Materials Science
A Hybrid Quantum Neural Network to Analyse Big Experimental Powder X-ray Diffraction Data
H. Dong, S.D.M. Jacques, M.Q. Hlatshwayo et al. (+4 more)
Quantitative analysis of experimental powder X-ray diffraction data remains challenging when evaluating complex multiphase materials and noisy measurements. We introduce a hybrid
quantum neural network framework designed to extract quantitative parameters, such as phase weight fractions and scale factors, directly from one-dimensional powder diffraction patterns without iterative refinement. The model combines noise-aware classical simulator pre-training with fast downstream fine-tuning on
quantum processing unit features, ensuring stability against hardware decoherence. We demonstrate the practical utility of this approach by deploying the trained network onto an IBM
quantum computer to analyse experimental X-ray diffraction computed
tomography datasets from a three-phase solid oxide fuel
cell containing ca. 10,000 patterns and a four-phase lithium-ion battery containing ca. 20,000 patterns). The network successfully reconstructs quantitative spatial phase maps in strong agreement with classical Rietveld refinement, paving the way for using
quantum computing hardware to analyse real-world materials characterisation data.
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All authors H. Dong, S.D.M. Jacques, M.Q. Hlatshwayo, E. Papoutsellis, K. Georgopoulos, A. M. Beale, A. Vamvakeros
Materials Science
From Ferroionic Instability to Domain Patterns at an Exposed Surfaces of Multiaxial Ferroelectrics
Sergei V.Kalinin
We analyze the formation of domain structures in multiaxial ferroelectrics with an open, electrochemically compensated surface. The model combines vector polarization, surface electrochemistry, electrostatics, compatible strain, and competitive adsorption on common sites. We construct homogeneous phase maps and analyze polarization instabilities, first assuming perturbations that are uniform through the film thickness and then allowing depth-dependent polarization profiles. Nonlinear continuation follows the growth of these modulations into developed domains. Optimization of their period and tests of their stability establish how the initial instability wavelength relates to the preferred spacing of an established domain structure. We also consider surface ordering above a stable, weakly anisotropic bulk as a constitutive limit relevant to ferroelectric relaxors, providing insight into possible origins of their periodic surface modulations. Surface energies with the same quadratic terms can produce the same initial instability but favor different developed states, including periodic domains and uniform in-plane polarization. This analysis provides a procedure for connecting the initial development of ferroelectric modulations to amplitude selection, wavelength adjustment, and the subsequent
evolution of the resulting domain structures.
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Materials Science
Polymer-free Assembly of Unencapsulated van der Waals Heterostructure Devices
Han Xuan Wong, Junjie Yu, Yuyi Yan et al. (+2 more)
Van der Waals (vdW)
heterostructures provide a versatile platform for exploring emergent
quantum phenomena, yet their fabrication is often limited by interfacial contamination and incompatibility with surface-sensitive characterization. Here, we demonstrate muscovite mica as a
polymer-free platform for assembling and patterning vdW
heterostructure devices. Mica-mediated transfer enables clean exposed surfaces suitable for atomic-resolution scanning tunneling microscopy (STM) following mild thermal annealing, without aggressive post-processing. Mica also serves as a mechanically robust support for sequential pickup assembly, eliminating intermediate release steps. Furthermore, exfoliated mica flakes function as removable shadow masks for contact deposition, enabling straightforward patterning without conventional lithography. We quantify the temperature dependence of mica-mediated
graphene pickup and demonstrate gate-dependent transport in a three-terminal
graphene/hBN device fabricated using the approach. By integrating transfer, sequential assembly, and contact patterning within a single materials platform, mica provides a simple and accessible route to unencapsulated vdW
heterostructures for surface-sensitive spectroscopy and
quantum-device applications.
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All authors Han Xuan Wong, Junjie Yu, Yuyi Yan, Adam Cronin, Felix R. Fischer
Materials Science
Mechanism of charge transfer and electrostatic field fluctuations in complex metallic alloys
Wai-Ga D. Ho, Wasim Raja Mondal, Swarnava Ghosh et al. (+6 more)
Complex metallic
alloys exhibit rich disorder-driven electronic,
magnetic, and vibrational behavior arising from strong chemical disorder, leading to unconventional structure-property relationships with applications in extreme-environment materials, catalysis, spintronics, and thermoelectrics. Despite their technological relevance, the microscopic nature of charge redistribution and electrostatic fluctuations in chemically disordered
alloys remains incompletely understood. Here, we develop a theoretical framework that uncovers universal statistical trends of disorder-driven charge transfer and Madelung-field fluctuations. Our analytical formalism demonstrates that local charge transfer and electrostatic potentials exhibit Gaussian-like statistics and universal linear charge-potential (qV) correlations emerging directly from the underlying disorder landscape. We identify the physical origin of these correlations in the interplay between electronic screening and impurity scattering and show how their statistical properties depend on carrier density, disorder strength, and compositional complexity. We further derive scaling relations governing qV trends across binary and multicomponent
alloys, including high-
entropy materials. Large-supercell density-functional theory (DFT) calculations show good quantitative agreement with the predicted statistical behavior for representative metallic
alloys. Our results provide a computationally efficient framework for incorporating disorder-driven electrostatic fluctuations into effective-medium electronic-structure theories and establish a statistical-physics foundation for the predictive design of complex
alloys.
