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DOE OSTI2022

Bandgap analysis and carrier localization in cation-disordered ZnGeN 2

The bandgap of ZnGeN 2 changes with the degree of cation site disorder and is sought in light emitting diodes for emission at green to amber wavelengths. By combining the perspectives of carrier localization and defect states, we analyze the impact of different degrees of disorder on electronic properties in ZnGeN 2 , addressing a gap in current studies, which largely focus on dilute or fully disordered systems. The present study demonstrates changes in the density of states and localization of carriers in ZnGeN 2 calculated using bandgap-corrected density functional theory and hybrid calculations on partially disordered supercells generated using the Monte Carlo method. We use localization and density of states to discuss the ill-defined nature of a bandgap in a disordered material and identify site disorder and its impact on the structure as a mechanism controlling electronic properties and potential device performance. Decreasing the order parameter results in a large reduction of the bandgap. The reduction in bandgap is due, in part, to isolated, localized states that form above the valence band continuum associated with nitrogen coordinated by more zinc than germanium. The prevalence of defect states in all but the perfectly ordered structure creates challenges for incorporating disordered ZnGeN 2 into optical devices, but the localization associated with these defects provides insight into the mechanisms of electron/hole recombination in the material.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Emergence of Fermi arcs due to magnetic splitting in an antiferromagnet

The Fermi surface plays an important role in controlling the electronic, transport and thermodynamic properties of materials. As the Fermi surface consists of closed contours in the momentum space for well-defined energy bands, disconnected sections known as Fermi arcs can be signatures of unusual electronic states, such as a pseudogap. Another way to obtain Fermi arcs is to break either the time-reversal symmetry or the inversion symmetry of a three-dimensional Dirac semimetal, which results in formation of pairs of Weyl nodes that have opposite chirality, and their projections are connected by Fermi arcs at the bulk boundary. Here, we present experimental evidence that pairs of hole- and electron-like Fermi arcs emerge below the Neel temperature (TN) in the antiferromagnetic state of cubic NdBi due to a new magnetic splitting effect. The observed magnetic splitting is unusual, as it creates bands of opposing curvature, which change with temperature and follow the antiferromagnetic order parameter. This is different from previous theoretically considered and experimentally reported cases of magnetic splitting, such as traditional Zeeman and Rashba, in which the curvature of the bands is preserved. Therefore, our findings demonstrate a type of magnetic band splitting in the presence of a long-range antiferromagnetic order that is not readily explained by existing theoretical ideas.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Elastocaloric signatures of symmetric and antisymmetric strain-tuning of quadrupolar and magnetic phases in DyB 2 C 2

The adiabatic elastocaloric effect measures the temperature change of a given system with strain and provides a thermodynamic probe of the entropic landscape in the temperature-strain space. Here, we demonstrate that the DC bias strain-dependence of AC elastocaloric effect allows decomposition of the latter into symmetric (rotation-symmetry-preserving) and antisymmetric (rotation-symmetry-breaking) strain channels, using a tetragonal f -electron intermetallic DyB 2 C 2 —whose antiferroquadrupolar order breaks local fourfold rotational symmetries while globally remaining tetragonal—as a showcase example. We capture the strain evolution of its quadrupolar and magnetic phase transitions using both singularities in the elastocaloric coefficient and its jumps at the transitions, and the latter we show follows a modified Ehrenfest relation. We find that antisymmetric strain couples to the underlying order parameter in a biquadratic (linear-quadratic) manner in the antiferroquadrupolar (canted antiferromagnetic) phase, which are attributed to a preserved (broken) global tetragonal symmetry, respectively. The broken tetragonal symmetry in the magnetic phase is further evidenced by elastocaloric strain-hysteresis and optical birefringence. Additionally, within the staggered quadrupolar order, the observed elastocaloric response reflects a quadratic increase of entropy with antisymmetric strain, analogous to the role magnetic field plays for Ising antiferromagnetic orders by promoting pseudospin flips. Our results demonstrate AC elastocaloric effect as a compact and incisive thermodynamic probe into the coupling between electronic degrees of freedom and strain in free energy, which holds the potential for investigating and understanding the symmetry of a wide variety of ordered phases in broader classes of quantum materials.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Fingerprinting Superconductors by Disentangling Andreev and Quasiparticle Currents Across Tunable Tunnel Junctions

