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Theory of disordered superconductors with applications to nonlinear current response

I present a review of the theory and basic equations for charge transport in superconducting alloys starting from the Keldysh formulation of the quasiclassical transport equations developed by Eilenberger, Larkin and Ovchinnikov, and Eliashberg. This formulation is the natural extension of Landau’s theory of normal Fermi liquids to the superconducting state of strongly correlated metals. For dirty metals the transport equations reduce to equations for charge diffusion, with the current response given by the Drude conductivity at low temperatures. The extension of the diffusion equation for the charge and current response of a strongly disordered normal metal to the superconducting state yields Usadel’s equations for the nonequilibrium quasiclassical Keldysh propagator. The conditions for the applicability of the Usadel equations are discussed, the pair-breaking effect of disorder on the current response, including the nonlinear current response to an electromagnetic field in the dirty limit, τ ≪ ℏ/Δ, are reported. The same nonlinearity is shown to lead to source currents for photon generation and nonlinear Kerr rotation driven by the nonlinear response to excitation of the superconductor by a multi-mode electromagnetic field. The potential relevance of the nonlinear source currents to superconducting radio-frequency cavities as detectors of axion-like dark matter candidates is briefly discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Revealing the frequency-dependent oscillations in the nonlinear terahertz response induced by the Josephson current

ABSTRACT Nonlinear responses of superconductors to intense terahertz radiation has been an active research frontier. Using terahertz pump-terahertz probe spectroscopy, we investigate the c-axis nonlinear optical response of a high-temperature superconducting cuprate. After excitation by a single-cycle terahertz pump pulse, the reflectivity of the probe pulse oscillates as the pump-probe delay is varied. Interestingly, the oscillatory central frequency scales linearly with the probe frequency, a fact widely overlooked in pump-probe experiments. By theoretically solving the nonlinear optical reflection problem on the interface, we show that our observation is well explained by the Josephson-type third-order nonlinear electrodynamics, together with the emission coefficient from inside the material into free space. The latter results in a strong enhancement of the emitted signal whose physical frequency is around the Josephson plasma edge. Our result offers a benchmark for and new insights into strong-field terahertz spectroscopy of related quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Intensity measure adequacy assessment for nonlinear site response using Information Theory

Nonlinear site response modeling is a crucial aspect of Probabilistic Seismic Hazard Analysis. Site amplification models routinely rely on a rock intensity measure to characterize the strength of the bedrock motion. However, the adequacy of such intensity measures towards predicting amplifications across the oscillator period range has not been investigated in the literature. This paper analyzes the adequacy of rock intensity measures using state of the art criterion established in Performance-Based Earthquake Engineering and techniques from Information Theory. The efficiency and the sufficiency of several rock intensity measure are assessed. It was found that spectral accelerations at low periods usually are adequate for predicting amplifications across the period range. This supports the current practice of using Peak Ground Acceleration in Ground Motion Models. However, for extremely soft sites, which demonstrate nonlinear effects well into the period range, it is better practice to ensure that amplification and spectral acceleration share the same oscillator period. Lastly, for predicting the peak shear strain (an important parameter that controls nonlinearity of site response), Peak Ground Velocity is generally adequate, and this conclusion is in line with the definition of proxy shear strain.

42 ENGINEERING↗

Effect of relative humidity on the nonlinear elastic response of granular media

We study the influence of relative humidity (RH) on the nonlinear elastic response of granular media. Previous work has shown that the nonlinear elastic response of consolidated granular media like rocks likely arises from two distinct mechanisms; however, we do not have a clear understanding of their physical origins at the microscopic scale. Here, we conduct dynamic acousto-elastic testing (DAET) on samples of glass beads under dry (~10%), ambient (~60%), and humid (~100%) conditions at room temperature and a constant static stress of 4 MPa. DAET allows us to retrieve the full nonlinear elastic response, including transient softening and hysteretic effects. We find that the elastic nonlinearity of humid samples is an order of magnitude larger than dry samples. Moreover, we find that all extracted nonlinear parameters increase with RH. This overall increase in nonlinearity is consistent with findings from previous studies and with the hypothesis that water adsorption on the grains makes the contact junctions weaker and prone to greater disturbances when subjected to dynamic stressing. Our results also suggest that, if indeed both mechanisms coexist, they are affected in a similar fashion in these glass bead samples and cannot be distinguished by varying RH.

