* Förster-Schreiber et al. (2011) Förster-Schreiber, N. M., Shapley, A. E., Genzel, R., et al. 2011, The Astrophysical Journal, 739, 45
  * Gardner et al. (2023) Gardner, J. P., Mather, J. C., Abbott, R., et al. 2023
  * Geach et al. (2017) Geach, J. E., Dunlop, J. S., Halpern, M., et al. 2017, Monthly Notices of the Royal Astronomical Society, 465, 1789
  * Grogin et al. (2011) Grogin, N. A., Kocevski, D. D., Faber, S. M., et al. 2011, The Astrophysical Journal Supplement Series, 197, 35
  * Guo et al. (2012) Guo, Y., Giavalisco, M., Cassata, P., et al. 2012, The Astrophysical Journal, 749, 149
  * Gómez-Guijarro et al. (2022a) Gómez-Guijarro, C., Elbaz, D., Xiao, M., et al. 2022a, Astronomy & Astrophysics, 658, A43
  * Gómez-Guijarro et al. (2022b) Gómez-Guijarro, C., Elbaz, D., Xiao, M., et al. 2022b, Astronomy & Astrophysics, 659, A196
  * Gómez-Guijarro et al. (2023) Gómez-Guijarro, C., Magnelli, B., Elbaz, D., et al. 2023, Astronomy & Astrophysics, 677, A34, arXiv:2304.08517 [astro-ph]
  * Hainline et al. (2011) Hainline, L. J., Blain, A. W., Smail, I., et al. 2011, The Astrophysical Journal, 740, 96
  * Hodge et al. (2019) Hodge, J. A., Smail, I., Walter, F., et al. 2019, The Astrophysical Journal, 876, 130
  * Hopkins et al. (2023) Hopkins, P. F., Gurvich, A. B., Shen, X., et al. 2023, What Causes The Formation of Disks and End of Bursty Star Formation?
  * Huang et al. (2023) Huang, R., Battisti, A. J., Grasha, K., et al. 2023, Exploring the Intrinsic Scatter of the Star-Forming Galaxy Main Sequence at redshift 0.5 to 3.0
  * Ikarashi et al. (2017) Ikarashi, S., Caputi, K. I., Ohta, K., et al. 2017, The Astrophysical Journal, 849, L36
  * Jiménez-Andrade et al. (2019) Jiménez-Andrade, E. F., Magnelli, B., Karim, A., et al. 2019, Astronomy & Astrophysics, 625, A114
  * Jiménez-Andrade et al. (2021) Jiménez-Andrade, E. F., Murphy, E. J., Heywood, I., et al. 2021, The Astrophysical Journal, 910, 106
  * Jin et al. (2018) Jin, S., Daddi, E., Liu, D., et al. 2018, The Astrophysical Journal, 864, 56
  * Jog & Combes (2009) Jog, C. J. & Combes, F. 2009, Physics Reports, 471, 75
  * Kalita et al. (2022) Kalita, B. S., Daddi, E., Bournaud, F., et al. 2022, Astronomy & Astrophysics, 666, A44
  * Kamieneski et al. (2023) Kamieneski, P. S., Frye, B. L., Pascale, M., et al. 2023, Are {}JWST\/NIRCam color gradients in the lensed \z=2.3\ dusty star-forming galaxy {}El\textasciitildeAnzuelo\ due to central dust attenuation or inside-out galaxy growth?
  * Kannan et al. (2015) Kannan, R., Macciò, A. V., Fontanot, F., et al. 2015, Monthly Notices of the Royal Astronomical Society, 452, 4347
  * Kartaltepe et al. (2023) Kartaltepe, J. S., Rose, C., Vanderhoof, B. N., et al. 2023, The Astrophysical Journal Letters, 946, L15
  * Kodra et al. (2022) Kodra, D., Andrews, B. H., Newman, J. A., et al. 2022, Optimized Photometric Redshifts for the Cosmic Assembly Near-Infrared Deep Extragalactic Legacy Survey (CANDELS)
  * Koekemoer et al. (2011) Koekemoer, A. M., Faber, S. M., Ferguson, H. C., et al. 2011, The Astrophysical Journal Supplement Series, 197, 36
  * Kriek et al. (2015) Kriek, M., Shapley, A. E., Reddy, N. A., et al. 2015, The Astrophysical Journal Supplement Series, 218, 15
  * Lapiner et al. (2023) Lapiner, S., Dekel, A., Freundlich, J., et al. 2023, Monthly Notices of the Royal Astronomical Society, 522, 4515
  * Lindegren et al. (2021) Lindegren, L., Klioner, S. A., Hernández, J., et al. 2021, Astronomy & Astrophysics, 649, A2
  * Liu et al. (2018) Liu, D., Daddi, E., Dickinson, M., et al. 2018, The Astrophysical Journal, 853, 172
  * Lorenz et al. (2023) Lorenz, B., Kriek, M., Shapley, A. E., et al. 2023, An Updated Dust-to-Star Geometry: Dust Attenuation Does Not Depend on Inclination in \1.3\textbackslashleq z\textbackslashleq 2.6\ Star-Forming Galaxies from MOSDEF
  * Lutz et al. (2011) Lutz, D., Poglitsch, A., Altieri, B., et al. 2011, Astronomy & Astrophysics, 532, A90
  * Ma et al. (2016) Ma, X., Hopkins, P. F., Faucher-Giguère, C.-A., et al. 2016, Monthly Notices of the Royal Astronomical Society, 456, 2140
  * Mandelker et al. (2014) Mandelker, N., Dekel, A., Ceverino, D., et al. 2014, Monthly Notices of the Royal Astronomical Society, 443, 3675
  * Matthews et al. (1998) Matthews, L. D., van Driel, W., & Gallagher III, J. S. 1998, The Astronomical Journal, 116, 1169
  * Miller et al. (2022) Miller, T. B., Whitaker, K. E., Nelson, E. J., et al. 2022, Early JWST imaging reveals strong optical and NIR color gradients in galaxies at \z\textbackslashsim2\ driven mostly by dust
  * Momcheva et al. (2016) Momcheva, I. G., Brammer, G. B., van Dokkum, P. G., et al. 2016, The Astrophysical Journal Supplement Series, 225, 27
  * Nandra et al. (2015) Nandra, K., Laird, E. S., Aird, J. A., et al. 2015, The Astrophysical Journal Supplement Series, 220, 10
  * Noeske et al. (2007) Noeske, K. G., Weiner, B. J., Faber, S. M., et al. 2007, The Astrophysical Journal, 660, L43
  * Noguchi (1999) Noguchi, M. 1999, The Astrophysical Journal, 514, 77, arXiv:astro-ph/9806355
  * Oliver et al. (2012) Oliver, S. J., Bock, J., Altieri, B., et al. 2012, Monthly Notices of the Royal Astronomical Society, 424, 1614
  * Press et al. (1992) Press, W., Teukolski, S., Vetterling, W., & Flannery, B. 1992, Numerical Recipes in C. The Art of Scientific Computing, 2nd edn. (Cambridge Univ. Press)
  * Puglisi et al. (2019) Puglisi, A., Daddi, E., Liu, D., et al. 2019, The Astrophysical Journal, 877, L23
  * Puglisi et al. (2021) Puglisi, A., Daddi, E., Valentino, F., et al. 2021, Monthly Notices of the Royal Astronomical Society, 508, 5217
  * Puschnig et al. (2023) Puschnig, J., Hayes, M., Agertz, O., et al. 2023, Unveiling the gravitationally unstable disc of a massive star-forming galaxy using NOEMA and MUSE
  * Rieke et al. (2023) Rieke, M. J., Kelly, D. M., Misselt, K., et al. 2023, Publications of the Astronomical Society of the Pacific, 135, 028001
  * Rodighiero et al. (2011) Rodighiero, G., Daddi, E., Baronchelli, I., et al. 2011, The Astrophysical Journal, 739, L40
  * Rujopakarn et al. (2019) Rujopakarn, W., Daddi, E., Rieke, G. H., et al. 2019, The Astrophysical Journal, 882, 107
  * Rujopakarn et al. (2023) Rujopakarn, W., Williams, C. C., Daddi, E., et al. 2023, JWST and ALMA imaging of dust-obscured, massive substructures in a typical \z \textbackslashsim 3\ star-forming disk galaxy
  * Salpeter (1955) Salpeter, E. E. 1955, The Astrophysical Journal, 121, 161
  * Sancisi et al. (2008) Sancisi, R., Fraternali, F., Oosterloo, T., & van der Hulst, J. M. 2008, The Astronomy and Astrophysics Review, 15, 189
  * Schreiber et al. (2015) Schreiber, C., Pannella, M., Elbaz, D., et al. 2015, Astronomy & Astrophysics, 575, A74
  * Schreiber & Wuyts (2020) Schreiber, N. M. F. & Wuyts, S. 2020, Annual Review of Astronomy and Astrophysics, 58, 661
  * Stefanon et al. (2017) Stefanon, M., Yan, H., Mobasher, B., et al. 2017, The Astrophysical Journal Supplement Series, 229, 32
  * Tacchella et al. (2016) Tacchella, S., Dekel, A., Carollo, C. M., et al. 2016, Monthly Notices of the Royal Astronomical Society, 458, 242
  * Tacconi et al. (2008) Tacconi, L. J., Genzel, R., Smail, I., et al. 2008, The Astrophysical Journal, 680, 246
  * Tadaki et al. (2020) Tadaki, K.-i., Belli, S., Burkert, A., et al. 2020, The Astrophysical Journal, 901, 74
  * Tadaki et al. (2017) Tadaki, K.-i., Kodama, T., Nelson, E. J., et al. 2017, The Astrophysical Journal, 841, L25
  * van der Wel et al. (2014) van der Wel, A., Franx, M., van Dokkum, P. G., et al. 2014, The Astrophysical Journal, 788, 28
  * van der Wel et al. (2023) van der Wel, A., Martorano, M., Haussler, B., et al. 2023, Stellar Half-Mass Radii of \0.5\textlessz\textless2.3\ Galaxies: Comparison with JWST/NIRCam Half-Light Radii
  * Varela-Lavin et al. (2023) Varela-Lavin, S., Gómez, F. A., Tissera, P. B., et al. 2023, Monthly Notices of the Royal Astronomical Society, stad1724
  * Wang et al. (2017) Wang, W., Faber, S. M., Liu, F. S., et al. 2017, Monthly Notices of the Royal Astronomical Society, 469, 4063
  * Whitaker et al. (2011) Whitaker, K. E., Labbé, I., van Dokkum, P. G., et al. 2011, The Astrophysical Journal, 735, 86
  * Wuyts et al. (2012) Wuyts, S., Schreiber, N. M. F., Genzel, R., et al. 2012, The Astrophysical Journal, 753, 114
  * Zaritsky et al. (2013) Zaritsky, D., Salo, H., Laurikainen, E., et al. 2013, The Astrophysical Journal, 772, 135
  * Zavala et al. (2017) Zavala, J. A., Aretxaga, I., Geach, J. E., et al. 2017, Monthly Notices of the Royal Astronomical Society, 464, 3369
  * Zavala et al. (2022) Zavala, J. A., Casey, C. M., Spilker, J., et al. 2022, The Astrophysical Journal, 933, 242
  * Zick et al. (2018) Zick, T. O., Kriek, M., Shapley, A. E., et al. 2018, The Astrophysical Journal, 867, L16


