# Lead perovskites as CE$\nu$NS detectors

César Jesús-Valls<EMAIL_ADDRESS>University of Tokyo, Kavli
Institute for the Physics and Mathematics of the Universe (WPI), University of
Tokyo Institutes for Advanced Study, Kashiwa, Japan  Federico Sánchez
University of Geneva, Section de Physique, DPNC, 1205 Genève, Switzerland

###### Abstract

The recent discovery of Coherent Elastic neutrino-Nucleus Scattering
(CE$\nu$NS) has created new opportunities to detect and study neutrinos. The
interaction cross-section in CE$\nu$NS scales quadratically with the number of
neutrons, making heavy-nuclei targets such as active lead-based detectors
ideal. In this Letter, we discuss for the first time the potential of
semiconductor lead perovskites for building neutrino detectors. Lead
perovskites have emerged in the last decade as revolutionary materials for
radiation detection due to their heavy and flexible element composition and
their unique optoelectronic properties that result in an excellent energy
resolution at an economic cost. While dedicated research and development will
be necessary, we find great benefits and no inherent obstacles for the
development of lead perovskites as CE$\nu$NS detectors.

##  I Introduction

Neutrinos are the only known fermions carrying exclusively weak charge and
therefore are clean probes of the weak interaction and unique messengers of
dense matter environments, unaffected by the strong and electromagnetic
interactions. This appeals, however, result in a notably suppressed
interaction cross-sections, hampering the study of neutrino physics and
rendering most applications impractical.
In 1974, the existence of coherent elastic neutrino-nucleus scattering
(CE$\nu$NS) was pointed out to be a consequence of the Standard Model [1]. In
CE$\nu$NS, a neutrino transfers momentum to a whole nucleus via the exchange
of a virtual Z boson, forcing it to recoil. The interaction cross-section for
this process is

$\displaystyle\frac{d\sigma^{{}_{\text{CE}\nu\text{NS}}}}{dE_{R}}=$
$\displaystyle\frac{G^{2}_{F}}{8\pi\cdot(\hbar
c)^{4}}(N+(1-4\sin^{2}\theta_{W})Z)^{2}$ $\displaystyle\cdot
m_{N}\cdot(2-E_{R}m_{N}/E_{\nu}^{2})|f(q)|^{2}\,,$ (1)

where $G_{F}$ is the Fermi constant, N (Z) is the number of neutrons
(protons), $\theta_{W}$ is the Weinberg angle and $m_{N}$ and $E_{R}$ are the
nucleon mass and its recoil energy respectively. The nuclear form factor
$f(q)$ characterizes the loss of coherence as a function of the transferred
momentum $q$=$\sqrt{2m_{N}E_{R}}/\hbar$ and it is close to unity for small
$q$, associated to typical neutrino energies $E_{\nu}\lesssim 50$ MeV.
Notably, given that $4\sin^{2}\theta_{W}\sim 1$ ,
$\sigma^{{}_{\text{CE}\nu\text{NS}}}\mathrel{\vbox{
\offinterlineskip\halign{\hfil$#$\cr\propto\cr\kern
2.0pt\cr\sim\cr\kern-2.0pt\cr}}}N^{2}$ [2]. This remarkable interaction cross-
section enhancement, however, offers a very challenging detection signal, as
the nucleon recoil needs to be identified. The maximum recoil energy scales as
$E^{\text{max}}_{R}\approx 2E^{2}_{\nu}/m_{N}$, so that detectors need to be
able to measure recoil energies of, at most, several tens of keV. Due to this,
it has not been until recently, thanks to progress in detector technology,
that CE$\nu$NS have been experimentally demonstrated by the COHERENT
collaboration, using a CsI target [3] and an Ar target [4].

