Providers may also be a consumer and vice-versa. Providers
receive rewards based on the amount of shared energy.

##  IV Open challenges

Unlocking the full potential of sharing energy among IoT devices in a
crowdsourced environment requires addressing several challenges. These
challenges can be grouped into three major components, the crowd, the enabling
technology, and the deployment of the system (See Fig.4). In what follows, we
list the encountered challenges for each component.

###  IV-A Crowd

Sharing energy among IoT devices strongly depends on the crowd. The crowd, in
this context, is defined by the owners of the IoT devices. The human factor
determines the willingness of participation in the energy sharing ecosystem.
Typically, the IoT devices owners tend to resist sharing their energy
resources [17]. Additionally, the dynamic behavior of the crowd may result in
volatile energy services. We discuss below the key factors causing the
resistance of participation and the volatility of energy services.

####  IV-A1 Resistance of provision

Crowdsourcing energy services create an inexpensive and convenient alternative
to charge IoT devices [9]. Presumably, people are motivated to participate in
the crowdsharing ecosystem as they can easily reach nearby energy sources.
However, they might resist sharing their energy [17]. Service resistance
refers to the unwillingness to provide services due to limited resources. In
our context, resistance is defined as the reluctance to provide energy among
IoT devices. The resistance of the provider is influenced by the provider’s
available resources, the service’s required resources, and the current state
of the surrounding environment. Therefore, one of the challenges is to predict
the resistance of energy providers in offering their energy service and
determine a method to overcome their resistance.

####  IV-A2 Volatility

The volatility of the energy services, in our context, refers to the dynamic
and unpredictable change in energy services, i.e, change in the energy
delivery rate of service. The volatility of the energy services is impacted by
the following three key aspects. (i) The availability of energy services, (ii)
the connectivity between the consuming and the providing IoT devices, and
(iii) the consistency of the wireless energy delivery. The aforementioned
aspects are influenced by the mobility of the crowd, their usage behavior and
their preferences. The mobility of the crowd affects the availability of
energy services around an energy consumer. It may also alter the connectivity
between the IoT devices. Energy services are provided from IoT devices which
are already in use by their owners. Hence, delivering consistent wireless
energy from an IoT device to another depends on the usage regularity of the
device owners. The IoT users’ spatio-temporal preferences vary which impacts
the availability of the energy services. The impact of each factor is
discussed below. .

  * •

Mobility: IoT devices change their locations frequently according to the
movement of their owners. The mobility of the crowd has several effects on the
crowdsharing ecosystem. First, the mobility of the crowd, across microcells,
determines the availability of energy services and requests. Second, mobility
impacts the connectivity between IoT devices. Since energy services deliver
energy through wireless communication channels, they are sensitive to the
distance. Therefore, The high mobility of IoT devices within a microcell may
result in disconnecting the wireless energy transfer. The disconnection in the
delivery off the energy service may result in its failure [26] [21].
Therefore, managing the mobility of IoT users is a major challenge for
providing and consuming energy services in highly dynamic environments.

  * •

Usage behavior: The providers’ energy usage behavior impacts the consistency
of delivering energy services [18]. A highly dynamic usage behavior of the
energy providers affects the quality of the shared energy service (QoS). IoT
energy service providers may advertise their surplus energy as an energy
service while using their devices at the same time. The energy capacity of
providing IoT devices changes over time due to the owner’s consumption
behavior [27]. Energy services may fluctuate due to the usage of the device
owners. Therefore, the energy usage behavior of IoT devices needs to be
modeled to ensure a consistent provision of energy services.

  * •

Preferences: The spatio-temporal features of the IoT energy services and
requests are defined based on the preferences of their owners. The preferences
are modeled based on the time pattern spent by the IoT owners in regularly
visited places, e.g., Workplaces, coffee shops, and food courts. The spatio-
temporal preferences of IoT devices are defined using the owners’ daily
activity model in a smart city [28]. Matching energy services and requests in
a crowdsourced environment is challenging due to the uncertain availability of
the services and requests. Predicting the availability of energy services
depends on defining the context (i.e., location and time of the day) and the
energy consumption behavior of the IoT devices. The contextual information,
induced from the daily routines of IoT users, annotates the availability time
and location of energy services and requests. The energy consumption behavior
determines the amount of the provided or requested energy.

###  IV-B Enabling Technology:

The implementation of the crowdsharing energy ecosystem strongly depends on
the recent technology of wireless charging. Although there is increasing
development in the wireless charging technology, there are some limitations in
the technology that hinder the full implementation of the ecosystem [23].
Technology limitations include battery capacity, computation capacity, and
energy loss. In what follows, we discuss each of these limitations.

####  IV-B1 Limited battery capacity

The design of IoT batteries has been developed to increase the length of their
stand-by time. However, it remains a big challenge to keep these devices
working while they share energy with other devices. Thus, it is critical to
provide an energy-saving technique to increase the IoT devices’ working time
as long as possible while providing their energy services.

####  IV-B2 Limited computing capacity

The limited computing capabilities of the IoT devices present major challenges
to share wireless energy. The computing resources are drained by the transfer
of energy, the connection establishment, and the conversion of the energy
electromagnetic signal between the exchanging devices [29]. Accordingly,
crowdsharing energy algorithms have to consider the required computing
resources during wireless energy delivery between devices.

####  IV-B3 Energy loss

Energy services’ provided amount may vary from small amounts shared by tiny
IoT devices to considerable amounts shared by bigger devices. In the case of
small amounts, a consumer may spend more energy to receive the requested
energy. The spent energy may include the energy required for service discovery
and connection establishment between the consumer and the provider [29].