10ptrevtex4-2

# Ultrafast Melting of Superconductivity in an Iron-Based Superconductor

D. Nevola<EMAIL_ADDRESS>Condensed Matter Physics and Materials Science
Department, Brookhaven National Laboratory, Upton, New York 11973, USA  N.
Zaki  Condensed Matter Physics and Materials Science Department, Brookhaven
National Laboratory, Upton, New York 11973, USA  J.M. Tranquada  Condensed
Matter Physics and Materials Science Department, Brookhaven National
Laboratory, Upton, New York 11973, USA  W.-G. Yin  Condensed Matter Physics
and Materials Science Department, Brookhaven National Laboratory, Upton, New
York 11973, USA  G.D. Gu  Condensed Matter Physics and Materials Science
Department, Brookhaven National Laboratory, Upton, New York 11973, USA  Q. Li
Condensed Matter Physics and Materials Science Department, Brookhaven National
Laboratory, Upton, New York 11973, USA  Department of Physics and Astronomy,
Stony Brook University, Stony Brook, New York 11794-3800, USA  P. D. Johnson
<EMAIL_ADDRESS>Condensed Matter Physics and Materials Science Department,
Brookhaven National Laboratory, Upton, New York 11973, USA

###### Abstract

Intense debate has recently arisen regarding the photoinduced changes to the
iron-chalcogenide superconductors, including the enhancement of
superconductivity and a metastable state. Here, by employing high energy
resolution, we directly observe the melting of superconductivity on ultrafast
timescales. We demonstrate a distinctly nonequilibrium response on short
timescales, where the gap fills in prior to the destruction of the
superconducting peak, followed by a metastable response. We propose that the
former is due to pair phase decoherence and speculate that the latter is due
to the increase in double stripe correlations that are known to compete with
superconductivity. Our results add to exciting new developments on the iron-
based superconductors, indicating that the photoinduced metastable state
possibly competes with superconductivity.

##  I Introduction

The superconducting iron chalcogenides have recently generated considerable
attention with the recognition that they bring together superconductivity,
topology and magnetism in a single materialZhang  _et al._ (2018); Rameau  _et
al._ (2019); Zaki  _et al._ (2021). Superconductivity and topology offer the
possibility of topological superconductivity which in turn presents a platform
for hosting Majorana Fermions, potentially important in qubit technologyWang
_et al._ (2018). Magnetism and topology on the other hand offer a platform for
the Quantum Anomalous Hall Effect (QAHE). However, superconductivity and the
QAHE represent competing statesWu  _et al._ (2021), and it is therefore
important that an understanding is obtained of the different phenomena driving
the system one way or the other. The FeSe1-xTex (FST) phase diagram is complex
with the system displaying superconductivity for x = 0 and antiferromagnetism
for x = 1. At around x = 0.5 and higher the possibility of a topological state
existing on the surface has also been predictedXu  _et al._ (2016). The chiral
nature of the latter topological surface state (TSS) has been demonstrated
using spin polarized photoemission in one studyZhang  _et al._ (2018) and
incident circularly polarized light in anotherRameau  _et al._ (2019). It has
also been shown that for x $>$ 0.5 ferromagnetism develops in the surface
region with the superconducting transitionMcLaughlin  _et al._ (2021). The
associated time reversal symmetry breaking (TRSB) results in a gap at the
Dirac point in the TSSZaki  _et al._ (2021).

