Nematic fluctuations in the cuprate superconductor Bi2Sr2CaCu2O8+δ

Abstract

Establishing the presence and the nature of a quantum critical point in their phase diagram is a central enigma of the high-temperature superconducting cuprates. It could explain their pseudogap and strange metal phases, and ultimately their high superconducting temperatures. Yet, while solid evidences exist in several unconventional superconductors of ubiquitous critical fluctuations associated to a quantum critical point, in the cuprates they remain undetected until now. Here using symmetry-resolved electronic Raman scattering in the cuprate Bi2Sr2CaCu2O8+δ, we report the observation of enhanced electronic nematic fluctuations near the endpoint of the pseudogap phase. While our data hint at the possible presence of an incipient nematic quantum critical point, the doping dependence of the nematic fluctuations deviates significantly from a canonical quantum critical scenario. The observed nematic instability rather appears to be tied to the presence of a van Hove singularity in the band structure. Solid evidence of quantum fluctuations associated to a quantum critical point in cuprate superconductors remains elusive. Here, Auvray et al. report Raman scattering evidence of enhanced electronic nematic fluctuations near the endpoint of the pseudogap phase in Bi2Sr2CaCu2O8+δ.

Full text

ARTICLE
Nematic fluctuations in the cuprate superconductor
Bi
2
Sr
2
CaCu
2
O
8+δ
N. Auvray 1, B. Loret1, S. Benhabib1, M. Cazayous1, R.D. Zhong 2, J. Schneeloch2, G.D. Gu2, A. Forget3,
D. Colson3, I. Paul1, A. Sacuto 1& Y. Gallais 1*
Establishing the presence and the nature of a quantum critical point in their phase diagram is
a central enigma of the high-temperature superconducting cuprates. It could explain their
pseudogap and strange metal phases, and ultimately their high superconducting tempera-
tures. Yet, while solid evidences exist in several unconventional superconductors of ubiqui-
tous critical fluctuations associated to a quantum critical point, in the cuprates they remain
undetected until now. Here using symmetry-resolved electronic Raman scattering in the
cuprate Bi2Sr2CaCu2O8þδ, we report the observation of enhanced electronic nematic fluc-
tuations near the endpoint of the pseudogap phase. While our data hint at the possible
presence of an incipient nematic quantum critical point, the doping dependence of the
nematic fluctuations deviates significantly from a canonical quantum critical scenario. The
observed nematic instability rather appears to be tied to the presence of a van Hove sin-
gularity in the band structure.
https://doi.org/10.1038/s41467-019-12940-w OPEN
1Université de Paris, Matériaux et Phénomènes Quantiques, CNRS UMR 7162, F-75205 Paris, France. 2Condensed Matter Physics and Materials Science
Department, Brookhaven National Laboratory, Upton, NY 11973, USA. 3Service de Physique de lÉtat Condensé, DRF/IRAMIS/SPEC (UMR 3680 CNRS), CEA
Saclay, 91191 Gif-sur-Yvette cedex, France. *email: yann.gallais@univ-paris-diderot.fr
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Unconventional superconductivity (SC) is often linked to
the proximity of an electronically ordered phase whose
termination at a quantum critical point (QCP) is located
inside a superconducting dome-like region1,2. This observation
suggests quantum criticality as an organizing principle of their
phase diagram. The associated critical fluctuations could act as
possible source for enhanced superconducting pairing3–5and
explain their ubiquitous strange metal phases which often
show non-Fermi liquid behavior, like a linear in temperature
resistivity7. However whether the quantum critical point scenario
holds for high-Tcsuperconducting cuprates has remained largely
unsettled6–8. This can be traced back to two fundamental reasons.
First the exact nature of the pseudogap (PG) state, the most
natural candidate for the ordered phase, remains mysterious.
