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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Evidence for an odd-parity nematic phase above the charge-density-wave transition in a kagome metal

The search for quantum states arising from the interplay between correlation, frustration and topology is a central topic for condensed-matter physics. Recently discovered non-magnetic kagome metals AV 3 Sb 5 (A = K, Cs or Rb) with charge-density-wave and superconducting instabilities may host such exotic states. Here we report evidence that an odd-parity electronic nematic state emerges at a higher temperature than the charge density wave in CsV 3 Sb 5 . Our torque measurements reveal a two-fold in-plane magnetic anisotropy that breaks the crystal rotational symmetry. Moreover, in the temperature range between the formation of the charge density wave and a nematic state, rotating an external magnetic field in a conical fashion yields a distinct first-order phase transition, indicating time-reversal symmetry breaking. These results provide thermodynamic evidence for the emergence of an odd-parity nematic order. In addition, elastoresistance shows no discernible anomalies near the onset of nematicity, consistent with the odd-parity order. In conclusion, these findings suggest that an exotic loop current state precedes the charge-density-wave transition in CsV 3 Sb 5 .

36 MATERIALS SCIENCE↗
DOE OSTI2022

Forest Canopy Density Effects on Snowpack Across the Climate Gradients of the Western United States Mountain Ranges

Limitations inherent to field studies such as limited spatial and temporal coverage has made it very challenging, if not impossible, to explicitly disentangle the effect of canopy density from climate on snowpack dynamics. Hence, our understanding of how variations in canopy density can affect snow processes under diverse climate conditions has been limited. To address this knowledge gap, this study uses a physics-based modeling approach to represent most key processes that drive snow accumulation and melt in the open and forest with varied forest density, across the climate gradients of the Western U.S. mountain ranges, as represented by 228 Snow Telemetry (SNOTEL) locations. Simulations suggest that, under most winter climate conditions, canopy density exerts a strong influence on under-canopy snowpack dynamics and their controlling processes. Changing canopy density can shift the direction of the modeled differential peak snow accumulation and snow disappearance date (SDD) between the open and forest. For example, while simulated snowpack lasts longer in the open than the high-density forest at most wet/warm and dry/cold locations by up to 55 days, about 90% of all locations show a longer snow duration in the low-density forest by up to 27 days as compared to the open. Interannual variability in climate can also change the magnitude and direction of canopy impact on snow processes. By comparing model simulations to published field observations, and we also identify conditions that require additional field observations to improve process-scale understanding of forest-snow interaction.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Anderson acceleration stability in NDA-accelerated k-eigenvalue problems

Anderson acceleration (AA) has been used to improve the stability and convergence rate of multiphysics iterative methods for reactor analysis. Most applications studied assume a tightly converged solution for the different physics problems, and AA is usually applied to state variables like temperature, density, and heat generation rate. In this paper, we study the theoretical performance of AA in NDA-accelerated k-eigenvalue problems. The problems and algorithms studied are simplified from the coupled iteration scheme adopted by MPACT and many other high-fidelity whole-core reactor codes. Compared to previous analyses of AA for these iteration schemes, we study the case with a partially converged neutronics solution and possibly partially converged nonlinear diffusion acceleration (NDA)/coarse mesh finite difference (CMFD) solutions. We observe that the performance of the iteration scheme with AA is very sensitive to the initial guess and is affected by the partially converged CMFD solutions. When the NDA solution is fully converged, using AA cannot achieve the optimal convergence rate in large-sized problems. Conversely, if the NDA solution is partially converged, the iteration scheme with AA can diverge or converge extremely slowly. It is found that the loss of robustness for AA is due to the fact that it is applied to the iterative subspace of state variables rather than the fundamental unknowns of the governing equations. To improve the robustness, the scalar flux should also be considered in the implementation of AA. After considering the residuals of flux, we observe that the stability is regardless of the partial convergence of NDA solutions. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Phonon spectrum in the spin-Peierls phase of CuGeO 3