There have also been a number of studies of this material using time-resolved
pump-probe techniques where the system is pumped out of equilibrium and the
pathway back to equilibrium provides further insights into the complex
interactions that take place between the electrons and collective modesLuo
_et al._ (2012); Bonavolontà  _et al._ (2013); Yang  _et al._ (2015); Gerber
_et al._ (2017); Suzuki  _et al._ (2019); Yang  _et al._ (2021).

Such techniques also have been applied to the cuprate superconductors for
Fermi surface wave vectors ranging from the nodal direction to the anti-nodal
direction. In general, these studies show a return to equilibrium via
different stages. First the non-equilibrium state decays via e-e interactions
on time scales of the order of 100 femtoseconds, establishing a state with a
“pseudo-equilibrium” Fermi-Dirac distributionPerfetti  _et al._ (2007); Cortés
_et al._ (2011); Smallwood  _et al._ (2012); Parham  _et al._ (2017); Piovera
_et al._ (2015); Rameau  _et al._ (2014); Konstantinova  _et al._ (2018);
Rameau  _et al._ (2016). At longer time-scales, of the order of picoseconds,
energy is subsequently transferred to the lattice via electron-phonon
interactions. Studies have also concluded that with IR excitation, the
superconducting gap fills in, rather than closing, due to loss of coherence of
the superconducting condensate near the nodeBoschini  _et al._ (2018); Piovera
_et al._ (2015), while more exotic behavior due to Mott physics may be present
at the antinodeDakovski  _et al._ (2015); Cilento  _et al._ (2018).

Pump-probe studies of the Fe-chalcogenide superconductors show a different
behavior. These systems still show the fast electron-electron equilibration
but then the material appears to enter a metastable phase that exists on the
order of nanoseconds or longerFanfarillo  _et al._ (2021); Yang  _et al._
(2021); Suzuki  _et al._ (2019). The nature of this metastable behavior has
been the topic of considerable discussion. Photoemission studies have
speculated about various behaviors, ranging from light-induced
superconductivitySuzuki  _et al._ (2019) to light-induced nematicityFanfarillo
_et al._ (2021). The concept of light-induced or enhanced superconductivity
appears to follow the pioneering studies on this subject in a number of
materials by Cavalleri and coworkersMankowsky  _et al._ (2014); Mitrano  _et
al._ (2016); Mankowsky  _et al._ (2017); Budden  _et al._ (2021). By the very
nature of the experimental probes, these studies have tended to focus on high
timing resolution. In the present study we take a different approach.
Acknowledging that the light induced state is metastable and therefore long
lived, we reduce the timing resolution and push for high energy resolution in
the probe beam. Such an approach offers immediate and important new insights
into the metastable state. Not only can we now for the first time identify the
coherent peak associated with the bulk superconductivity in a time-resolved
study of this material, but we clearly demonstrate from its transient behavior
that the incident infrared (IR) pulse kills the superconductivity and that it
does not recover in the time scale associated with the metastable phase.

In systems with closely competing quantum states, it is known that an incident
IR pulse can push the system from one state to another. In the FST materials,
it is well established that two different spin or magnetic configurations
exist. The low temperature superconducting phase is characterized by spin
correlations of the single-stripe typeLi  _et al._ (2021). At slightly higher
temperatures above 40 K the material adopts double-stripe spin correlations
that do not support superconductivityTranquada  _et al._ (2020). Equilibrium
studies have suggested that this second phase is closely related to the
electron coupling with the $A_{1g}$ phonon mode, which is the out-of-plane
oscillation of the chalcogen atomsLiu  _et al._ (2013). Interestingly, the
out-of-plane chalcogen position has been theoretically tied to the magnetic
phase, supporting the significant role of the electron-$A_{1g}$ phonon
coupling in determining the magnetic ground stateYin  _et al._ (2010, 2012).
Similarly, out-of-equilibrium studies have shown that the pump-induced,
metastable state is distinctly related to the $A_{1g}$ phonon mode, eventually
leading to a renormalized chalcogen positionGerber  _et al._ (2017); Yang  _et
al._ (2021). This renormalized position shows an increased c-axis lattice
constant, consistent with increasing the value of x on the FeSe1-xTex phase
diagramTranquada  _et al._ (2020). It is then naturally expected that this
metastable state will lead to an associated modification of the
superconducting and magnetic behavior. In the present study we find that
superconductivity is not supported in this metastable phase, and therefore
postulate that it reflects a transition from the superconducting single-stripe
phase to the double-stripe non-superconducting state, driven by photoinduced
orbital fluctuations.

##  II Methods

Single crystals were grown by the unidirectional solidification method. The
superconducting properties of the single crystals studied here were previously
characterized by magnetization measurements, having a superconducting
transition temperature, Tc of 14.5 KZaki  _et al._ (2021).

The time-resolved ARPES was performed at Brookhaven National Laboratory using
a SES-2002 analyzer. The probe pulse was generated using the output of a
Coherent Vitara-T/RegA 9050 setup, which consists of 70 fs long, 800 nm pulses
at 250 kHz. A cascade of nonlinear process was then used to produce the fourth
harmonic (200 nm). The fourth harmonic pulses were finally passed through a
monochromator before entering the vacuum chamber. The 800 nm fundamental
pulses were used to pump the system. The energy and time resolutions were 6.6
meV and 500 fs, respectively. Space charge effects were carefully monitored
before each experiment. The temperature-dependent measurements were acquired
first at 5 K, then by increasing to 15 K, and finally reproduced again at 5 K
on the sample spot, in order to ensure that the effect was reproducible over a
full temperature cycle. The results in this paper have been repeated on
multiple cleaves.

The fits in Fig. 3c consisted of the sum of two exponentially modified
Gaussians (EMG’s), which is the analytical form for an exponential convolved
with a Gaussian. The decay time of the longer one was fixed to be 1 ns in
order to mimic the constant offset, and the width of the Gaussian corresponds
to the time resolution. The fits in Fig. 3d consisted of the sum of an error
function and EMG, where the widths in both correspond to the resolution and
were fixed to be the same.