Experimentally a wealth of broken symmetry phases have been
reported at, or below, the somewhat the loosely defined PG
temperature T9. It is currently unclear which, if any, of these
orders is the main driver of the PG phase as they could be all
secondary instabilities of a pre-existing PG state. Second there is
little direct evidence for critical fluctuations above T, questioning
the very existence of a QCP associated to the termination of a
second order phase transition at a critical doping p(see Fig. 1a).
AF fluctuations do not appear to be critical close to the putative
QCP, at least for hole-doped cuprates10,11, and critical CDW
fluctuations are only observed below T12. Fluctuations associated
to the more subtle intra-unit-cell orders13–17 are more elusive and
have not been reported up to now.
Recently nematicity, an electronic state with broken rotational
symmetry but preserved translational invariance of the under-
lying lattice18 (see Fig. 1b), has emerged as a potential candidate
for the origin of the PG phase. A second order phase transition to
a nematic phase, breaking the C4rotational symmetry of the
CuO2plane, has been reported by torque magnetometry in
YBa2Cu3O6þδclose to the TTreported by other techniques19.In
a separate study a divergent electronic specific heat coefficient was
observed at the endpoint of the PG phase in several cuprates and
was interpreted as a thermodynamical hallmark of a QCP20. The
nature of the ordered state associated to this putative QCP is
however not yet settled, and nematicity stands as a potential
candidate. To assess its relevance and the role of nematic degrees
of freedom in driving the PG order, probing the associated
fluctuations is thus essential.
Because it probes uniform (q=0) dynamical electronic fluctua-
tions in a symmetry selective way, electronic Raman scattering can
access nematic fluctuations without applying any strain even in
nominally tetragonal systems21. For metallic systems, the nematic
fluctuations probed by Raman scattering can be thought as dyna-
mical Fermi surface deformations which break the lattice point
group symmetry. In the context of iron-based superconductors (Fe
SC) ubiquitous critical nematic fluctuations were observed by
Raman scattering in several compounds22–24.Theywereshownto
drive the C4symmetry breaking structural transition from the
tetragonal to the orthorhombic lattice, and to persist over a sig-
nificant portion of their phase diagram21. In the context of cuprates
nematicity along Cu-O-Cu bonds has been reported via several
techniques, mostly in YBa2Cu3O6þδ14–17,19,25,26. The associated
order parameter is an uniform traceless tensor of B1g(or x2−y2)
symmetry, which switches signs upon interchanging the xand y
axis of the CuO2square plane (Fig. 1b). Nematicity along different
directions has also been found in one layer mercury-based cuprate
HgBa2CuO427, and overdoped La1xSrxCuO428. In the former case
nematicity develops along the diagonal of the CuO2plane and thus
transforms as the B2g(or xy) symmetry. The ability of Raman
scattering to resolve the symmetry of the associated order parameter
is therefore crucial.
Results
Doping and symmetry dependent Raman spectra. We present
Raman scattering measurements on 6 single crystals of the cuprate
Bi2Ca2SrCu2O8þδ(Bi2212) covering a doping range between p=
0.12 and p=0.23. A particular emphasis was put in the doping
region bracketing p0:22 close to where the PG was shown to
terminate, i.e., between p=0.20 and p=0.2329–36. At these dop-
ings a relatively wide temperature range is accessible above both T
and Tcto probe these fluctuations, and look for fingerprints of a
nematic QCP. The polarization resolved Raman experiments were
performed in several configurations of in-plane incoming and
outgoing photon polarizations in order to extract the relevant
irreducible representations, or symmetries, of the D4hgroup: B1g
which transforms as x2−y2
;B2g(xy)andA1g. As indicated above
while the former two correspond to nematic orders along and at 45
degrees of the Cu–O–Cu bonds, respectively, the latter one is fully
symmetric and is not associated to any symmetry breaking. The
recorded spectra were corrected by the Bose factor and are thus
proportional to the imaginary part of the frequency dependent
Raman response function χ00
μðωÞin the corresponding symmetry μ
where μ=B1g;B2g;A1g(see Methods section for more details on
the Raman scattering set-up and polarization configurations).