Tunneling Andreev reflection (TAR) spectroscopy provides a new approach to identify superconducting pairing symmetry at the atomic scale. Using atomistic superconducting transport simulations, we reveal the mechanism by which TAR can distinguish between pairing symmetries, which is complementary to traditional conductance-based techniques. In particular, owing to the additivity of the excess tunneling decay rate, the TAR spectrum is a weighted average of the contributions from quasiparticle currents, Andreev reflection, and higher-order scattering processes, and their relative weights depend on both the superconducting order parameter and the coupling strength. Within the local tunneling model, TAR dominates mid-gap conductance for s-wave superconductors, is suppressed for d-wave, and coexists with quasiparticle tunneling in sign-changing symmetries if the expectation value for the superconducting gap remains finite. Meanwhile, higher-order processes generally enhance the TAR signal when GN exceeds approximately 0.1G0. As a result, TAR provides a rich spectral fingerprint of the underlying pairing symmetry and electronic structure, enabling atomically resolved identification of unconventional superconducting states.

Maksymovych, Petro [Clemson University]↗

DOE OSTI2025

Dynamics and Formation of Antiferromagnetic Textures in MnBi 2 Te 4 Single Crystal

We report coherent X-ray imaging of antiferromagnetic (AFM) domains and domain walls in MnBi 2 Te 4 , an intrinsic AFM topological insulator. This technique enables direct visualization of domain morphology without reconstruction algorithms, allowing us to resolve antiphase domain walls as distinct dark lines arising from the A-type AFM structure. The wall width is determined to be 550(30) nm, in good agreement with earlier magnetic force microscopy results. The temperature dependence of the AFM order parameter extracted from our images closely follows previous neutron scattering data. Remarkably, however, we find a pronounced hysteresis in the evolution of domains and domain walls: upon cooling, dynamic reorganizations occur within a narrow ∼1 K interval below 𝑇 𝑁 , whereas upon warming, the domain configuration remains largely unchanged until AFM order disappears. These findings reveal a complex energy landscape in MnBi 2 Te 4 , governed by the interplay of exchange, anisotropy, and domain-wall energies, and underscore the critical role of AFM domain-wall dynamics in shaping its physical properties. These sharply defined and hysteretically evolving walls may provide a controllable AFM texture in MnBi 2 Te 4 , hinting at potential use in low-power spintronic devices based on domain-wall dynamics.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Temporal and spatial separations between spin glass and short-range order

Broken-symmetry-induced order parameters account for many phenomena in physics. For spin glasses, this framework dictates the theoretical construction, whereas experiments have only established dynamical behaviors but not the physical entity. Experimental techniques have limitations when the spin glass is probed as an isolated state. Here, we create an evolution from a long-range order using well-controlled non-magnetic substitution on a sublattice. Neutron magnetic diffuse scattering of pico-second timescale reveals that the dynamics of short- and long-range order formation are not affected by disorder, but their spatial ranges are. Across all specimens, the inflection point of spin correlation length’s temperature dependence fully matches with the peak in heat capacity, while spin glass can freeze at millisecond timescale either above or below this characteristic temperature of spin-order formation. Our results identify the spin glass as single, uncorrelated spins at domain walls between spin clusters, and an uncorrelated coexistence of the two.