Figure 1: Band structure of FeSe0.45Te0.55. (a) and (b) schematically show the
band structures near the $\Gamma$ point above and below Tc, respectively, and
are based off of the results in References Zhang  _et al._ (2018); Rameau  _et
al._ (2019); Zaki  _et al._ (2021)

. The bands in blue and red represent bulk and surface contributions. The
green box is representative of the angular window probed by the experiment.
Static ARPES, probed with p-polarized light at 15 K (c) and 5 K (d). Energy
distribution curves centered at $k=0$ (e) and $k=0.03\leavevmode\nobreak\
\r{A}$ (f). The momentum integration windows were $0.03\r{A}^{-1}$ and
$0.02\r{A}^{-1}$ for (e) and (f). Red and blue EDC’s represent those at 15 K
and 5 K, respectively. The data in (e) and (f) has been smoothed for clarity.

##  III Band Structure

We start by reviewing the changes to the band structure near the $\Gamma$
point though the superconducting transition, schematically shown in Fig. 1a,b
(for a more comprehensive understanding of the band structure, the reader is
directed to Refs.Zhang  _et al._ (2018); Zaki  _et al._ (2021); Rameau  _et
al._ (2019), from which the schematics in Figures 1a,b are based). We focus
mainly on the three bands closest to the zone center, which is comprised of
two bulk bands and a topological surface state. Above Tc, the outer-most bulk
band forms a hole pocket that crosses EF near $\pm 0.15\leavevmode\nobreak\
\r{A}^{-1}$Johnson  _et al._ (2015). At the zone center is another hole-like
band that reaches its maximum $\sim\leavevmode\nobreak\ 16\leavevmode\nobreak\
$meV below EFZaki  _et al._ (2021); Zhang  _et al._ (2018); Rameau  _et al._
(2019). These bulk bands are typically referred to as the $\alpha_{2}$ and
$\alpha_{1}$ bands, respectively. The topological surface state emerges from
the top of the $\alpha_{1}$ band to form a small, electron-like pocketZhang
_et al._ (2018); Zaki  _et al._ (2021); Rameau  _et al._ (2019). Recent
efforts have demonstrated that the band inversion leading to the TSS results
from the combination of spin-orbit effects in the Te atoms and hybridization
from the Fe dxz/yz and Te pz orbitalsLohani  _et al._ (2020); Xu  _et al._
(2016). Theoretical efforts to reproduce the ground state band structure
highlight the role of strong electronic correlations that we believe play a
vital role in the metastable behavior observed in time-angle resolved
photoelectron spectroscopy (trARPES), as will be discussed in more detail
later. For example, in one study, density functional theory requires a strong
renormalization to reproduce the experimentally observed energy scalesLohani
_et al._ (2020), while another study directly shows that the inclusion of
magnetic correlations overcomes this discrepancyJohnson  _et al._ (2015).

The system undergoes several changes upon cooling through the superconducting
transition (Fig. 1b). First, superconducting gaps open up in both the bulk and
surface Fermi pockets, with values of $2\Delta\sim$ 4 and 3.6 meV
respectivelyOkazaki  _et al._ (2014); Zhang  _et al._ (2018). Additionally, a
weakly dispersive superconducting peak (SP) develops in the vicinity of
EFLubashevsky  _et al._ (2012); Okazaki  _et al._ (2014); Hashimoto  _et al._
(2020). At the same time, a 5 meV gap opens at the Dirac point in the TSS and
has been used to associate the onset of superconductivity with the formation
of ferromagnetic orderZaki  _et al._ (2021). The polarization-dependent matrix
elements have proved a useful method for enhancing or suppressing these bands.
For example, s-polarized light enhances the $\alpha_{1}$ band and the TSS,
whereas p-polarized light enhances the $\alpha_{2}$ band and the SPRinott  _et
al._ (2017); Zaki  _et al._ (2021). As we will argue later, such a strong
polarization dependence of the SP may reflect its sensitivity to orbital
fluctuations, which can be strongly altered by even a weak photoexcitation.
For the present study, we probe with p-polarized light because we are
interested in the pump-induced changes to superconductivity.

##  IV Results

Next, we demonstrate the high energy resolution of the trARPES experimental
configuration by showing the static ARPES results above and below Tc
respectively (Figs. 1c,d). The low energy scales associated with the bands of
interest emphasize the requirement for such resolution. Above Tc, the
$\alpha_{1}$ band is clearly visible. However, we note that the $\alpha_{2}$
band is outside of our momentum window, which is shown schematically by the
green rectangles in Fig. 1a,b. We also observe the TSS as a weak intensity
plateau extending from the top of the $\alpha_{1}$ band. This is more clearly
seen in the energy distribution curve (EDC) through the $\Gamma$ point in Fig.
1e, where the green arrow indicates the Dirac point. Above the Dirac point at
15 K, the plateau corresponding to the TSS is visible. As alluded to earlier
and discussed elsewhere, below TC two gaps appear in the spectral response,
one at the chemical potential associated with superconductivity and one at the
Dirac point reflecting TRSB. We are unable to clearly resolve the topological
gap because a better momentum resolution is required than available in the
present study. The superconducting gap is seen by observing the shift of the
leading edge midpoints, shown by the black ticks in figure 1e,f, by 2.5
meVZaki  _et al._ (2021). The formation of the superconducting gap results in
the development of a peak just below the Fermi level. Finally, there is a
subtle shift towards higher binding energy of the $\alpha_{1}$ band that
occurs in conjunction with the formation of the gap at the Dirac point (Fig.
1e). All of these changes are also made evident when applying the Lucy-
Richardson deconvolution algorithm Rameau  _et al._ (2010)[see Supplemental].
Having established the ability to resolve the low-energy effects associated
with superconductivity, we now turn to the pump-induced modifications to the
superconducting band structure.

Figure 2: Photoinduced changes to the k-integrated band structure below (a)
and above (b) Tc at an incident pump fluence of 1.2 $\mu$J/cm2. Red and blue
indicate an intensity increase and decrease respectively. (c) Energy
distribution curves at various delay times. (d) Intensity dynamics just above
and below EF out to long delay times. The data was averaged over a 7 meV
energy range. For clarity, the data below EF was offset and normalized to
match the change above EF.

Figure 2a shows the k-integrated changes to the band structure below Tc upon
pumping with an infrared laser pulse. Two features are observed that are
absent when pumped above Tc (Fig.2b): 1) an intensity increase just above EF
and 2) a sharp intensity drop just below EF. As these changes are not observed
above the superconducting transition, they must be associated with
superconductivity. Examination of the momentum-integrated EDC’s in Fig. 2c
shows that these intensity changes correspond to the filling of the
superconducting gap, and destruction of the SP, respectively. These changes
are consistent with the static results in Fig. 1 and indicate that
superconductivity is melted on ultrafast timescales. Identifying the
mechanisms responsible for this phenomenon, as well as its recovery, is a
novel pathway towards understanding iron-based superconductivity. We now turn
to the time dependence for further insight into these processes.