In Fig. 1c is displayed the evolution of the normal state Raman
spectrum in the B1gsymmetry as a function of doping. From
previous Raman studies, OD60 (Tc=60K) sample lies very close
to the termination point of the PG, p0.22 and no signature of
PG is seen for OD60, OD55 (Tc=55K), and OD52 (Tc=52K)
compositions36. Other samples, OD74 (Tc=74K), OD80 (Tc=
80K), and UD85 (Tc=85K) display PG behavior. The normal
state spectra are consistent with previously published Raman data
for the doping compositions where they overlap37. In particular
while the spectrum shows little temperature dependence in the
underdoped composition UD85, it acquires a significant tem-
perature dependence in the overdoped regime where the overall
B1gRaman response increases upon cooling. The low-frequency
slope of the Raman response being proportional to the lifetime of
the quasiparticles, this evolution was previously attributed to an
increase metallicity of anti-nodal quasiparticles, located at (π,0)
and equivalent points of the Brillouin zone with overdoping37.
However the increase of intensity upon cooling observed in
overdoped compositions, p>0:2, is not confined to low
frequencies as expected in a naive Drude model, but extends
over wide energy range up to at least 500 cm1. This suggests that
it is not a simple quasiparticle lifetime effect but, as we show
immediately below, it is rather associated to a strongly
temperature dependent static nematic susceptibility. It is also
evident in Fig. 1c that this evolution is non-monotonic with
doping as the OD60 spectra shows significantly more temperature
dependence than at any other dopings.
Symmetry-resolved susceptibilities. To analyze the observed
temperature dependence and its link to a nematic instability, it is
useful to extract the symmetry resolved static susceptibility
χμðω¼0Þ=χ0
μfrom the measured finite frequency response
χ00
μðωÞusing Kramers-Kronig relations:
χ0
μ¼ZΛ
0
dωχ00ðωÞ
ωð1Þ
where μstands for the symmetry and Λa high-energy cut-off. In
order to perform the integration, the spectra were interpolated to
zero frequency either linearly, or using a Drude lineshape (see
Supplementary Note 2 and Supplementary Figs. 2 and 3).
The integration was performed up to Λ=800 cm−1, above
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which the spectra do not show any appreciable temperature
dependence in the normal state (see Supplementary Fig. 4). For
B1gsymmetry χ0
B1gis directly proportional to the static electronic
nematic susceptibility, and its evolution as a function of doping
and temperature is shown in Fig. 2a. For a comparison the same
quantity, extracted for 3 crystals in the complementary symme-
tries (see Supplementary Note 1 for the spectra), B2gand A1g,is
also shown. In order to compare different compositions and since
3
0
SC
PG
ab
c
T
T*
p*
es
el
p
y
x
C4C2

–
0
kx
ky
UD85
OD80
OD74
OD52
OD55
OD60
61 K 83 K 63 K 70 K
88 K
108 K
128 K
148 K
168 K
188 K
208 K
228 K
248 K
268 K
288 K
308 K
73 K
162 K
191 K
221 K
250 K
275 K
300 K
82 K
97 K
113 K
137 K
128 K
148 K
168 K
188 K
208 K
248 K
268 K
303 K
81 K 120 K 102 K 99 K
113 K
137 K
162 K
187 K
211 K
236 K
260 K
281 K
301 K
112 K
139 K
164 K
193 K
222 K
250 K
276 K
302 K
128 K
158 K
188 K
218 K
248 K
268 K
298 K
85 K
90 K
95 K
100 K
105 K
110 K
115 K
88 K
93 K
98 K
103 K
108 K
65 K
70 K
74 K
79 K
2
″
B1g
(norm. at 800 cm–1)
1
0
3
2
1
0
0 200 400 600 0 200 400