Dronova, Margarita G [Okinawa Institute of Science↗

DOE OSTI2023

Quantum textures of the many-body wavefunctions in magic-angle graphene

Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that often reflect electronic correlation effects, broken symmetries, and novel collective excitations. A wide range of quantum phases has been discovered in MATBG, including correlated insulating, unconventional superconducting, and magnetic topological phases. The lack of microscopic information, including precise knowledge of possible broken symmetries, has thus far hampered our understanding of MATBG's correlated phases. Here we use high-resolution scanning tunneling microscopy to directly probe the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlated insulators, pseudogap, and superconducting phases, show distinct patterns of broken symmetry with a √3 x √3 super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moiré superlattice scale. We introduce a symmetry-based analysis to describe our measurements of the wavefunctions of MATBG's correlated phases with a set of complex-valued local order parameters. For the correlated insulators in MATBG, at fillings of ±2 electrons per moiré unit cell relative to charge neutrality, we compare the observed quantum textures to those expected for proposed theoretical ground states. In typical MATBG devices, the textures of correlated insulators' wavefunctions closely match those of the theoretically proposed IKS order, while in ultra-low-strain samples our data has local symmetries like those of a T-IVC phase. Here, we also study the wavefunction of MATBG's superconducting state, revealing strong signatures of intervalley coherence that can only be distinguished from those of the insulator with our phase-sensitive measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Long-Range Lamellar Alignment in Diblock Bottlebrush Copolymers via Controlled Oscillatory Shear

A simple strategy is presented to achieve well-ordered nanostructures in microphase-separated diblock bottlebrush copolymers (dbBB) for potential opportunities in nanotechnology that require large grain sizes and directed orientation. The unique architecture and relaxation processes of dbBBs offer a pathway to enhanced dynamic ordering and reorientation over macroscopic scales. Here, controlled shear is used to align lamellar domains. The high molecular mobility of dbBBs in the melt state, as shown by linear and nonlinear viscoelastic characterization, supports this alignment process. When subjected to large-amplitude oscillatory shear at controlled frequency (ω), strain amplitude (γ), and temperature (T shear ), microphase-separated lamellae transition into highly aligned states as determined by small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). High throughput synchrotron SAXS is used to rapidly characterize microphase separation and lamellar alignment across the entire bulk sample. Lamellae align parallel to shear planes with an orientation order parameter (S) approaching S = 0.8 over a large cubic volume (V ~ mm 3 ).

36 MATERIALS SCIENCE↗

DOE OSTI2021

Topological and nematic superconductivity mediated by ferro-SU(4) fluctuations in twisted bilayer graphene

We propose an SU(4) spin-valley-fermion model to investigate the superconducting instabilities of twisted bilayer graphene (TBG). In this approach, bosonic fluctuations associated with an emergent SU(4) symmetry, corresponding to combined rotations in valley and spin spaces, couple to the low-energy fermions that comprise the flat bands. These fluctuations are peaked at zero wave vector, reflecting the “ferromagnetic-like” SU(4) ground state recently found in strong-coupling solutions of microscopic models for TBG. Focusing on electronic states related to symmetry-imposed points of the Fermi surface, dubbed here “valley hot-spots” and “van Hove hot-spots,” we find that the coupling to the itinerant electrons partially lifts the huge degeneracy of the ferro-SU(4) ground state manifold, favoring intervalley order, spin-valley coupled order, ferromagnetic order, spin-current order, and valley-polarized order, depending on details of the band structure. Here, these fluctuations, in turn, promote attractive pairing interactions in a variety of closely competing channels, including a nodeless f-wave state, a nodal i-wave state, and topological d+id and p+ip states with unusual Chern numbers 2 and 4, respectively. Nematic superconductivity, although not realized as a primary instability of the system, appears as a consequence of the near-degeneracy of superconducting order parameters that transform as one-dimensional and two-dimensional irreducible representations of the point group D 6 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Perturbative Stability and Error-Correction Thresholds of Quantum Codes

Topologically ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We connect the two notions of stability by constructing classical statistical mechanics models for decoding general Calderbank-Shor-Steane codes and classical linear codes. Our construction encodes correction success probabilities under uncorrelated bit-flip and phase-flip errors, and simultaneously describes a generalized ℤ 2 lattice-gauge theory with quenched disorder. We observe that the clean limit of the latter is precisely the discretized imaginary-time path integral of the corresponding quantum code Hamiltonian when the errors are turned into a perturbative 𝑋 or 𝑍 magnetic field. Motivated by error-correction considerations, we define general order parameters for all such generalized ℤ 2 lattice-gauge theories, and show that they are generally lower bounded by success probabilities of error correction. For CSS codes satisfying the low-density parity-check condition and with a sufficiently large code distance, we prove the existence of a low-temperature ordered phase of the corresponding lattice-gauge theories, particularly for those lacking Euclidean spatial locality and/or when there is a nonzero code rate. We further argue that these results provide evidence for stable phases in the corresponding perturbed quantum Hamiltonians, obtained in the limit of continuous imaginary time. To do so, we distinguish space- and timelike defects in the lattice-gauge theory. A high free-energy cost of spacelike defects corresponds to a successful “memory experiment” and suppresses the energy splitting among the ground states, while a high free-energy cost of timelike defects corresponds to a successful “stability experiment” and points to a nonzero gap to local excitations.