Figure 2d shows that after the initial melting of superconductivity, the
changes persist up to $>\leavevmode\nobreak\ 100$ ps without showing any clear
sign of recovery. However, we note that slight deviations from a constant
offset after the first few picoseconds can be attributed to noise, slight
drift of the pump beam, or acoustic oscillations that have been observed to
occur on these timescalesLuo  _et al._ (2012). This is also seen when
comparing the k-integrated EDC’s at 9 ps to that at 100 ps in Fig. 2c. Indeed,
similar long time behavior has been observed in other optical experiments that
have used similar pump fluences to the ones used in this workLuo  _et al._
(2012). This lack of decay on $\sim$100 ps timescales is intriguing when
considering the metastable behavior that has attracted recent
interestFanfarillo  _et al._ (2021); Yang  _et al._ (2021); Suzuki  _et al._
(2019). Importantly, the main difference between those studies and the present
one is the pump fluence used (much lower in the present case). Furthermore,
the linear fluence dependence of the metastable changes with no threshold
establishes this long-lived behavior as a derivative of the ground state,
meaning that its existence owes to the interactions present in the ground
stateGerber  _et al._ (2017). Thus, the decay bottleneck that is ultimately
responsible for the metastable behavior must still be present at the low
fluences used in this work. We believe that the reduction of superconductivity
is a property of the pump-induced electronic redistribution, and the long-
lived behavior results from the same mechanism as the well-reported
metastability in FST when pumped at higher fluenceGerber  _et al._ (2017);
Fanfarillo  _et al._ (2021); Suzuki  _et al._ (2019); Yang  _et al._ (2021).
However, it is also expected that pumping a superconductor at T $<$ Tc
naturally leads to the melting of superconductivity on picosecond timescales
due to equilibrium heating from the incident laser pulse. The dynamics that we
observe at shorter delays do not show the expected picosecond recovery
typically associated with lattice heating and must therefore correspond to
time-dependent changes to the spectral function, $A(k,\omega,t)$.

Figure 3: Fluence-dependent dynamics at short delay times. (a) EDC’s before
(blue) and after (red) the pump pulse at 4 $\mu$J/cm2. (b) Same as (a), but
with a pump fluence of 2 $\mu$J/cm2. The dashed black line is the red curve in
(a) for comparison. Dynamics of the momentum integrated, difference images
just above (c) and below (d) EF that correspond to the superconducting gap and
quasiparticle peak, respectively. Solid lines correspond to fits.

We consider the results for two different fluences. Figure 3 shows the
dynamics at shorter delays for two different pump fluences. At the higher
fluence of 4 $\mu$J/cm2, the superconducting peak is destroyed, as shown by
the difference between the EDC’s at negative and positive delay times recorded
away from the zone center (Fig, 3a). However, most of the reduction is
achieved with the lower fluence of 2 $\mu$J/cm2 (Fig. 3c), which is made clear
when comparing the off $\Gamma$ EDC at +5 ps (red curve) to the same EDC at 4
$\mu$J/cm2 (dashed black curve). Comparing the amplitudes at +5 ps for the two
fluences allows us to estimate the complete disappearance of the SP at a
critical fluence of 3 $\mu$J/cm2 (assuming a linear dependence on fluence).

Figures 3c,d, show the intensity dynamics at the indicated fluences above and
below EF, respectively. Careful analysis of the dynamical data reveals rapid
changes equal to the resolution, followed by fluence-dependent picosecond
dynamics. The initial change in signal is attributed to a combination of the
direct transitions associated with the pump, and subsequent electron-electron
interactions that are expected to be reasonably strong in the iron-based
superconductors. Although we are only able to determine an upper bound to this
timescale to be 500 fs due to our resolution, reflectivity studies have shown
that these initial changes occur within 100 fsBonavolontà  _et al._ (2013);
Luo  _et al._ (2012). At the higher fluence, the positive signal (orange
markers in Fig. 3c) shows a partial recovery on a timescale of 3 $\pm$ 1.5 ps,
while the negative signal (orange markers in Fig. 3d) shows an initial change
equal to the resolution followed by no observable recovery. We interpret the 3
ps timescale as the dissipation of heat into the lattice. However, that this
same timescale is not observed in the lower fluence means that this energy
dissipation corresponds to excess heat after superconducting order has been
melted. Similarly, temperature dependent reflectivity studies on FST show a
similar picosecond timescale that disappears near TcLuo  _et al._ (2012);
Bonavolontà  _et al._ (2013).

Figure 4: (a)Time dependent energy profiles through the data in figure 2a at
delay times of 0.5 ps, 9 ps and 100 ps. The pump fluence used was 1.2
$\mu$J/cm2. (b) Modeled difference curves as described in the text. The red
curve includes only a finite $\Gamma_{p}$ and the green curve includes both a
finite $\Gamma_{p}$ and decreased spectral function amplitude, as further
described in the supplementary information.

The dynamics of the SP (Figure 3d) tell a slightly different story. Both
fluences probed show no observed recovery on picosecond timescales. With the
higher fluence, it would be expected that we would not observe the
reappearance of the SP if there is excess energy after melting
superconductivity. This can also be understood in the context of the two-
temperature model with a final lattice temperature greater than TcAllen
(1987). If the melting of superconductivity was thermal, we would observe a
recovery of the SP on a $\sim 3$ ps timescale, similar to that above.
Furthermore, it would be obvious since the SP is the brightest feature in the
difference spectrum in figure 2a, and is particularly sensitive to the
temperature in equilibrium. Bonavolanta et al. also determined the temperature
to only increase by a maximum of 3 K when using a fluence several times those
used in this work, making a thermal heating explanation unlikelyBonavolontà
_et al._ (2013). Closer examination of the lower fluence data reveals an
initial decrease equal to the resolution followed by a further decrease on a
timescale of 0.8 $\pm$ 0.5 ps. This second timescale suggests that another
scattering mechanism is involved in the melting of superconductivity as will
be discussed in the next section. Additionally, since we remain below Tc and
observe no recovery of the condensate within the 100 ps measurement window, we
conclude that the melting of superconductivity is metastable.

To further emphasize the behavior at short delays, we display the difference
EDCs (figure 4a), which are energy profiles through the data in figure 2a. For
the intensity loss, we see an evolution in going from the shortest delay at
0.5 ps to 9 ps. However, for the intensity gain, we do not see the same
evolution. After the maximum intensity change is reached within the first 0.5
ps, it remains constant to within the noise. This means that at short delays,
the filling of the gap occurs first on timescales of $<\leavevmode\nobreak\
500$ fs.

##  V Discussion

The most obvious implication of the results in this work is to demonstrate
that superconductivity is melted on ultrafast timescales and does not return
within the measured time window. This direct demonstration contradicts the
conclusions in two recent works that have suggested enhanced superconductivity
due to photoexcitationIsoyama  _et al._ (2021); Suzuki  _et al._ (2019). One
is an all-optical study that suggests a temporary, picosecond,
enhancementIsoyama  _et al._ (2021), and another is a trARPES study with lower
energy resolution that associates superconductivity with the metastable
stateSuzuki  _et al._ (2019). Interestingly, the former study does clearly
demonstrate nonequilibrium behavior at short delays.