##  II Motivations

The discovery of CE$\nu$NS and its enhanced cross-section has the potential to
mitigate the elusiveness of neutrinos and therefore to revolutionize its study
at energies on the order of a few tens of MeV, which includes geonetrinos [5],
reactor neutrinos [6], accelerator neutrinos from meson decays at rest [7, 8,
9, 10], solar neutrinos [11] and supernova neutrino bursts [12].
Characterizing the cross-section of CE$\nu$NS is also essential for dark
matter searches, as CE$\nu$NS constitute an irreducible background, the so-
called neutrino floor [13]. Being mediated by flavor insensitive neutral
currents, the detection of CE$\nu$NS provides extended sensitivity to sterile
neutrinos [14, 15, 16] and other new physics signatures [17, 18, 19, 20] and
allows the study of the neutrino magnetic moment [21, 22], its effective
charge radius [23] and the nuclear neutron form factor [24, 25]. Applications,
such as deploying neutrino detectors to increase nuclear security [26, 27]
might also be possible. Moreover, CE$\nu$NS is relevant to theoretical
astrophysics, as a key actor during stellar collapse [28, 29, 30].

##  III CE$\nu$NS experiments

Because of all of the above, an increasing number of CE$\nu$NS detector
technologies have been proposed [31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41,
42] and several experiments are ongoing or have been proposed: COHERENT [43],
using CsI, NaI, high-purity Ge (HPGe) and liquid-Ar targets; CONUS [44],
NCC-1701[45, 46] and $\nu$GEN [47] using cryogenic HPGe; MINER [48], using
cryogenic HPGe/Si; NUCLEUS [49] using cryogenic CaWO4 and Al2O3; CONNIE [44],
using Si charge coupled devices (CCDs); TEXONO [50] using p-type point-contact
Ge; RES-NOVA using cryogenic PbWO4 [51, 52]; RICOCHET [53] using cryogenic
HPGe bolometers; and RED100 [54] using liquid-Xe.
To get the most from CE$\nu$NS, an ideal detector should be inexpensive to
produce and operate, have excellent energy resolutions to measure nuclear
recoils with an energy of a few keV and be made of heavy nuclear target to
exploit the quadratic scaling of the cross-section. In this Letter, we point
out for the first time the excellent prospects of lead perovskites to build up
future CE$\nu$NS detectors.

##  IV Lead perovskites

Figure 1: Schematic of the perovskite ABX3 crystal structure.

Lead halide perovskites (LHP) are novel semiconductors with exceptional
optoelectronic properties, versatile chemical composition and low cost
synthesis. They typically consist of crystals with structure APbX3, see Fig.
1, where A is CH3NH3+ (MA+), CHNH${}_{3}^{+}$ (FA+), or Cs+; B is Pb2+; and X
is Cl-, Br-, and I- [55].
The study of halide perovskites as photosensors was sparked about a decade ago
in the context of solar cell development [56] and quickly emerged as an active
field of research due to record energy conversion efficiencies [57, 58, 59,
60, 61, 62, 63, 64]. Along the process, much has been learned about the basic
properties of this material, which combines a low exciton binding energy on
the order of few meV [65] with exceptionally long electron-hole diffusion
lengths exceeding 1 micrometer [66], a tunable band gap in the range of
1.2-2.4 eV [67, 68], and a high bulk resistivity of 10${}^{7-10}\Omega\cdot$cm
at room temperature [69]. The combination above is unique, as it pairs
efficient charge carrier production and mobility at low voltage bias with a
high bulk resistivity, orders of magnitude higher than those of Si and Ge,
suppressing dark current and noise. Moreover, LHP naturally allow to
manufacture crystals with very high atomic numbers, such as CsPbI3, and to
design application-specific perovskite sensors by means of stoichiometry
engineering [70, 71]. Furthermore, the synthesis of LHP is easy and flexible
through techniques such as solution processing. The production cost is also
low, with an estimated price of $<0.3$$/cm3 [55], namely, at the density of 4
g/cm3 an inexpensive cost of $75$$/kg. Finally, LHP can be operated
inexpensively at room temperature.