quantum error correction↗

NASA NTRS1994

Penetration experiments in aluminum and Teflon targets of widely variable thickness

The morphologies and detailed dimensions of hypervelocity craters and penetration holes on space-exposed surfaces faithfully reflect the initial impact conditions. However, current understanding of this postmortem evidence and its relation to such first-order parameters as impact velocity or projectile size and mass is incomplete. While considerable progress is being made in the numerical simulation of impact events, continued impact simulations in the laboratory are needed to obtain empirical constraints and insights. This contribution summarizes such experiments with Al and Teflon targets that were carried out in order to provide a better understanding of the crater and penetration holes reported from the Solar Maximum Mission (SMM) and the Long Duration Exposure Facility (LDEF) satellites. A 5-mm light gas gun was used to fire spherical soda-lime glass projectiles from 50 to 3175 microns in diameter (D(sub P)), at a nominal 6 km/s, into Al (1100 series; annealed) and Teflon (Teflon(sup TFE)) targets. Targets ranged in thickness (T) from infinite halfspace targets (T approx. equals cm) to ultrathin foils (T approx. equals micron), yielding up to 3 degrees of magnitude variation in absolute and relative (D(sub P)/T) target thickness. This experimental matrix simulates the wide range in D(sub P)/T experienced by a space-exposed membrane of constant T that is being impacted by projectiles of widely varying sizes.

Hoerz, F.↗

NASA NTRS1978

Electron paramagnetic resonance studies of slowly tumbling vanadyl spin probes in nematic liquid crystals

An analysis of EPR line shapes by the method of Polnaszek, Bruno, and Freed is made for slowly tumbling vanadyl spin probes in viscous nematic liquid crystals. The use of typical vanadyl complexes as spin probes for nematic liquid crystals is shown to simplify the theoretical analysis and the subsequent interpretation. Rotational correlation times tau and orientational ordering parameters S sub Z where slow tumbling effects are expected to be observed in vanadyl EPR spectra are indicated in a plot. Analysis of the inertial effects on the probe reorientation, which are induced by slowly fluctuating torque components of the local solvent structure, yield quantitative values for tau and S sub Z. The weakly ordered probe VOAA is in the slow tumbling region and displays these inertial effects throughout the nematic range of BEPC and Phase V. VOAA exhibits different reorientation behavior near the isotropic-nematic transition temperature than that displayed far below this transition temperature.

Bruno, G. V.↗

DOE OSTI2024

Nanosecond Structural Dynamics during Electrical Melting of Charge Density Waves in 1⁢T-TaS 2

Electrical control of charge density waves has been of immense interest, as the strong underlying electron-lattice interactions potentially open new, efficient pathways for manipulating their ordering and, consequently, their electronic properties. However, the transition mechanisms are often unclear as electric field, current, carrier injection, heat, and strain can all contribute and play varying roles across length scales and timescales. Here, we provide insight on how electrical stimulation melts the room temperature charge density wave order in 1T-TaS 2 by visualizing the atomic and mesoscopic structural dynamics from quasistatic to nanosecond pulsed melting. Using a newly developed ultrafast electron microscope setup with electrical stimulation, we reveal the order and strain dynamics during voltage pulses as short as 20 ns. The order parameter dynamics across a range of pulse amplitudes and durations support a thermally driven mechanism even for fields as high as 19 kV cm -1 . In addition, time-resolved imaging reveals a heterogeneous, mesoscopic strain response across the flake, including MHz-scale acoustic resonances that emerge during sufficiently short pulsed excitation which may modulate the order. In conclusion, these results suggest that metallic charge density wave phases like studied here may be more robust to electronic switching pathways than insulating ones, motivating further investigations at higher fields and currents in this and other related systems.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Dynamic pair-breaking current, critical superfluid velocity, and nonlinear electromagnetic response of nonequilibrium superconductors