###  IV-C Deployment of Energy Crowdsharing

The number of subscribers to the energy crowdsharing ecosystem is expected to
scale largely with the expansion of the IoT devices. This expansion would
magnify the threats to energy providers and consumers. It is needed to
consider security, privacy, trust, and reliability to achieve the full reach
of the crowdsharing ecosystem.

####  IV-C1 Security

Security of IoT devices aims to prevent and protect from IoT attacks and
failure of services [30]. The attacks on IoT devices may invade the privacy
and confidentiality of the users, infrastructures, data, and devices of the
IoT [31]. In addition, IoT attacks such as denial-of-service attacks may
hinder the provision of services to IoT Users. Securing IoT systems is one of
the critical challenges in IoT ecosystems as users may not adopt many IoT
systems without a good level of security [32]. Existing security architectures
and protocols are difficult to implement in IoT devices since IoT devices
usually have limited resources in terms of computing power and storage size
[33]. In addition, the current architecture of IoT does not effectively meet
the security requirements posed by IoT-specific vulnerabilities such as GPS
spoofing attacks[34].

####  IV-C2 Privacy

The size of the worldwide digital data created by IoT devices is expected to
grow up to 180 Zettabytes by 2020 [35]. Therefore, the protection of the IoT
data and the privacy of the users who generate or consume the data became a
major concern in research and industry [36]. Privacy is defined as “The claim
of individuals, groups, or institutions to determine for themselves when, how
and to what extent information about them is communicated to others” [37].
Maintaining privacy in IoT ecosystems may conflict with utilizing IoT data to
achieve their functions[38]. For instance, IoT Data are needed to enhance the
energy sharing process by profiling providers and consumers. In the case of
energy sharing, the collected IoT data may be considered as personal
information such as the IoT users’ mobility behavior and their energy
consumption model. Therefore, the balance between the privacy and utilization
of IoT data is an ongoing challenge.

####  IV-C3 Trust

Trust has been defined as “The confidence, belief, and expectation regarding
the reliability, integrity, ability, and other characteristics of an
entity”[39]. Trust is required in crowdsourced IoT systems to insure offering
high-quality services that will attract users and sustain IoT ecosystems. In
energy sharing, the trust assessment needs to determine the trust level of the
energy provider and the energy consumer. The trustworthiness of the energy
providers may represent an indication of the reputation of the provider, the
reliability of their services, and their security level[40]. Energy consumers’
trustworthiness may be an indication of their consuming reputation and their
security level. Although trust management has been studied intensively in
other domains, it remains a challenge in IoT ecosystems due to several reasons
[38]. First, the dynamic nature of crowdsourced IoT environments makes it
challenging to keep an accurate record of the devices’ reputations. For
instance, IoT devices are usually moving and their existence may not be for
long periods. Second, IoT devices usually have no global identity which makes
it challenging to keep a globally accessible profile for IoT devices. Third,
the relations among IoT devices are usually temporary which makes it difficult
to rely on social relations in evaluating their trust level. Therefore, novel
trust management frameworks are needed to determine the reputation of IoT
devices [38].

####  IV-C4 Reliability of providers

Reliable energy services increase the participation of IoT users in the energy
crowdsharing ecosystem [9]. The reliability of an energy provider refers to
the probability that an IoT energy service will be successfully delivered with
the same advertised Quality of Service (QoS) parameters. The reliability of
energy service is impacted by the available energy. The source of energy
services is an “in-use” IoT devices. Therefore, the consistency of the energy
transfer may get affected by the usage of the device. The fluctuating behavior
of the provider’s energy usage may impact the provision of crowdsourced IoT
energy services. Hence, it is vital to consider reliability while designing
and provisioning energy services.

##  V Future directions

This section proposes promising new research directions in crowdsharing. The
goal is not to exhaustively list the potential topics, but rather to present
some possible directions based on the aforementioned open challenges.

  * •

Incentive Models: Several incentive models have been proposed in crowdsourcing
environments to increase participation in providing services [41]. However,
most of the existing research did not consider the context of crowdsharing
energy services [17]. Incentives may be used to encourage providers to share
their energy. Designing the incentive model shall consider the context of the
environment and the behavior of the IoT users. Therefore, designing incentive
models is a promising research direction to increase participation in energy
provision [20].

  * •

Energy balancing in crowdsharing networks: Typically, the initial distribution
of energy providers may not be ideal. Some areas might be oversupplied or
undersupplied. An area is considered to be undersupplied if the number of
energy providers is less than the number of consumers and vice versa.
Therefore, the redistribution of energy providers is required to achieve
better-balanced energy availability in each area. One possible direction is
the use of an incentive model to encourage the migration of providers from
oversupplied areas to undersupplied areas.

  * •

Fairness: Fairness is a key criterion to efficiently provision energy services
and accommodate energy requests. It is challenging to allocate energy and
fulfill the requirements of multiple requests when there are limited energy
services. Unsatisfied requests would discourage consumers to participate and
commit to the crowdshared energy market. Efficient scheduling algorithms
present a possible solution to encourage consumers and maximize energy
utilization.

##  VI Conclusion

We presented a novel paradigm for energy crowdsharing to enable IoT devices to
exchange wireless energy services. We highlighted the advantages of adopting
energy crowdsharing on the environment and IoT users. We then envisioned and
designed an architecture to implement the energy crowdsharing ecosystem.
Lastly, we discussed the open challenges and recommended a road-map for the
required solutions.

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