CuGeO 3 has long been studied as a prototypical example of the spin-Peierls transition in a 𝑆 = 1/2 Heisenberg chain. Despite intensive investigation of this quasi-one-dimensional material, systematic measurements and calculations of the phonon excitations in the dimerized phase have not to date been possible, leaving certain aspects of the spin-Peierls phenomenon unresolved. We perform state-of-the-art density functional theory (DFT) calculations to compute the electronic structure and phonon dynamics in the low-temperature dimerized phase. We also perform high-resolution neutron spectroscopy to measure the full phonon spectrum over multiple Brillouin zones. We find excellent agreement between our numerical and experimental results that extend to all measurement temperatures. Notable features of our phonon spectra include a number of steeply dispersive modes, nonmonotonic dispersion features, and specific phonon anticrossings, which we relate to the mode eigenvectors. By calculating the magnetic interactions within DFT and studying the effects of different phonon modes on the superexchange paths, we discuss the possibility of observing spin-phonon hybridization effects in experiments performed both in and out of equilibrium.

density functional theory↗
DOE OSTI2025

Ligand-Driven Electrochemical Tuning of Co 6 Se 8 Chevrel Clusters

Molecular “Chevrel-type” clusters of the formula Co 6 Se 8 L 6 (L = neutral ligand) are a well-studied class of clusters due to their utility as molecular analogues to the Chevrel extended solid phase and their application as subunits in hierarchical materials. However, their solution and optical properties remain relatively underexplored. Aiming to develop the fundamental relationships between the molecular and electronic structures of these clusters and their electrochemical and photophysical properties, this work reports the preparation of a series of Co 6 Se 8 (P­(C 6 H 4 R) 3 ) 6 -type clusters with R = Cl (1), F (2), H (3), CH 3 (4), and OCH 3 (5) via a stepwise synthetic approach. Solution and solid-state experimental characterization and density functional theory calculations reveal that the Co 6 Se 8 cores of 1–5 maintain consistent electronic and structural properties despite the variation of the triarylphosphine ligand para-substituent Hammett parameters (σ p ). However, cyclic voltammetry measurements indicate that the electron transfer energetics of 1–5 are strongly influenced by ligand substitution, with the E 1/2 of a given redox event spanning ∼0.5 V depending on the triarylphosphine ligand’s σ p . In conclusion, these findings support the characterization of Co 6 Se 8 clusters as atomically precise nanoclusters with both the structural robustness and the electrochemical tunability needed to act as components in larger charge transfer assemblies.

Wheaton, Amelia M. [Argonne National Laboratory (A↗
DOE OSTI2026

Deterministic Control of Sn 3+ Valence and Electronic Phase Evolution in AgSnSe 2

Understanding how unusual oxidation states influence material properties is important for both fundamental science and energy applications. AgSnSe 2 is particularly intriguing because it stabilizes the rare and long-debated Sn 3+ oxidation state, whose true existence and role have remained enigmatic for many years. Here, in this work, we employ X-ray photoelectron spectroscopy, Mössbauer spectroscopy, and X-ray absorption spectroscopy to directly probe the oxidation state of Sn and its evolution under chemical substitution. All experimental evidence consistently confirms the presence of Sn in the +3 oxidation state in AgSnSe 2 . Complementary density functional theory calculations further corroborate this assignment. By substituting Sn with Sb, we systematically control the electronic state and its impact on the material’s physical properties. At low Sb concentrations, AgSnSe 2 retains superconductivity with a transition temperature of ∼5 K, while increasing Sb content deterministically drives a metallic-to-semiconducting transition through progressive suppression of superconductivity. Spectroscopic analyses show that Sb substitution provides deterministic control of the Sn oxidation state, evolving from a uniform +3 configuration in AgSnSe 2 to a mixed +2/+4 valence-skipping regime at higher Sb levels, thereby establishing a direct chemical handle over the material’s electronic phase. This tunability demonstrates that the Sn oxidation state in AgSnSe2 can be precisely engineered through Sb substitution, enabling controlled electronic phase transitions and establishing AgSnSe 2 as a promising platform for quantum and energy-related applications

crystal structure↗
DOE OSTI2020

Spin-Canting-Induced Band Reconstruction in the Dirac Material Ca 1 – x Na x MnBi 2