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All authors Wai-Ga D. Ho, Wasim Raja Mondal, Swarnava Ghosh, Hanna Terletska, Ka-Ming Tam, Mariia Karabin, Markus Eisenbach, Yang Wang, Vladimir Dobrosavljević
Materials Science · Cross-listed from cond-mat.mes-hall
Bend Contour Electron Tomography (BCET): Quantitative strain and topography mapping
Henry G. Bell, Chenhang Xu, Arthur McCray et al. (+5 more)
Freestanding thin films of
quantum materials naturally develop sub-micrometer, nonuniform strain fields that strongly affect their electronic,
magnetic, and structural properties in both
equilibrium and nonequilibrium conditions. However, current methods to quantitatively resolve these mesoscopic features are primarily restricted to scanning probes, making it challenging for dynamical measurements such as single-shot imaging and femtosecond microscopy. Here, we present a new computational framework which we denote as bend contour electron
tomography (BCET), which efficiently converts bend contours in transmission electron microscope images into quantitative two-dimensional maps of strain and topography. By iteratively minimizing a designed loss function between experimental and simulated bend contour images, BCET retrieves both surface morphology and in-plane strain tensor fields without requiring scanning or diffraction mapping. We applied BCET to freestanding SrTiO$_3$ thin films, demonstrating the successful reconstruction of the local strain distribution and
curvature field with high fidelity. Our approach provides a quantitative framework for characterizing mesoscale structures in freestanding films using wide-field imaging, opening new avenues to investigate how spatial inhomogeneity governs phase transitions and nonequilibrium dynamics in two-dimensional
quantum materials.
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All authors Henry G. Bell, Chenhang Xu, Arthur McCray, Minyong Han, Yicheng Zhuang, Harold Y. Hwang, Colin Ophus, Alfred Zong
Materials Science
Dual-Sublattice Ferromagnetism Driven by Cooperative Double Exchange and Superexchange at NdNiO$_3$/CaMnO$_3$ Interfaces
Sharup Sheikh, Uditha M. Jayathilake, Michael Terilli et al. (+7 more)
Engineering emergent ferromagnetism at correlated-oxide interfaces offers a powerful route to creating collective states that do not exist in the parent materials. Here, we show that interfacial valence reconstruction in NdNiO$_3$/CaMnO$_3$ superlattices generates dual-sublattice ferromagnetism involving both Mn and Ni. Depth-resolved standing-wave X-ray photoelectron spectroscopy reveals enhanced Mn$^{3+}$ character on the CaMnO$_3$ side of the interface and enhanced Ni$^{2+}$ character on the NdNiO$_3$ side, establishing the configurations required for Mn$^{4+}$-O-Mn$^{3+}$ double exchange and Ni$^{2+}$-O-Mn$^{4+}$ superexchange, respectively. At low temperature, element-specific XMCD reveals ferromagnetic responses from both sublattices, with the Ni response concentrated predominantly in the Ni$^{2+}$-derived spectral component that SW-XPS independently shows to be enhanced at the interface. Together, these results show that cooperative double exchange within CaMnO$_3$ and superexchange across the interface couple the Mn and Ni sublattices, providing a general strategy for engineering interfacial ferromagnetism in correlated oxides.
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All authors Sharup Sheikh, Uditha M. Jayathilake, Michael Terilli, Mikhail Kareev, Jay R. Paudel, Arian Arab, Christoph Klewe, Tien-Lin Lee, Jak Chakhalian, Alexander X. Gray
Materials Science · Cross-listed from cond-mat.mes-hall
Singular high-harmonic transport above a quantum threshold
Yugo Onishi, Su-Yang Xu and Liang Fu
We show that Landau-Zener tunneling in a small-gap
insulator produces a singular DC current–voltage relation, and correspondingly, strong high-harmonic generation in AC transport. Remarkably, high-harmonic responses decrease subexponentially with harmonic order, which is parametrically slower than in ordinary conductors and PN diodes. We further derive a scaling law for the current amplitude at frequency $n\omega$ produced by the applied electric field $E$ at fundamental frequency $\omega$. Our work offers a promising route to THz generation based on frequency multiplication in solids.