##  V Existing metrics as $x$/$\gamma$-ray detectors

Their striking performance as solar cells and their high atomic
numberiiiPhoton attenuation increases $\propto Z^{4}$, where Z is the atomic
number. quickly attracted the interest of the medical imaging community
towards lead perovskites [72, 73, 74, 75, 76, 77, 78, 79, 80]. In 2015, MAPbI3
was proven to detect $\gamma$-rays from 137Cs [81] and first x-ray images were
obtained [82]. That same year the first detection of single photons in LHP was
achieved [82], resolving at room temperature the $E_{\gamma}=59.6$ keV
emission from 241Am with about 35% resolution at full-width-half-maximum
(FWHM). In 2016, the reported X-ray sensitivities at a small bias of 0.1 V
were already four-fold those of commercial $\alpha$-Se detectors [83], the
dominating material for x-ray imaging. In 2017 perovskites where successfully
integrated with CMOS read-out circuitry leading to an almost 30-fold
improvement on the x-ray sensitivity [73]. In 2017, the spectrum of 137Cs
$\gamma$-ray energy spectrum was obtained, reaching a 6.5% energy resolution
(ER) for the 662 keV peak [84]. This same metric increased to 3.9% in 2018
[85] using small 10 mm2 crystals. In 2021, the ER at room temperature for 662
keV photons to 1.4% while using large CsPbBr3 crystals of 1.5 inches (3.75 cm)
in diameter and achieving a stable operation of the sensors for over 18 months
[86]. In that study, the spectrum of multiple radioactive sources was
resolved, such as 22 keV 109Cd x-rays at a FWHM ER of 19.7%. In 2021,
promising results were also achieved with CsPbI3, i.e. 20% ER for 122 keV
photons from 59Co. In 2022, LHP crystals of unprecedented quality have been
reported, leading to the best x-ray sensitivities yet achieved in any material
[87, 88].

##  VI Prospects as CE$\nu$NS detectors

Existing measurement with $x$-rays and $\gamma$-rays are the most abundant
tests of lead perovskites as prospective materials to build up radiation
detectors. In addition, perovskites-based devices have been already
demonstrated to be able to detect $\alpha$ [89] and $\beta$ [90] particles, as
well as neutrons using a hybrid configuration [91]. For the detection of
CE$\nu$NS it is important to note that nuclear and electronic recoils have
different ionization efficiencies. For Ge it has been measured that nuclear
recoils generate about a third of the ionization signal of their electronic
counterparts [92]. For lead perovskites this fraction, the so-called
quenching, is still unknown. Nonetheless the demonstrated ability of
perovskites to resolve energy deposits of few tens of keV is encouraging. The
observation of low energy spectral lines, such as 59Co 22 keV $x$-rays with
19.7% FWHM ER, suggests that detecting nuclear recoils with energies below 100
keV might be already possible if quenching values are not drastically larger
than those in Ge. If lead perovskites are proven to be succesful as nuclear
recoil detectors, they have enormous potential as future CE$\nu$NS detectors.
Firstly, as earlier reviewed a large fraction of existing or planned CE$\nu$NS
detectors use semiconductor materials, typically HPGe, a choice driven by its
gold-standard energy resolution. Lead perovskites are rapidly approaching
their ultimate energy resolution expected to be similar to that of HPGe [86].
Consequently, in the medium-term LHP might be directly competing with HPGe
detectors.

Figure 2: CE$\nu$NS interaction cross-section per nucleus, $\sigma$,
multiplied by the detector efficiency, $\epsilon$, as a function of the recoil
energy threshold, $E^{\textup{recoil}}_{\textup{threshold}}$. Solid (dashed)
lines correspond to CsPbI3 (Ge).