Isoyama et al. found an increase in both the real and imaginary parts to the
conductivity within the first 1-2 ps, contradicting equilibrium measurements
that showed an increase and decrease in the real and imaginary parts to the
optical conductivity, respectively, with increasing temperatureIsoyama  _et
al._ (2021). Additionally, these changes occur on an energy scale $<2$ meV,
less than the superconducting gap, $2\Delta$, and the same magnitude of the
observed leading edge midpoint shift(see Supplemental). One possible
interpretation is an increase in the size of the condensate, as they
suggested, but this would manifest as an increased spectral weight within the
superconducting peaks on either side of the Fermi level, which we do not
observe. Alternatively, we propose the destruction of phase coherence among
the Cooper pairs caused by their scattering with nonequilibrium bosonic
excitationsBoschini  _et al._ (2018). This mechanism may explain both the
increases to the realXi  _et al._ (2010) and imaginaryLemonik and Mitra (2018)
parts of the optical conductivity. It can be modeled by the inclusion of a
finite pair scattering rate in the self energy that describes a
superconductorKwon and Dorsey (1999); Franz and Millis (1998); Boschini  _et
al._ (2018):

$\Sigma(\omega)=-i\Gamma_{s}+\frac{\Delta^{2}}{\omega+i\Gamma_{p}}.$ (1)

Here, $\omega$ is the energy, $\Delta$ is the gap amplitude, $\Gamma_{s}$ is
the single particle scattering rate, and $\Gamma_{p}$ is the pair scattering
rate, indicative of pair scattering with phase fluctuationsBoschini  _et al._
(2018). An increase in $\Gamma_{p}$ increases the spectral weight inside the
gap, and was recently found to describe the nonequilibrium changes to the
near-nodal spectral function in an optimally doped cuprateBoschini  _et al._
(2018).

To provide a more quantitative picture, we modeled the difference curves by
using the self-energy in equation 1 (see Supplemental for more details).
First, we show the experimental data at three delay times in figure 4a (the
data correspond to energy profiles at the specified delay times selected from
the data in figure 2a). The amplitudes of the positive and negative signals
are nearly identical in the 0.5 ps (resolution limited) data, while the
negative signal grows on a picosecond timescale, and remains constant for $>$
100 ps. As shown in figure 4b, including a finite $\Gamma_{p}$, while keeping
all other parameters constant, is enough to reproduce the experimental data at
0.5 ps. The data at longer delays was reproduced by reducing the amplitude of
the spectral function, which we think resembles the breaking of Cooper pairs.
That we are able to reproduce the curve shape at 0.5 ps by including the pair
scattering rate, which is a nonequilibrium parameter, supports our hypothesis
that the pump induces phase fluctuations caused by electronic correlations.

The photoinduced changes that we observed contain three timescales that offer
further insight into the microscopic mechanisms responsible for the ultrafast
melting of superconductivity. First, the gap filling occurs within our
resolution. This suggests that the phase fluctuations are of electronic
origin. The fluctuations may be caused by the scattering of Cooper pairs with
nonequilibrium bosonsBoschini  _et al._ (2018). We speculate that these bosons
are of the form of magnetic excitations. Second, the persistent decrease in
the SP occurs on a picosecond timescale, We attribute this to the breaking of
pairs by optical phonons that are generated upon the decay of high energy
quasiparticles. A similar, temperature dependent, timescale was observed in
time-resolved reflectivityBonavolontà  _et al._ (2013) and was also ascribed
to phonons. The final timescale is the recovery of the superconducting
features, which are longer than our temporal window, indicating that the
changes mentioned above are metastable. The key question is why they are
metastable, for which we offer two possible explanations that are based off of
our observed timescales.

It is reasonable to assume that the mechanisms responsible for melting
superconductivity also play a role in its recovery. As mentioned above, we
observe electronic and phononic timescales that contribute to the melting of
superconductivity.

The first explanation is that pairs are reformed by the absorption of low
energy (acoustic) phonons, which can occur on nanosecond timescales. Indeed,
this was used to explain the recovery of superconductivity after
photoexcitation in the BCS superconductor MgB2, which has similar gap sizes to
the present materialDemsar  _et al._ (2003). However, two main issues with
this explanation are that (1) even in the case of MgB2, some recombination is
observed on a 100 ps timescale, and (2) it neglects the role of electronic and
magnetic correlations that are known to play a key role in mediating iron-
based superconductivityTranquada  _et al._ (2020).

The second possibility is that the pairs are prevented from recombining
because of the disruption to the correlations caused by the electronic
redistribution. For example, direct excitations can occur at different
locations throughout the Brillouin zone. The natural pathways for relaxation
may cause most holes to relax to the $\Gamma$ point, and most electrons to the
M point in the Brillouin zone. This redistribution of particles modifies the
correlations that are key to mediating iron-based superconductivity. Though it
is difficult to narrow down the specific correlations that would be impacted,
examining the changes that occur at higher excitation densities, where the
changes are more apparent, may offer further insight. Thus, we turn to recent
works that have identified a photoinduced metastable state in FST for clues.
Properties of this metastable state include the renormalizations of the band
structure and chalcogen positions that resemble the ground state effects of
increasing the Te concentrationGerber  _et al._ (2017); Fanfarillo  _et al._
(2021); Yang  _et al._ (2021). We therefore hypothesize that the photoinduced
changes to the correlations are similar to those in higher Te concentrations.

At higher Te concentrations, the correlations favor double stripe magnetism.
Additionally, these magnetic correlations are known to compete with
superconductivityTranquada  _et al._ (2020). We therefore hypothesize that the
photoexcitation causes an orbital redistribution that favors double stripe
magnetic correlations, which act to melt superconductivity. Indeed, the
sensitivity of superconductivity to the orbital redistribution is supported by
electron diffraction work on Ba(Fe1-xCox)2As2 that directly images the orbital
configurationMa  _et al._ (2014), as well as the strong polarization-dependent
matrix elements of the SP observed in ARPESRameau  _et al._ (2019); Zaki  _et
al._ (2021) and scanning tunneling microscopySingh  _et al._ (2015) because
they demonstrate the strong orbital dependence of the superconducting bands.
Additionally, theoretical studies have demonstrated how the subtle balance
among the band filling, the nearest and next-nearest superexchange
interactions, and the Hund’s coupling strength, which may be particularly
sensitive to a pump-induced orbital redistribution, determine the magnetic
ground stateYin  _et al._ (2010, 2012).

##  VI Conclusion

In conclusion, we directly show, for the first time, the pump-induced changes
to the electronic band structure of FST below Tc. Our observations show a
reduction of two features that are directly associated with superconductivity,
namely the superconducting peak and gap. We observe changes both on electronic
and picosecond timescales, and find that they are metastable, lasting for $>$
100 ps. Close examination of the initial changes to the band structure are
indicative of nonequilibrium behavior that shows the filling of the
superconducting gap occurring before the reduction of the SP. We hypothesize
that the orbital fluctuations directly induced by the pump-induced electronic
redistribution are linked to double stripe magnetic correlations known to
compete with superconductivity. A better theoretical understanding of the
precise electronic excitations and relaxation pathways would be crucial in
understanding the changes to the orbital occupancy that results from the pump.
Furthermore, experiments aimed at directly imaging the photoinduced orbital
and magnetic changes, as well as trARPES with high energy resolution extending
out to the edge of the Brillouin zone, would be needed in order to corroborate
this picture, and may ultimately yield clues to understanding the interactions
that lead to iron-based superconductivity.