The ternary A MnBi 2 ( A is alkaline as well as rare-earth atom) materials provide an arena for investigating the interplay between low-dimensional magnetism of the antiferromagnetic MnBi layers and the electronic states in the intercalated Bi layers, which harbor relativistic fermions. We report on a comprehensive study of the optical properties and magnetic torque response of Ca 1–x Na x MnBi 2 . Our findings give evidence for a spin canting occurring at T s ~50–100 K. Thus, with the support of first-principles calculations we establish a direct link between the spin canting and the reconstruction of the electronic band structure, having immediate implications for the spectral weight reshuffling in the optical response, signaling a partial gapping of the Fermi surface, and the dc transport properties below T s .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Unraveling the CO Oxidation Mechanism over Highly Dispersed Pt Single Atom on Anatase TiO 2 (101)

Catalysts with noble metals deposited as single atoms on metal oxide supports have recently been studied extensively due to their maximized metal utilization and potential for performing difficult chemical conversions owing to their unique electronic properties. Understanding of the reaction mechanisms on supported single-metal atoms is still limited but is highly important for designing more efficient catalysts. In this study, we report the complexity of the CO oxidation reaction mechanism on Pt single atoms supported on anatase TiO 2 (Pt SA /a-TiO 2 ) by coupling density functional theory (DFT) calculations and microkinetic analysis with kinetic measurements, in situ/operando infrared, and X-ray absorption spectroscopies. Starting from the adsorbed Pt SA occupying an O vacancy induced by reductive pretreatment, we show that CO oxidation follows a complex mechanism consisting of initiation steps to reorganize the active site and multibranch reactive cycles, with the Pt SA /a-TiO 2 catalyst not returning to its initial configuration. The initiation step consists of CO and O 2 adsorption healing the O vacancy, followed by CO oxidation using gas-phase CO to form Pt(CO). The reactive cycle alternates O 2 adsorption and dissociation to oxidize the catalyst to Pt(O)(O)(CO) and branching pathways of competing Langmuir–Hinshelwood (LH)- or Eley–Rideal (ER)-type CO oxidation steps to reduce it again to Pt(CO). In situ/operando infrared experiments, including cryogenic CO adsorption and isotopic CO exchange, confirm the combined involvement of strongly adsorbed CO and gas-phase CO in an Eley–Rideal step along the reaction cycle. Microkinetic modeling shows that Pt single atoms are present in a mixture of Pt(CO), Pt(CO)(O 2 ), Pt(O)(CO)(O 2 ), and Pt(CO)(CO 3 ) structures as the main intermediates during steady-state CO oxidation, all having the C–O vibrational stretch close to the experimentally observed value of 2115 cm –1 . Microkinetic modeling also shows that the fractional orders of CO and O 2 measured experimentally originate from multiple steps with a high degree of rate control and not from a simple competitive adsorption. The results demonstrate the complex reaction pathways that even CO oxidation on a simple single-atom system can follow, providing mechanistic insights for designing efficient Pt-based single-atom catalysts. Here, we further show that microkinetic modeling results are sensitive to changes in energies of intermediate and transition states within errors of density functional theory, which can ultimately lead to incorrect conclusions regarding the reaction pathways and most abundant reaction intermediates if not accounted for by experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Sharp Page transitions in generic Hamiltonian dynamics

Here, we consider the entanglement dynamics of a subsystem initialized in a pure state at high energy density (corresponding to negative temperature) and coupled to a cold bath. The subsystem's Rényi entropies 𝑆 𝛼 first rise as the subsystem gets entangled with the bath and then fall as the subsystem cools. We find that the peak of the min-entropy, lim 𝛼→∞ ⁡𝑆 𝛼 , sharpens to a cusp in the thermodynamic limit at a well-defined time we call the Page time. We construct a hydrodynamic ansatz for the evolution of the entanglement Hamiltonian, which accounts for the sharp Page transition as well as the intricate dynamics of the entanglement spectrum before the Page time. Our results hold both when the bath has the same Hamiltonian as the system and when the bath is taken to be Markovian. Our ansatz suggests conditions under which the Page transition should remain sharp even for Rényi entropies of finite index 𝛼.