Raman shift (cm–1)
600 0 200 400 600
UD85
OD80
OD74
OD52
B1g
OD55 OD60
Fig. 1 Dynamical nematic fluctuations in Bi2Sr2CaCu2O8þδaTemperature-doping generic phase diagram of hole-doped cuprates. The pseudogap phase
ends at a putative quantum critical point (QCP) located at the doping p.bNematic order breaking the C4rotational symmetry of the Cu square lattice
down to C2symmetry. The corresponding order parameter has B1gsymmetry: in reciprocal space it transforms as k2
x
−k2
yand switches sign upon
90 degrees rotation x!y(color scale is defined as blue: negative values, red: positive values and white: 0). cTemperature dependence of the B1gRaman
spectrum in the normal state for several doping levels in Bi2Sr2CaCu2O8þδ. The B1gsymmetry is obtained using cross-photon polarizations at 45 degrees of
the Cu–O–Cu direction (see insets)
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we do not have access to the susceptibilities in absolute units, all
extracted susceptibilities have been normalized to their average
value close to 300 K, and we focus on their temperature depen-
dences. The temperature dependence of the B1gnematic sus-
ceptibility is strongly doping dependent. In the normal state it is
only weakly temperature dependent for UD85 (p=0.13), while
for overdoped compositions it displays a significant enhancement
upon cooling. The pronounced divergent-like behavior for OD60
is only cut-off by the entrance to the SC state. This effect is
however reduced for p>p
(OD55 and OD52), mirroring the
non-monotonic behavior already apparent in the raw spectra.
While our focus here is on the normal state, it is notable that the
nematic susceptibility is suppressed upon entering the super-
conducting state for all doping studied, suggesting that the
nematic instability is suppressed by the emergence of the super-
conducting order. In addition a weak but distinct suppression of
χ0
μis also observed above Tcfor UD85 (200 K), close to the value
of Tdetermined by other techniques in Bi2212 for similar doping
levels33,38. By contrast the static susceptibilities extracted in B2g
and A1gsymmetries, while displaying some mild enhancement,
are essentially doping independent above Tc. This symmetry
selective behavior unambiguously demonstrates the nematic nat-
ure of the critical fluctuations observed close to p0.22.
Curie-Weiss analysis of the B1gnematic susceptibility. Further
insight into the doping dependence of these critical nematic
fluctuations can be gained by fitting the B1gstatic nematic sus-
ceptibility using a Curie-Weiss law:
1
χ0
B1g
¼A´ðTT0Þð2Þ
In a mean-field picture of the electronic nematic transition, such a
behavior is expected on the high temperature tetragonal side of a
second order phase transition which would set in at T0.A
negative T0implies that the ground state is on the symmetry
unbroken side of the phase transition. Fig. 2(b) shows linear fits
of the inverse susceptibility for all doping studied. Since clear
deviations to linear behavior for 1
χ0
B1g
are seen below Tand Tc(see
inset of Fig. 2b), we restrict our fits to temperatures above Tfor
doping levels below p, and above Tcfor doping level above p*.
The fits allows us to extract T0, the mean-field nematic transition
temperature, which quantifies the strength of the nematic
instability: graphically T0corresponds to the zero temperature
intercept of the inverse susceptibility.