##  VII Acknowledgements

We acknowledge Chris Homes, Mengkun Liu, and Abhay Narayan Pasupathy for
insightful discussions. Work at Brookhaven National Laboratory was supported
by the U.S. Department of Energy, Office of Science, Office of Basic Energy
Sciences, under Contract No. DE- SC0012704.

## References

  * Zhang  _et al._ (2018) P. Zhang, K. Yaji, T. Hashimoto, Y. Ota, T. Kondo, K. Okazaki, Z. Wang, J. Wen, G. D. Gu, H. Ding, and S. Shin, Science 360, 182 (2018), https://www.science.org/doi/pdf/10.1126/science.aan4596 .
  * Rameau  _et al._ (2019) J. D. Rameau, N. Zaki, G. D. Gu, P. D. Johnson, and M. Weinert, Phys. Rev. B 99, 205117 (2019).
  * Zaki  _et al._ (2021) N. Zaki, G. Gu, A. Tsvelik, C. Wu, and P. D. Johnson, Proceedings of the National Academy of Sciences 118 (2021), 10.1073/pnas.2007241118, https://www.pnas.org/content/118/3/e2007241118.full.pdf .
  * Wang  _et al._ (2018) D. Wang, L. Kong, P. Fan, H. Chen, S. Zhu, W. Liu, L. Cao, Y. Sun, S. Du, J. Schneeloch, R. Zhong, G. Gu, L. Fu, H. Ding, and H.-J. Gao, Science 362, 333 (2018), https://www.science.org/doi/pdf/10.1126/science.aao1797 .
  * Wu  _et al._ (2021) X. Wu, S. B. Chung, C. Liu, and E.-A. Kim, Phys. Rev. Research 3, 013066 (2021).
  * Xu  _et al._ (2016) G. Xu, B. Lian, P. Tang, X.-L. Qi, and S.-C. Zhang, Physical review letters 117, 047001 (2016).
  * McLaughlin  _et al._ (2021) N. J. McLaughlin, H. Wang, M. Huang, E. Lee-Wong, L. Hu, H. Lu, G. Q. Yan, G. Gu, C. Wu, Y.-Z. You, and C. R. Du, Nano Letters 21, 7277 (2021), pMID: 34415171, https://doi.org/10.1021/acs.nanolett.1c02424 .
  * Luo  _et al._ (2012) C. W. Luo, I. H. Wu, P. C. Cheng, J.-Y. Lin, K. H. Wu, T. M. Uen, J. Y. Juang, T. Kobayashi, D. A. Chareev, O. S. Volkova, and A. N. Vasiliev, Physical Review Letters 108, 257006 (2012).
  * Bonavolontà  _et al._ (2013) C. Bonavolontà, L. Parlato, G. P. Pepe, C. de Lisio, M. Valentino, E. Bellingeri, I. Pallecchi, M. Putti, and C. Ferdeghini, Superconductor Science and Technology 26, 075018 (2013).
  * Yang  _et al._ (2015) S. Yang, J. A. Sobota, D. Leuenberger, A. F. Kemper, J. J. Lee, F. T. Schmitt, W. Li, R. G. Moore, P. S. Kirchmann, and Z.-X. Shen, Nano letters 15, 4150 (2015).
  * Gerber  _et al._ (2017) S. Gerber, S.-L. Yang, D. Zhu, H. Soifer, J. A. Sobota, S. Rebec, J. J. Lee, T. Jia, B. Moritz, C. Jia, A. Gauthier, Y. Li, D. Leuenberger, Y. Zhang, L. Chaix, W. Li, H. Jang, J.-S. Lee, M. Yi, G. L. Dakovski, S. Song, J. M. Glownia, S. Nelson, K. W. Kim, Y.-D. Chuang, Z. Hussain, R. G. Moore, T. P. Devereaux, W.-S. Lee, P. S. Kirchmann, and Z.-X. Shen, Science 357, 71 (2017).
  * Suzuki  _et al._ (2019) T. Suzuki, T. Someya, T. Hashimoto, S. Michimae, M. Watanabe, M. Fujisawa, T. Kanai, N. Ishii, J. Itatani, S. Kasahara, Y. Matsuda, T. Shibauchi, K. Okazaki, and S. Shin, Communications Physics 2, 115 (2019).
  * Yang  _et al._ (2021) L. X. Yang, G. Rohde, Y. J. Chen, W. J. Shi, Z. K. Liu, F. Chen, Y. L. Chen, K. Rossnagel, and M. Bauer, Journal of Electron Spectroscopy and Related Phenomena 250, 147085 (2021).
  * Perfetti  _et al._ (2007) L. Perfetti, P. A. Loukakos, M. Lisowski, U. Bovensiepen, H. Eisaki, and M. Wolf, Phys. Rev. Lett. 99, 197001 (2007).
  * Cortés  _et al._ (2011) R. Cortés, L. Rettig, Y. Yoshida, H. Eisaki, M. Wolf, and U. Bovensiepen, Physical Review Letters 107, 097002 (2011).
  * Smallwood  _et al._ (2012) C. L. Smallwood, J. P. Hinton, C. Jozwiak, W. Zhang, J. D. Koralek, H. Eisaki, D.-H. Lee, J. Orenstein, and A. Lanzara, Science 336, 1137 (2012).
  * Parham  _et al._ (2017) S. Parham, H. Li, T. J. Nummy, J. A. Waugh, X. Q. Zhou, J. Griffith, J. Schneeloch, R. D. Zhong, G. D. Gu, and D. S. Dessau, Phys. Rev. X 7, 041013 (2017).
  * Piovera  _et al._ (2015) C. Piovera, Z. Zhang, M. d’Astuto, A. Taleb-Ibrahimi, E. Papalazarou, M. Marsi, Z. Li, H. Raffy, and L. Perfetti, Physical Review B 91, 224509 (2015).
  * Rameau  _et al._ (2014) J. Rameau, S. Freutel, L. Rettig, I. Avigo, M. Ligges, Y. Yoshida, H. Eisaki, J. Schneeloch, R. Zhong, Z. Xu, _et al._ , Physical Review B 89, 115115 (2014).
  * Konstantinova  _et al._ (2018) T. Konstantinova, J. D. Rameau, A. H. Reid, O. Abdurazakov, L. Wu, R. Li, X. Shen, G. Gu, Y. Huang, L. Rettig, _et al._ , Science advances 4, eaap7427 (2018).
  * Rameau  _et al._ (2016) J. Rameau, S. Freutel, A. Kemper, M. A. Sentef, J. Freericks, I. Avigo, M. Ligges, L. Rettig, Y. Yoshida, H. Eisaki, J. Schneeloch, R. Zhong, Z. Xu, G. Gu, P. Johnson, and U. Bovensiepen, Nature communications 7, 1 (2016).
  * Boschini  _et al._ (2018) F. Boschini, E. H. da Silva Neto, E. Razzoli, M. Zonno, S. Peli, R. P. Day, M. Michiardi, M. Schneider, B. Zwartsenberg, P. Nigge, R. D. Zhong, J. Schneeloch, G. D. Gu, S. Zhdanovich, A. K. Mills, G. Levy, D. J. Jones, C. Giannetti, and A. Damascelli, Nature Materials 17, 416 (2018).