dynamical phase transitions↗
DOE OSTI2024

Combined Machine Learning and Molecular Dynamics Reveal Two States of Hydration of a Single Functional Group of Cationic Polymeric Brushes

The state of hydration of a macromolecular system regulates a plethora of different properties of such a system. In this article, we develop a novel machine learning (ML) approach, based on the unsupervised clustering algorithm, for probing the hydration behavior of the {N(CH 3 ) 3 } + functional group of the PMETAC [Poly(2-(methacryloyloxy)ethyl trimethylammonium chloride] polyelectrolyte (PE) brush system. The PE brushes and the brush-supported water molecules and counterions (chloride ions) are first described using all-atom molecular dynamics (MD) simulations. The simulation data is subsequently used in our ML framework to identify that (1) the {N(CH 3 ) 3 } + functional groups of the PMETAC brushes have two distinct hydration states with one state (state 1) being characterized by less structured water molecules and the other state (state 2) being characterized by more structured water molecules and (2) an enhancement in the brush grafting density leads to the progressive dissapparenace of state 2. An increase in the grafting density increases the number of chloride counterions in a given volume around the {N(CH 3 ) 3 } + functional group and increases the number of shared water molecules between the {N(CH 3 ) 3 } + and Cl - . The chloride counterions are associated with a hydration layer with much less structured water molecules. Therefore, with an increase in the grafting density, an increase in the percentage of shared water molecules leads to the prevalence of the hydration state [of the {N(CH 3 ) 3 } + moiety] with less structured water molecules. Finally, we explain how the present findings are commensurate with two key previous related results, namely a significantly large chloride ion mobility inside the PMETAC brush layer and the {N(CH 3 ) 3 } + -Cl - average distance remaining independent of the PMETAC brush grafting density. Furthermore, we anticipate that the combined ML-MD-simulation approach proposed in this study can be adapted to probe other soft matter systems to reveal new insights of the underlying mechanisms of emergent phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

A comprehensive ARPES study on the type-II Dirac semimetal candidate Ir 1-x Pt x Te 2

The transition metal dichalcogenide Ir 1-x Pt x Te 2 displays both superconductivity and a topological band structure. Using angle-resolved photoemission spectroscopy, we obtain a comprehensive understanding of the three-dimensional electronic structure in the normal state of Ir 1-x Pt x Te 2 for doping levels from x = 0.1 to 0.4, which spans the composition range of a superconducting state to a non-superconducting state. Many features of the electronic structure can be attributed to strong Te–Te interactions between the layers of the layered crystal structure and can be resolved by photon energy dependent measurements. We demonstrate that the type-II Dirac fermions can be successfully tuned via Pt doping, where the Dirac point lies close to the Fermi level for x = 0.1. The band evolution vs doping provides a clearer understanding of the relationship between the superconductivity and electronic structure. In addition, the β band in the superconducting samples locates the system close to a type-II van Hove singularity, where spin triplet paring symmetry has been predicted. Our results provide a comprehensive understanding of the band structure of Ir 1-x Pt x Te 2 , and we discuss the possibilities of the existence of topological superconductivity in this system.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Anisotropy of the magnetic and transport properties of EuZn 2 As 2

Several recent studies have shown that the anisotropy in the magnetic structure of EuCd 2 As 2 plays a significant role in stabilizing the Weyl nodes. Therefore, to investigate the relationship between magnetic anisotropy and Weyl physics, we present a comparative study between EuZn 2 As 2 and EuCd 2 As 2 that are isostructural but with different magnetic anisotropy. We performed structural analysis, electronic transport, and magnetization experiments on millimeter-sized single crystals of EuZn 2 As 2 , and compared the results to those of EuCd 2 As 2 . By combining the first principle calculations and neutron diffraction experiment, we identify the magnetic ground state of EuZn 2 As 2 as A-type antiferromagnetic order with a transition temperature (T_N = 19.6 K) twice that of EuCd 2 As 2 . Like EuCd 2 As 2 , the negative magnetoresistance of EuZn 2 As 2 is observed after suppressing the resistivity peak at T_N with increasing fields. However, the anisotropy in both transport and magnetization are much reduced in EuZn 2 As 2 . The difference could be ascribed to the weaker spin-orbit coupling, more localized d orbitals, and a larger contribution from the Eu s orbitals in the zinc compound, as suggested by the electronic band calculations. The same band structure effect could be also responsible for the observation of a smaller nonlinear anomalous Hall effect in EuZn 2 As 2 compared to EuCd 2 As 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Tuning the flat bands of the kagome metal CoSn with Fe, In, or Ni doping