Secondly, producing low activity lead perovskites should be possible, e.g.
CsPbI3 consists of Cs and I both used in the first historical detection of
CE$\nu$NS [3] and archaeological Pb has been recently demonstrated to be
adequate for CE$\nu$NS detection [93]. Moreover, CsPbI3 and other lead
perovskites are made up of strikingly heavy elements, significantly
advantaging the CE$\nu$NS interaction cross-section of mainstream alternative
materials and in particular that of Ge. However, the maximum recoil energy
decreases linearly with $m_{N}$ and therefore the ability of the detector to
identify the recoiling nucleus needs to be considered. To account for it, we
define the effective cross-section, $\sigma_{\textup{eff}}$, as a figure-of-
merit, defined as

$\displaystyle\sigma_{\textup{eff}}\equiv\int_{E^{\textup{recoil}}_{\textup{threshold}}}^{E^{\textup{max}}_{R}}\frac{d\sigma}{dE_{R}}\,\epsilon\,dE_{R}\,,$
(2)

which can be calculated from Eq. I if the detector efficiency, $\epsilon$, is
specified. Using it, in Fig.2 CsPbI3 and Ge targetsiiiiiiFor CsPbI3, the
weighted average (Cs+Pb+3I)/5 is used on the result of Eq. 2. are directly
compared for some neutrino energies assuming a detector with perfect (null)
efficiency above (below) a certain energy recoil threshold,
$E^{\textup{recoil}}_{\textup{threshold}}$. As expected, observing
interactions in CsPbI3 would require a smaller
$E^{\textup{recoil}}_{\textup{threshold}}$ than in Ge, but if the detection
threshold is achieved and mildly lowered it results in a large enhancement of
the interaction cross-section. This trade-off is characterized by the ratio
$\sigma_{\textup{eff}}^{CsPbI_{3}}/\sigma_{\textup{eff}}^{Ge}$ presented in
Fig.3 as a function of the neutrino energy and the recoil energy threshold.

Figure 3: The color map depicts the ratio of
$\sigma_{\textup{eff}}^{CsPbI_{3}}/\sigma_{\textup{eff}}^{Ge}$ as a function
of the neutrino energy, $E_{\nu}$, and the recoil energy threshold,
$E^{\textup{recoil}}_{\textup{threshold}}$. A ratio value of zero indicates
that $E^{\textup{recoil}}_{\textup{threshold}}$ is above the necessary level
to observe any recoil in CsPbI3. To help the visualization, values of some
particular integer ratios are highlighted by color lines.

Achieving $E^{\textup{recoil}}_{\textup{threshold}}$ below 20 keV would in
general result in an event rate advantage for CsPbI3 detectors compared to Ge
when dealing with neutrino energies similar to a few tens of MeV, e.g.
neutrinos from pion decays at rest, useful to study sterile neutrinos and NSI,
or neutrinos from the high-energy tail of supernova neutrino bursts. Reaching
even lower thresholds might result in additional applications involving
neutrinos from other sources but it will also likely require a longer term
R&D.
Lastly, perovskites are orders of magnitude cheaper to manufacture and
potentially to operateiiiiiiiiiPerovskites might be able to operate without
the need of cryogenic systems, as supported by existing $x$-ray data. than
existing alternatives, including HPGe. Due to their inexpensive production
cost, the budget to build a large perovskite detectors would be driven by the
number of electronic channels. If volumes similar to a fraction of 1 cm3 could
be adequately readout by a single channel, i.e. sizes slightly above of those
in use for x-ray detection, a ton of perovskite might be read by $O(10^{6})$
electronic channels, making it potentially scalable.

##  VII Discussion and outlook

In just one decade lead perovskites have been established as novel materials
with transformative potential as radiation detectors due to their unique
optoelectronic properties. In this Letter, we have pointed out their potential
as neutrino detectors for the first time and discussed its suitability for the
study of CE$\nu$NS. To bring perovskites to their ultimate detection potential
and enable their full range of applications active R&D is required.
Demonstrating and characterizing their ability to detect nuclear recoils in
the energy range of interest is an essential milestone.
Lastly, we note that CE$\nu$NS and some dark-matter models share the same
signal mechanism, i.e. the detection of nuclear recoils. Therefore, any
progress on that direction might benefit both the neutrino and the dark-matter
research communities.

## Acknoledgments

We acknowledge fruitful discussions with E. Palomares, and valuable feedback
from J.I. Collar and L. Pattavina. This project was partially inspired by the
ZPro project funded by the Barcelona Institute of Technology (BIST).

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