Here, we report numerical calculations of a dynamic pair-breaking current density $J_d$ and a critical superfluid velocity $v_d$ in a nonequilibrium superconductor carrying a uniform, large-amplitude AC current density $J(t) = J_a$sinΩ$\textit{t}$ with Ω well below the gap frequency Ω $\ll Δ_0/ℏ$. The dependencies $J_d$(Ω, $\textit{T}$) and $v_d$(Ω, $\textit{T}$) near the critical temperature $T_c$ were calculated from either the full time-dependent nonequilibrium equations for a dirty $\textit{s}$-wave superconductor or the time-dependent Ginzburg-Landau (TDGL) equations for a gapped superconductor, taking into account the GL relaxation time of the order parameter $τ_{\text{GL}}$ and the inelastic electron-phonon relaxation time of quasiparticles $τ_E$. We show that both approaches give similar frequency dependencies of $J_d$(Ω) and $v_d$(Ω) which gradually increase from their static pair-breaking GL values $J_c$ and $v_c$ at Ω$τ_E \ll$1 to $\sqrt{2}J_c$ and $\sqrt{2}v_c$ at Ω$τ_E \gg$ 1. Here $J_d, v_d$ and a dynamic superheating field at which the Meissner state becomes unstable were calculated in two different regimes of a fixed AC current and a fixed AC superfluid velocity induced by the applied AC magnetic field $H = H_a$ sinΩ$\textit{t}$ in a thin superconducting filament or a type-II superconductor with a large GL parameter. We also calculated a nonlinear electromagnetic response of a nonequilibrium superconducting state, particularly a dynamic kinetic inductance and a dissipative quasiparticle conductivity, taking into account the oscillatory dynamics of superconducting condensate and the kinetics of quasiparticles driven by a strong AC current. It is shown that an AC current density produces multiple harmonics of the electric field, the amplitudes of the higher-order harmonics diminishing as $τ_E$ increases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Symmetry Breaking and Ascending in the Magnetic Kagome Metal FeGe

Spontaneous symmetry breaking—the phenomenon in which an infinitesimal perturbation can cause the system to break the underlying symmetry—is a cornerstone concept in the understanding of interacting solid-state systems. In a typical series of temperature-driven phase transitions, higher-temperature phases are more symmetric due to the stabilizing effect of entropy that becomes dominant as the temperature is increased. However, the opposite is rare but possible when there are multiple degrees of freedom in the system. Here, we present such an example of a symmetry-ascending phenomenon upon cooling in a magnetic kagome metal FeGe by utilizing neutron Larmor diffraction and Raman spectroscopy. FeGe has a kagome lattice structure with simple A-type antiferromagnetic order below Néel temperature T N ≈ 400 K and a charge density wave (CDW) transition at T CDW ≈ 110 K , followed by a spin-canting transition at around 60 K. In the paramagnetic state at 460 K, we confirm that the crystal structure is indeed a hexagonal kagome lattice. On cooling to around T N , the crystal structure changes from hexagonal to monoclinic with in-plane lattice distortions on the order of 10 − 4 and the associated splitting of the double-degenerate phonon mode of the pristine kagome lattice. Upon further cooling to T CDW , the kagome lattice shows a small negative thermal expansion, and the crystal structure gradually becomes more symmetric upon further cooling. A tendency of increasing the crystalline symmetry upon cooling is unusual; it originates from an extremely weak structural instability that coexists and competes with the CDW and magnetic orders. These observations are against the expectations for a simple model with a single order parameter and hence can only be explained by a Landau free energy expansion that takes into account multiple lattice, charge, and spin degrees of freedom. Thus, the determination of the crystalline lattice symmetry as well as the unusual spin-lattice coupling is a first step towards understanding the rich electronic and magnetic properties of the system, and it sheds new light on intertwined orders where the lattice degree of freedom is no longer dominant. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Location and thermal evolution of the pseudogap due to spin fluctuations