36 MATERIALS SCIENCE↗

Simulating dielectric spectra: A demonstration of the direct electric field method and a new model for the nonlinear dielectric response

Here we demonstrate a method to compute the dielectric spectra of fluids in molecular dynamics (MD) by directly applying electric fields to the simulation. We obtain spectra from MD simulations with low magnitude electric fields (≈0.01 V/Å) in agreement with spectra from the fluctuation–dissipation method for water and acetonitrile. We examine this method’s trade-off between noise at low field magnitudes and the nonlinearity of the response at higher field magnitudes. We then apply the Booth equation to describe the nonlinear response of both fluids at low frequency (0.1 GHz) and high field magnitude (up to 0.5 V/Å). We develop a model of the frequency-dependent nonlinear response by combining the Booth description of the static nonlinear dielectric response of fluids with the frequency-dependent linear dielectric response of the Debye model. We find good agreement between our model and the MD simulations of the nonlinear dielectric response for both acetonitrile and water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

QuDPy: A Python-based tool for computing ultrafast non-linear optical responses

Nonlinear Optical Spectroscopy is a well-developed field with theoretical and experimental advances that have benefited multiple disciplines, including chemistry, biology, and physics. However, for the accurate interpretation of the corresponding multi-dimensional spectra, there is a need for precise quantum dynamical simulations based on model Hamiltonians. In this article, we present the initial release of our code, QuDPy (Quantum Dynamics in Python), which provides a robust numerical platform for performing quantum dynamics simulations based on model systems, including open quantum systems. Furthermore, a distinguishing feature of our approach is the ability to specify various high-order optical response pathways in the form of double-sided Feynman diagrams through a straightforward input syntax. This syntax outlines the time-ordering of ket-sided or bra-sided optical interactions acting on the time-evolving density matrix of the system. We utilize the quantum dynamics capabilities of QuTip to simulate the spectral response of complex systems, allowing us to compute virtually any $n$-th order optical response of the model system. To illustrate the utility of our approach, we provide a series of example calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Polarity-dependence of the nonlinear dielectric response in interfacial water

Molecular dynamics simulations are used to study the nonlinear dielectric responses of a confined aqueous film in a planar nanopore under perpendicular electric fields at varied voltages between confining graphene sheets. Dielectric saturation reminiscent of the bulk phase behavior is prevalent at very strong fields, whereas we observe a nonmonotonic permittivity dependence on the electric field at intermediate strengths where field-alignment and spontaneous polarization of interfacial water are of comparable magnitude. The coupling between the two effects results in distinct dielectric responses at opposite confinement walls. The normal component of both the differential dielectric constant and dielectric difference constant tensors averaged over the region closer to the wall under an incoming electric field (field pointing from the liquid to the solid phase) initially increases with the strength of the imposed field. The differential permittivity peaks at a field strength previously shown to offset the surface-induced orientation bias of hydration molecules at this wall. Further strengthening of the field results in a conventional saturation behavior. At the opposite wall (subject to outgoing field) and in the central region of the water slab, the nonlinear dielectric response resembles bulklike saturation. The conditions at the permittivity extremum coincide with the window of accelerated reorientation rates of interfacial water molecules under an incoming field we uncovered in earlier molecular dynamics analyses.

Chemistry↗

Observation of cupratelike nonlinear terahertz responses in superconducting infinite-layer nickelates via two-dimensional coherent spectroscopy

The 𝑑-wave pairing symmetry in newly discovered infinite-layer nickelates remains highly debated compared to the widely accepted 𝑑-wave superconductivity in cuprates, despite recent intense efforts using equilibrium optical and electrical transport measurements. A complementary approach involves characterizing THz coherent nonlinear responses, which is currently lacking but needed, as it would offer new insights into the superconducting gap structure by characterizing Higgs modes and quasiparticle excitations. Here, in this study, we report THz 2D coherent spectroscopy (THz-2DCS) responses from the superconducting state in an infinite-layer nickelate. The 2D spectra clearly demonstrate the absence of hallmark signatures of 𝑠-wave pairing symmetry, such as resonant 2⁢Δ peaks at superconducting gaps. Instead, we observe gapless 2D spectra in the nickelate, centered around the THz driving frequency, with no noticeable shift as the temperature increases. These findings closely resemble the nodal superconductivity behavior expected in cuprates. Together with our simulations, these findings suggest that 2⁢Δ signatures in the 2D spectra of 𝑑-wave gap structures can be obscured by significant nodal quasiparticle excitations at arbitrarily low energies. This contrasts with the long-lived Higgs modes, observed as distinct 2⁢Δ peaks in a controlled THz-2DCS experiment on niobium, a representative example of dirty-limit s-wave superconductors. Our results have implications for understanding the unconventional superconductivity in nickelates and highlight the need to explore their coherent nonlinear dynamics.