The evolution of T0as a function of doping is summarized in
Fig. 3in a phase diagram showing the corresponding evolution of
the nematic susceptibility in a color-coded plot. Coming from the
strongly overdoped regime, p0.23, T0increases towards
p0.22 but upon further reducing doping, instead of
crossing-over to positive temperatures T0reverses its behavior
and decreases strongly, suggesting a significant weakening of the
nematic instability below p. While the T0values remain negative
at all doping suggesting the absence of true nematic quantum
criticality, two aspects should be borne in mind. First the three T0
values above pextrapolate to T=0 K at a doping level above the
one corresponding to OD74, indicating the possible presence of a
nematic QCP located between the doping levels corresponding to
OD74 and OD60 crystals. Second, as shown in the context of Fe
SC, the extracted susceptibility from Raman measurements does
not include the contribution of the electron-lattice coupling21.In
particular the linear nemato-elastic coupling is expected to
increase the nematic transition temperature above T0and shift
accordingly the location of the QCP39. This lattice-induced shift
2
a
1.0
0.5
1
2
1
2A1g0
UD85 K
OD80 K
OD74 K
UD85 K
OD80 K
OD74 K
OD60 K
OD55 K
OD52 K
OD60 K
OD55 K
OD52 K
B2g
B1g
1
0 100 200 300 100 200
Temperature (K)
Temperature (K)
0
1.5
1/B1g
(norm.)
1.0
100
Tc = 85 K
Tc = 74 K
T* = 200 K
T* = 125 K
200 300
Temperature (K)
300


–
0


–
0


–
1/0 (norm. at 300 K)
B1g
(300 K)

0 (T)/0

b
Fig. 2 Symmetry resolved static susceptibilities. aTemperature dependences of the static susceptibility in 3 different symmetries, B1g;B2g, and A1g,asa
function of doping. The form factors for each symmetry are depicted in reciprocal space in insets. They are given in terms of the lowest order Brillouin zone
harmonics: cos(kx)−cos(ky) for B1g, sin(kx)sin(ky) for B2g, cos(kx)+cos(ky) and cos(kx)cos(ky) for A1g. The error bars correspond to the standard error of
the low energy fits used for the low energy extrapolation (see supplementary note 1). bCurie-Weiss fits of the inverse B1gnematic susceptibility for
temperatures above max(TcT). The inset shows the full temperature dependence of the inverse susceptibility of OD74 and UD85 where deviation from
Curie-Weiss law are observed at T, and an additional upturn is observed at Tc. Full and open symbol correspond to data above and below T, respectively
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of T0is on the order of 30–60 K in Fe SC21, but is not known in
the case of cuprates. Recent elasto-resistance measurements
suggest that the nemato-elastic coupling might be weaker in
cuprates39–41. Irrespective of the presence of a nematic QCP, it is
clear that the doping evolution of T0contrasts with the canonical
behavior of a QCP where T0would evolve monotonically as a
function of the tuning parameter.
Discussion
We now discuss the possible origin of the observed nematic
fluctuations, and then elaborate on the implications of our find-
ings for the phase diagram of the cuprates. Theoretically two
routes for nematicity have been proposed in the context of cup-
rates. The first route is via the melting of an uni-axial density
wave order, like stripe or charge density wave, and is expected to
apply to the underdoped regime where the tendency towards
these orders is strongest42. It is unlikely to be relevant to our
findings since the nematic susceptibility is almost featureless
above Tin the underdoped crystal, and only shows significant
enhancement in the overdoped regime. A second route is via a
Pomeranchuk instability of the Fermi liquid, where the Fermi
surface spontaneously deforms and breaks the underlying lattice
rotational symmetry (see inset of Fig. 3). Theoretically, such an
instability was indeed shown to be relevant to the cuprates close
to doping levels where the density of states passes through a van
Hove singularity (vHs) at the (π, 0) and equivalent points of the
Brillouin zone43–45. This is consistent with our results since p=
0.22 corresponds to the doping level where one of the Fermi
surface sheets of Bi2212 changes from electron-like to hole-like,
and passes through a van Hove singularity (vHs) at (π,0)
29,36.