We study pseudogap behavior in a metal near a spin density wave (SDW) instability due to thermal magnetic fluctuations. We consider the t–t' Hubbard model on a square lattice at a finite doping, at intermediate coupling strength, and analyze the thermal evolution of the electron spectral function between a SDW ordered state at low temperatures and a normal Fermi liquid at high temperatures. We argue that for proper description of the pseudogap one needs to sum up infinite series of diagrams for both the fermionic self-energy and the SDW order parameter in the SDW state or the magnetic correlation length in the paramagnetic state. We use the eikonal approach to sum up an infinite series of diagrammatic contributions from thermal fluctuations. Earlier studies found that in the SDW state the spectral function A k (ω) of a hot fermion at a finite T is exponentially small below the energy scale Δ(T), which scales with SDW order and vanishes at the ordering temperature T N , and has a hump at a larger frequency Δ PG , comparable to the zero-temperature SDW gap Δ(T = 0). We argue that the hump, which we associate with the pseudogap, survives in some T range above T N . We show that this range is split by regions of strong and weak pseudogap behavior. In the first region, Δ PG is weakly temperature dependent, despite the fact that it comes from thermal fluctuations. Such a behavior has been seen in numerical studies of the Hubbard model. We show that to obtain it one needs to go beyond the one-loop approximation and sum up the infinite series of diagrams. In the second regime, Δ PG decreases with increasing T and eventually vanishes. Here, we further argue that a magnetic pseudogap at a finite T emerges only if the ground state is magnetically ordered. We present the phase diagram and apply the results to high-T c cuprates.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Observation of Giant Optical Linear Dichroism in a Zigzag Antiferromagnet FePS 3

Direct optical probing of the antiferromagnetic order parameter in atomically thin samples is challenging, for example, via magneto-optical spectroscopy, due to the lack of net magnetization. Here, we report zigzag-antiferromagnetism (AFM) induced optical linear dichroism (LD) in layered transition-metal thiophosphate FePS3 down to the monolayer limit. The observed LD is giant despite having the optical wave vector parallel to the Neel vector. The LD is at least one order of magnitude larger than those reported in other antiferromagnetic systems, where the optical wave vector is orthogonal to the Neel vector. The large LD enables the probe of 60 degrees orientated zigzag-AFM domains. The optical anisotropy in FePS 3 originates from an electronic anisotropy associated with the zigzag direction of the AFM order and is independent of the spin-pointing direction. Furthermore, our findings point to a new optical approach for the investigation and control of zigzag or stripe magnetic order in strongly correlated systems.

2D magnet↗

DOE OSTI2022

Quantum coherence tomography of light-controlled superconductivity

The coupling between superconductors and oscillation cycles of light pulses, i.e., lightwave engineering, is an emerging control concept for superconducting quantum electronics. Although progress has been made towards terahertz-driven superconductivity and supercurrents, the interactions able to drive non-equilibrium pairing are still poorly understood, partially due to the lack of measurements of high-order correlation functions. In particular, the sensing of exotic collective modes that would uniquely characterize light-driven superconducting coherence, in a way analogous to the Meissner effect, is very challenging but much needed. Here we report the discovery of parametrically driven superconductivity by light-induced order-parameter collective oscillations in iron-based superconductors. The time-periodic relative phase dynamics between the coupled electron and hole bands drives the transition to a distinct parametric superconducting state out-of-equalibrium. This light-induced emergent coherence is characterized by a unique phase–amplitude collective mode with Floquet-like sidebands at twice the Higgs frequency. We measure non-perturbative, high-order correlations of this parametrically driven superconductivity by separating the terahertz-frequency multidimensional coherent spectra into pump–probe, Higgs mode and bi-Higgs frequency sideband peaks. We find that the higher-order bi-Higgs sidebands dominate above the critical field, which indicates the breakdown of susceptibility perturbative expansion in this parametric quantum matter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