We report CoSn is a Pauli paramagnet with relatively flat d bands centered about 100 meV below the Fermi energy, E F . Single crystals of CoSn lightly doped with Fe, In, or Ni are investigated using x-ray and neutron scattering, magnetic susceptibility and magnetization, AC susceptibility, specific heat, and resistivity measurements. Within the rigid-band approximation, hole doping with a few percent of Fe or In should move the flat bands closer to E F , whereas electron doping with Ni should move the flat bands further away from E F . We provide evidence that this indeed occurs. Fe and In doping drive CoSn toward magnetism, while Ni doping suppresses CoSn's already weak magnetic response. The resulting ground state is different for Fe versus In doping. For Fe-doped crystals, Co 1-x Fe x Sn, with 0.02< x <0.27, the magnetic and specific-heat data are consistent with the formation of a spin glass, with a glass temperature, T g , ranging from 1 K for x = 0.02 to 10 K for x = 0.27. Powder and single-crystal neutron diffraction found no evidence of long-range magnetic order below T g for samples with x ≈ 0.17. For In-doped crystals, CoSn 1-y In y , both the magnetic susceptibility and the Sommerfeld coefficient, γ, increase substantially relative to pure CoSn, but with no clear indication of a magnetic transition for 0.05< y <0.2. CoSn crystals doped with Ni (Co 0.93 Ni 0.07 Sn) have a significantly smaller magnetic susceptibility and γ than pure CoSn, consistent with flat bands further from E F .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Enhancement of charge-neutral fermionic excitations near the spin-flop transition in the magnetic Kondo material YbIr 3 Si 7

The new Kondo material YbIr 3 Si 7 , similar to other Kondo insulators, has been reported to exhibit charge-neutral fermionic excitations through measurements of specific heat and thermal conductivity at low temperatures. We performed 29 Si-NMR on YbIr 3 Si 7 to investigate the magnetic response of charge-neutral fermions from a microscopic perspective. In low magnetic fields parallel to the c axis, a single NMR peak in the paramagnetic state splits into three peaks below TN. In contrast, only a slight shift of the single NMR peak was observed in high magnetic fields. This spectral change as a function of the c-axis magnetic field is interpreted as a spin-flop transition, at which the magnetic moments oriented along the c axis antiferromagnetic (AFM-I) phase are rotated to the ab plane with a ferromagnetic component along the c-axis (AFM-II phase). In the vicinity of the spin-flop magnetic field H M , the nuclear spin-lattice relaxation rate 1/T 1 was found to be proportional to temperature at low temperatures, indicating the existence of charge-neutral fermions. Furthermore, a peak of 1/T 1 versus the c-axis magnetic field suggests that the charge-neutral fermions in YbIr 3 Si 7 are closely related to its magnetic properties. Our findings shed light on the origin of charge-neutral fermions in insulators.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Integrated machine learning-molecular dynamics framework for electrolyte property prediction

Electrochemical stability windows determine the operating range of battery electrolytes, yet accurate prediction remains challenging because stability emerges from statistical ensembles of local solvation environments rather than single ground-state molecular structures. Traditional density functional theory calculations on energy-minimized clusters cannot capture the thermal variations in local coordination environments and geometries that govern decomposition, while SMILES-based machine learning methods lack explicit representation of three-dimensional solvation structure and ion pairing. Here, we introduce a structure-aware machine learning framework that predicts frontier orbital energies (HOMO and LUMO) directly from molecular dynamics-sampled solvation configurations, achieving sub-0.6 eV accuracy at computational costs 3–4 orders of magnitude lower than first-principles methods. Across twelve representative battery electrolytes, we demonstrate that solvent-separated and contact ion pairs exhibit strong size- and local chemistry dependent electronic stability, with variations in coordination shifts of HOMO or LUMO level by 2–3 eV, and that extended solvation structure and partially desolvated environment further modulate stability by up to 3 eV. By encoding the statistical nature of electrochemical failure through ensemble sampling of explicit solvation geometries, our approach enables high-throughput screening and rational design of next-generation battery electrolytes with mechanistic understanding of structure–property relationships.