The link between the nematic instability and the closeness of the
vHs singularity also naturally explains the non-monotonic
behavior of T0as a function of doping, which is also found in
mean field theories of vHs induced nematicity46,47. Interestingly
non-Fermi liquid behavior has been argued to occur generically
near a nematic QCP if the coupling to the lattice is weak
enough39,48,49, and the observed critical nematic fluctuations may
therefore play a central role in the the strange metal properties
observed in this doping range. While our results suggest that the
nematic instability is linked to the proximity of vHs, we stress
that the observed enhancement cannot be merely a consequence
of a high-density of states at the (π, 0) points: both B1gand A1g
form factors have finite weight at these points, but only the
nematic B1gsusceptibility shows fingerprints of critical behavior
at p. Thus electronic interactions in the nematic channel appears
to be essential to explain our observation. We note that the key
role of interactions, beyond density of state effects, was also
argued to explain the divergence of the electronic specific heat
coefficient which was observed at the PG end-point of several
one-layer cuprates20.
What are the consequences of our findings for the nature of the
PG state? The above discussion and the doping dependence of T0
allow us to conclude that the PG is likely not driven by a nematic
instability. If this was the case one would expect strong nematic
fluctuations close to Tin the underdoped composition and
a monotonic increase of T0, crossing-over to positive values,
as observed in the case of Fe SC22,50,51. It therefore appears that
nematic and PG instabilities are distinct, and possibly even
compete. Note however that since our analysis of T0has been
restricted to temperature above Tthe weakening of the nematic
fluctuations below pcannot be a simple consequence of the PG
order. Intriguingly, the states at the (π;0) point appears to be
critical for both orders: while the strength of nematic fluctuations
is closely tied to the closeness to the vHs at these points, it was
suggested that the PG regime is characterized by a strong deco-
herence at these hot-spots due to AF fluctuations that set in once
the Fermi surface reaches the (π, 0) points corresponding to the
AF zone boundary. This decoherence ultimately drives the Fermi
surface hole-like and induces a cross-over to a PG state at low
temperature52,53. Our results thus indicate that both nematicity
and the PG state depend critically on the Fermi surface topology
in the case of Bi2212. Further measurements on cuprates com-
pounds where the PG endpoint and the change in the Fermi
surface topology occur at distinct doping levels, like
Tl2Ba2CuO6þδ54,55 and YBa2Cu3O6þδ56,57, are needed in order to
clarify the nature of this link and confirm the connection between
the nematic instability and the presence of a vHs.
Methods
Samples. The Bi-2212 single crystals were grown by using a floating zone method.
First optimal doped samples with Tc=90 K were grown at a velocity of 0.2 mm per
hour in air. In order to get overdoped samples down to Tc=65 K, the as-grown
single crystal was put into a high oxygen pressured cell between 1000 and 2000 bars
and then was annealed from 350 C to 500C during 3 days. The overdoped
samples below Tc=60 K were obtained from as-grown Bi-2212 single crystals put
into a pressure cell (Autoclave France) with 100 bars oxygen pressure and annealed
from 9 to 12 days at 350 C . Then the samples were rapidly cooled down to room
temperature by maintaining a pressure of 100 bars. The underdoped sample was
obtained by annealing the as-grown sample in vacuum. The critical temperature Tc
for each crystal has been determined from magnetization susceptibility measure-
ments at a 10 Gauss field parallel to the c-axis of the crystal. The selected crystals
exhibit a quality factor of Tc
ΔTclarger than 7. ΔTcis the full width of the super-
conducting transition. A complementary estimate of Tcwas achieved from elec-
tronic Raman scattering measurements by defining the temperature from which
the B1gsuperconducting pair breaking peak collapses. Special care has been
devoted to select single crystals which exhibit the same SC pair-breaking peak
energy in the Raman spectra measured from distinct laser spots on a freshly cleaved
surface. The level of doping p was defined from Tcusing Presland and Tallons
equation58:
1T
Tc;max
¼82:6´ðp0:16Þ2ð3Þ
Details of the Raman spectroscopy experiments. Raman experiments have been
carried out using a triple grating JY-T64000 spectrometer in subtractive mode
300
250
200
150
Temperature (K)
1.9
1.7
1.6
1.4
1.2
1.0
1.8
0.7
100
50
Hole doping p
0
PG
SC
–500
–1000
0.14 0.16 0.18 0.20 0.22
T
c
T
0
T*
0
0


–

0
B
1g
Fig. 3 Phase diagram of critical nematic fluctuations. Color-coded plot
summarizing the evolution of the B1gnematic susceptibility as a function of
doping and temperature in Bi2212. The nematic Curie-Weiss temperature
T0is also shown along with the superconducting Tcand pseudogap T
temperatures. The lines are guide to the eye. The error bars for T0
correspond to the standard error of the Curie-Weiss fits. The inset shows
the Fermi surface deformation associated to the incipient Pomeranchuk
instability which breaks the C4symmetry
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using two 1800 grooves/mm gratings in the pre-monochromator stage and
600 grooves/mm or 1800 groove/mm grating in the spectrograph stage. The
600 grooves/mm grating was used for all measurements except those carried on the
OD80 sample, for which a 1800 grooves/mm grating was used. For several crystals,
both configurations were used at selected temperatures to check for consistency.