  * Dakovski  _et al._ (2015) G. L. Dakovski, T. Durakiewicz, J.-X. Zhu, P. S. Riseborough, G. Gu, S. M. Gilbertson, A. Taylor, and G. Rodriguez, Structural Dynamics 2, 054501 (2015).
  * Cilento  _et al._ (2018) F. Cilento, G. Manzoni, A. Sterzi, S. Peli, A. Ronchi, A. Crepaldi, F. Boschini, C. Cacho, R. Chapman, E. Springate, H. Eisaki, M. Greven, M. Berciu, A. F. Kemper, A. Damascelli, M. Capone, C. Giannetti, and F. Parmigiani, Science Advances 4, eaar1998 (2018), https://www.science.org/doi/pdf/10.1126/sciadv.aar1998 .
  * Fanfarillo  _et al._ (2021) L. Fanfarillo, D. Kopić, A. Sterzi, G. Manzoni, A. Crepaldi, D. T. Payne, W. Bronsch, V. Tsurkan, D. Croitori, J. Deisenhofer, F. Parmigiani, M. Capone, and F. Cilento, Journal of Electron Spectroscopy and Related Phenomena 250, 147090 (2021).
  * Mankowsky  _et al._ (2014) R. Mankowsky, A. Subedi, M. Först, S. O. Mariager, M. Chollet, H. Lemke, J. S. Robinson, J. M. Glownia, M. P. Minitti, A. Frano, _et al._ , Nature 516, 71 (2014).
  * Mitrano  _et al._ (2016) M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Riccò, S. R. Clark, _et al._ , Nature 530, 461 (2016).
  * Mankowsky  _et al._ (2017) R. Mankowsky, M. Fechner, M. Först, A. von Hoegen, J. Porras, T. Loew, G. Dakovski, M. Seaberg, S. Möller, G. Coslovich, _et al._ , Structural Dynamics 4, 044007 (2017).
  * Budden  _et al._ (2021) M. Budden, T. Gebert, M. Buzzi, G. Jotzu, E. Wang, T. Matsuyama, G. Meier, Y. Laplace, D. Pontiroli, M. Riccò, _et al._ , Nature Physics 17, 611 (2021).
  * Li  _et al._ (2021) Y. Li, N. Zaki, V. O. Garlea, A. T. Savici, D. Fobes, Z. Xu, F. Camino, C. Petrovic, G. Gu, P. D. Johnson, J. M. Tranquada, and I. A. Zaliznyak, Nature Materials 20, 1221 (2021).
  * Tranquada  _et al._ (2020) J. M. Tranquada, G. Xu, and I. A. Zaliznyak, Journal of Physics: Condensed Matter 32, 374003 (2020).
  * Liu  _et al._ (2013) Z. K. Liu, R.-H. He, D. H. Lu, M. Yi, Y. L. Chen, M. Hashimoto, R. G. Moore, S.-K. Mo, E. A. Nowadnick, J. Hu, T. J. Liu, Z. Q. Mao, T. P. Devereaux, Z. Hussain, and Z.-X. Shen, Phys. Rev. Lett. 110, 037003 (2013).
  * Yin  _et al._ (2010) W.-G. Yin, C.-C. Lee, and W. Ku, Physical review letters 105, 107004 (2010).
  * Yin  _et al._ (2012) W.-G. Yin, C.-C. Lee, and W. Ku, Superconductor Science and Technology 25, 084007 (2012).
  * Johnson  _et al._ (2015) P. D. Johnson, H.-B. Yang, J. D. Rameau, G. D. Gu, Z.-H. Pan, T. Valla, M. Weinert, and A. V. Fedorov, Phys. Rev. Lett. 114, 167001 (2015).
  * Lohani  _et al._ (2020) H. Lohani, T. Hazra, A. Ribak, Y. Nitzav, H. Fu, B. Yan, M. Randeria, and A. Kanigel, Physical Review B 101, 245146 (2020).
  * Okazaki  _et al._ (2014) K. Okazaki, Y. Ito, Y. Ota, Y. Kotani, T. Shimojima, T. Kiss, S. Watanabe, C.-T. Chen, S. Niitaka, T. Hanaguri, H. Takagi, A. Chainani, and S. Shin, Scientific Reports 4, 4109 (2014).
  * Lubashevsky  _et al._ (2012) Y. Lubashevsky, E. Lahoud, K. Chashka, D. Podolsky, and A. Kanigel, Nature Physics 8, 309 (2012).
  * Hashimoto  _et al._ (2020) T. Hashimoto, Y. Ota, A. Tsuzuki, T. Nagashima, A. Fukushima, S. Kasahara, Y. Matsuda, K. Matsuura, Y. Mizukami, T. Shibauchi, S. Shin, and K. Okazaki, Science Advances 6, eabb9052 (2020).
  * Rinott  _et al._ (2017) S. Rinott, K. B. Chashka, A. Ribak, E. D. L. Rienks, A. Taleb-Ibrahimi, P. L. Fevre, F. Bertran, M. Randeria, and A. Kanigel, Science Advances 3, e1602372 (2017).
  * Rameau  _et al._ (2010) J. Rameau, H.-B. Yang, and P. Johnson, Journal of Electron Spectroscopy and Related Phenomena 181, 35 (2010), proceedings of International Workshop on Strong Correlations and Angle-Resolved Photoemission Spectroscopy 2009\.
  * Allen (1987) P. B. Allen, Phys. Rev. Lett. 59, 1460 (1987).
  * Isoyama  _et al._ (2021) K. Isoyama, N. Yoshikawa, K. Katsumi, J. Wong, N. Shikama, Y. Sakishita, F. Nabeshima, A. Maeda, and R. Shimano, Communications Physics 4, 1 (2021).
  * Xi  _et al._ (2010) X. Xi, J. Hwang, C. Martin, D. Tanner, and G. Carr, Physical review letters 105, 257006 (2010).
  * Lemonik and Mitra (2018) Y. Lemonik and A. Mitra, Physical Review B 98, 214514 (2018).
  * Kwon and Dorsey (1999) H.-J. Kwon and A. T. Dorsey, Physical Review B 59, 6438 (1999).
  * Franz and Millis (1998) M. Franz and A. Millis, Physical Review B 58, 14572 (1998).
  * Demsar  _et al._ (2003) J. Demsar, R. Averitt, A. Taylor, V. Kabanov, W. Kang, H. Kim, E. Choi, and S. Lee, Physical review letters 91, 267002 (2003).
  * Ma  _et al._ (2014) C. Ma, L. Wu, W.-G. Yin, H. Yang, H. Shi, Z. Wang, J. Li, C. Homes, and Y. Zhu, Physical review letters 112, 077001 (2014).
  * Singh  _et al._ (2015) U. R. Singh, S. C. White, S. Schmaus, V. Tsurkan, A. Loidl, J. Deisenhofer, and P. Wahl, Science Advances 1, e1500206 (2015).