Pairing mechanisms↗

Inverse design of cellular structures with the targeted nonlinear mechanical response

Advanced additive manufacturing capabilities have enabled a transformational ability to create sophisticated cellular structures using diverse materials. By altering the topology of the unit cell, the mechanical behavior, such as the stress-strain response during compression, can be modulated. Nevertheless, identifying a printable topology within an enormous design space that would precisely deliver the targeted nonlinear material response is challenging. We propose a data-driven generative framework based on a conditional variational autoencoder (cVAE) architecture that can inverse design the cellular structure based on the intended nonlinear stress-strain response. Trained on a dataset of structure-property pairs, the cVAE learns a compact and expressive latent space that enables efficient mapping from targets to feasible geometries. Two inference modes are explored: (1) decoder-only generation, which enables the exploration of diverse designs conditioned solely on the desired mechanical response, and (2) encoder-decoder generation, which further allows for the incorporation of desired topologies, ensuring the generated structure conforms to both mechanical properties and to desired-topology constraints. The results demonstrate that the model can generate structurally plausible and mechanically accurate designs, with the predicted stress-strain curves closely matching the targets. Even under joint conditioning, the model effectively balances geometric fidelity and functional performance.

36 MATERIALS SCIENCE↗

Giant nonlinear optical responses from photon-avalanching nanoparticles

Avalanche phenomena use steeply nonlinear dynamics to generate disproportionately large responses from small perturbations, and are found in a multitude of events and materials. Photon avalanching enables technologies such as optical phase-conjugate imaging, infrared quantum counting and efficient upconverted lasing. However, the photon-avalanching mechanism underlying these optical applications has been observed only in bulk materials and aggregates, limiting its utility and impact. In this study we report the realization of photon avalanching at room temperature in single nanostructures-small, Tm 3+ -doped upconverting nanocrystals-and demonstrate their use in super-resolution imaging in near-infrared spectral windows of maximal biological transparency. Avalanching nanoparticles (ANPs) can be pumped by continuous-wave lasers, and exhibit all of the defining features of photon avalanching, including clear excitation-power thresholds, exceptionally long rise time at threshold, and a dominant excited-state absorption that is more than 10,000 times larger than ground-state absorption. Beyond the avalanching threshold, ANP emission scales nonlinearly with the 26th power of the pump intensity, owing to induced positive optical feedback in each nanocrystal. This enables the experimental realization of photon-avalanche single-beam super-resolution imaging with sub-70-nanometre spatial resolution, achieved by using only simple scanning confocal microscopy and without any computational analysis. Pairing their steep nonlinearity with existing super-resolution techniques and computational methods, ANPs enable imaging with higher resolution and at excitation intensities about 100 times lower than other probes. The low photon-avalanching threshold and excellent photostability of ANPs also suggest their utility in a diverse array of applications, including sub-wavelength imaging and optical and environmental sensing.

36 MATERIALS SCIENCE↗

Green’s Function Perspective on the Nonlinear Density Response of Quantum Many-Body Systems

We derive equations of motion for higher order density response functions using the theory of thermodynamic Green’s functions. We also derive expressions for the higher order generalized dielectric functions and polarization functions. Moreover, we relate higher order response functions and higher order collision integrals within the Martin–Schwinger hierarchy. We expect our results to be highly relevant to the study of a variety of quantum many-body systems such as matter under extreme temperatures, densities, and pressures.

Density Functional Theory↗

Heterogeneous Cluster Energetics and Nonlinear Thermodynamic Response in Supercritical Fluids

Microstructural heterogeneities arising from molecular clusters directly affect the nonlinear thermodynamic properties of supercritical fluids. We present a physical model to elucidate the relation between energy exchange and heterogeneous cluster dynamics during the transition from liquidlike to gaslike conditions. By analyzing molecular-dynamics data and employing physical principles, the model considers contributions from three key processes, namely, changing cluster density, cluster separation, and transfer of molecules between clusters. We show that the proposed model is consistent with the energetics at subcritical conditions and can be used to explain the nonlinear behavior of thermodynamic response functions, including the peak in the isobaric heat capacity.

42 ENGINEERING↗