Energy - Storage↗
DOE OSTI2024

Observation of paramagnetic spin-degeneracy lifting in EuZn 2 Sb 2

Taken together, time-reversal and spatial inversion symmetries impose a twofold spin degeneracy of the electronic states in crystals. In centrosymmetric materials, this degeneracy can be lifted by introducing magnetism, either via an externally applied field or through internal magnetization. However, a correlated alignment of spins, even in the paramagnetic phase, can lift the spin degeneracy of electronic states. Here, we report an in-depth study of the electronic band structure of the Eu-ternary pnictide EuZn 2 Sb 2 through a combination of high-resolution angle-resolved photoemission spectroscopy measurements and first-principles calculations. An analysis of the photoemission line shapes over a range of incident photon energies and sample temperatures is shown to reveal the presence of band spin-degeneracy lifting in the paramagnetic phase. Our angle-resolved photoemission spectroscopy results are in good agreement with theoretical ferromagnetic-phase calculations, which indicates the importance of ferromagnetic fluctuations in the system. Through our calculations, we predict that spin-polarized bands in EuZn 2 Sb 2 generate a single pair of Weyl nodes. Our observation of band splittingin EuZn 2 Sb 2 provides a key step toward realizing time-reversal symmetry breaking physics in the absence of long-range magnetic order.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Photoinduced band renormalization effects in the topological nodal-line semimetal ZrSiS

Out-of-equilibrium effects provide an elegant pathway for probing and understanding the underlying physics of topological materials. In particular, controlling electronic band structure properties using ultrafast optical pulses has shown promise for creating exotic states of matter. Of recent interest is band renormalization in Dirac and Weyl semimetals as it leads to direct physical observables through the enhancement of the effective mass or in the shift of resonant energies. Here, in this work, we provide experimental and theoretical signatures of photoinduced renormalization of the electronic band structure in the topological nodal-line semimetal ZrSiS. Specifically, we show how the change in the transient reflectivity spectra under femtosecond optical excitations is induced by out-of-equilibrium effects that renormalize the kinetic energy of electrons. We associate the observed spectral features with an enhancement of the effective mass and to a redshift of the resonant frequency as a function of pump field strength. Finally, we show that the transient relaxation dynamics of the reflectivity is primarily an electronic effect with a negligible phononic contribution. Our study presents conclusive modifications of electronic properties in ZrSiS using ultrashort pulses and demonstrates the potential of this approach in creating photoinduced phases in topological quantum matter through an all-optical route.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Emerging supersolidity in photonic-crystal polariton condensates

A supersolid is a counter-intuitive phase of matter in which its constituent particles are arranged into a crystalline structure, yet they are free to flow without friction. This requires the particles to share a global macroscopic phase while being able to reduce their total energy by spontaneous, spatial self-organization. The existence of the supersolid phase of matter was speculated more than 50 years ago1, 2, 3–4. However, only recently has there been convincing experimental evidence, mainly using ultracold atomic Bose–Einstein condensates (BECs) coupled to electromagnetic fields. There, various guises of the supersolid were created using atoms coupled to high-finesse cavities5,6, with large magnetic dipole moments7, 8, 9, 10, 11, 12–13, and spin–orbit-coupled, two-component systems showing stripe phases14, 15–16. Here we provide experimental evidence of a new implementation of the supersolid phase in a driven-dissipative, non-equilibrium context based on exciton–polaritons condensed in a topologically non-trivial, bound state in the continuum (BiC) with exceptionally low losses, realized in a photonic-crystal waveguide. We measure the density modulation of the polaritonic state indicating the breaking of translational symmetry with a precision of several parts in a thousand. Direct access to the phase of the wavefunction allows us to also measure the local coherence of the supersolid. We demonstrate the potential of our synthetic photonic material to host phonon dynamics and a multimode excitation spectrum.

Trypogeorgos, Dimitrios↗