The 600 grooves/mm configuration allows us to cover the low-energy part of the
spectrum down to 50 cm−1and up to 900 cm−1in a single frame. With the 1800
grooves/mm grating, measurements could be performed down to 15 cm−1, but
spectra must then be obtained in two frames. The resolution is set at 5 cm−1when
using the 600 grooves/mm configuration. The spectrometer is equipped with a
nitrogen cooled back illuminated CCD detector. We use the 532 nm excitation line
from a diode pump solid state laser. Measurements between 10 and 300 K have
been performed using an ARS closed-cycle He cryostat.
All the raw spectra have been corrected for the Bose factor and the instrumental
spectral response. They are thus proportional to the imaginary part of the Raman
response function χ00ðω;TÞ. A potential concern when correcting the raw spectra
with the Bose factor is the potential presence of non-Raman signal in the raw
spectra. To assess this potential non-Raman signal we note that a single effective
spot temperature was able to reproduce the measured Stokes spectrum from the
anti-Stokes spectrum between 20 and 600 cm1at room temperature. In addition
the raw Raman spectra were found to extrapolate very close to zero at zero Raman
shift at the lowest temperatures measured. Both facts indicates negligible non-
Raman background in the measured spectra.
The direction of incoming and outgoing electric fields are contained in the ðabÞ
plane. The A1gþB2ggeometries are obtained from parallel polarizations at 45
from the Cu–O bond directions; the B2gand B1ggeometries are obtained from
crossed polarizations along and at 45from the Cu–O bond directions,
respectively. The crystal was rotated in-situ using an Attocube piezo-rotator to
align the electric field with respect to the crystallographic axis. A1gspectra are
obtained from the previously listed geometries (see Supplementary Note 1 and
Supplementary Fig. 1).
Data availability
All data generated or analyzed during this study are included in the published
manuscript and the supplementary information files. The relevant raw data file are
available at the following url: https://doi.org/10.6084/m9.figshare.9906275.v1
Received: 25 April 2019; Accepted: 11 October 2019;
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Acknowledgements
We thank T. Shibauchi for fruitful discussions. The work at Brookhaven National
Laboratory was supported by the Office of Science, U.S. Department of Energy under
Contract No. DE-SC0012704.
Author contributions
N.A., B.L., and S.B. performed the Raman scattering experiments with the help of M.C.,
A.S., and Y.G. N.A. performed the data analysis and prepared the figures. R.D.Z., J.S., G.
Gu. grew the single crystals and the annealing procedure to obtain underdoped and
overdoped compositions. A.F. and D.C. performed the high-pressure annealing of the
crystals for the strongly overdoped compositions. I.P. provided theoretical insights. A.S.
and Y.G. supervised the project. Y.G. wrote the paper with inputs from all the authors.
Competing interests
The authors declare no competing interests
Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/s41467-
019-12940-w.
Correspondence and requests for materials should be addressed to Y.G.
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