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Materials Science
Faulted loop nucleation and dopant activation in Al-implanted 4H-SiC
Sabine Leroch, Robert Stella, Andreas Hössinger et al. (+1 more)
We present a molecular dynamics (MD) study of Al implantation in 4H-SiC to determine how implantation temperature and dose affect defect
evolution and dopant activation during annealing. Simulations use the Gao-Weber potential with a Morse Al-SiC interaction reparameterized to density functional theory
diffusion and kick-in/kick-out barriers. At Al concentrations above the saturation limit of ~2e20/cm3, implantation at 900 K promotes interstitial-rich planar clusters already during implantation. During annealing, these clusters trap Al and evolve into faulted interstitial loops, reducing substitutional Al incorporation. In contrast, lower implantation temperatures preserve stronger local disorder that is consumed during epitaxial regrowth, resulting in higher chemical activation within MD-accessible annealing times. Atomistic trajectories show a thermally activated transition to faulted loops once planar clusters reach about 60 interstitials. Rather than nucleating as a single coherent disk, several locally faulted regions form first and subsequently merge. The activation energy is ~1.1 eV for dislocation nucleation and ~2.1 eV for stacking-fault growth. Frank-type loops dominate at high temperature, while transient Shockley partials occur mainly at early stages and below 2000 K. As large planar defects form and dissolve, stable compensating Al-C complexes also emerge. These findings support the experimental hypothesis that secondary defects contribute to the reduced Al activation observed under supersaturation during annealing.
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All authors Sabine Leroch, Robert Stella, Andreas Hössinger, Lado Filipovic
Materials Science
Deformation-induced amorphous complexion transitions elevate strength and ductility
Masoud Ahmadi, Jin Qin, Gabrielle Tiphéne et al. (+6 more)
Grain boundary engineering is a major avenue for tailoring the mechanical behavior of polycrystalline materials. Grain boundary complexions, including amorphous intergranular films, are classically accessed through thermal driving forces and solute segregation. Here, we discover that plastic deformation can drive amorphous complexion transitions at room temperature in a chemically primed nanocrystalline binary CuZr
alloy. High-resolution and four-dimensional scanning transmission electron microscopy reveal that the amorphous complexions preferentially emerge at incoherent twin boundaries. Spatially-resolved electron pair distribution function analysis at the atomic scale, the local-order characterization of amorphous complexions, demonstrates short-range and medium-range order gradients from
crystal-templated interfaces to a metallic-glass-like core. We thus uncover a novel amorphous complexion transformation-induced plasticity mechanism that concurrently increases the yield strength, fracture strain, and tensile toughness about a factor of two relative to a designed reference material. Our findings establish mechanical deformation as a non-thermal pathway to trigger amorphous interfacial states for enhancing damage tolerance in nanostructured metals.
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All authors Masoud Ahmadi, Jin Qin, Gabrielle Tiphéne, Mohamed Charai, Alejandro Gómez-Pérez, Khalid Hoummada, Thomas Pardoen, Matteo Ghidelli, Hosni Idrissi
Materials Science · Cross-listed from cond-mat.str-el
Spacetime Dynamics of Altermagnetic Magnons
Ali Emami Kopaei, Karthik Subramaniam Eswaran and Krzysztof Wohlfeld
Distinguishing altermagnetism from conventional ferromagnetism and antiferromagnetism typically relies on momentum-space probes. Here, we show that the real-space spreading of a localized
spin excitation provides a distinctive dynamical fingerprint of altermagnetic order. Using linear
spin-wave theory on a two-dimensional checkerboard
lattice with nearest-neighbor and next-nearest-neighbor couplings J_1 and J_2, we demonstrate that finite J_2 produces direction-dependent
magnon group velocities and splits the two
magnon branches. The resulting propagation remains closer to that of an antiferromagnet than a ferromagnet, retaining an approximately circular outer wavefront, while the direction-dependent
magnon velocities produce a pronounced cross-like spatial structure inside this front. We further show that changing the sign of J_2 to enter the unfrustrated regime (J_2<0) increases the characteristic propagation velocities and interchanges the diagonal directions of enhanced propagation, corresponding to a pi/2 rotation of the anisotropic spatial pattern. These results establish spacetime dynamics as a complementary probe of altermagnetic
magnons, providing a route to identifying unconventional
magnetic order through real-space propagation patterns in solid-state and synthetic
quantum systems.
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Materials Science
A Gaussian process coarse-grained potential for Na-montmorillonite
Yalda Pedram, Yaoting Zhang, Laurent Brochard et al. (+2 more)
Hydraulic transport in compacted bentonite is
diffusion-controlled and governed by the hydration and microstructure of sodium montmorillonite (Na-MMT). Experiments cannot resolve how platelet interactions govern pore structure, transport and stiffness, while existing coarse-grained models smooth hydration oscillations or require manual corrections. We develop a tabulated potential combining Morse interactions between platelet centre and edge sites with a Gaussian process regression correction trained on all-atom potentials of mean force. It captures the hydration-induced complexity of the potential-of-mean-force profiles, including the three-water (3-W) hydration minimum and transfers across geometries, layer-charge variants and unseen configurations. Applied to monodisperse and polydisperse Na-MMT assemblies at dry densities of 0.8-1.3 g cm^-3, the model captures the 3-W to 1-W transition, loss of non-interlayer porosity and
evolution of pore structure, random-walk tortuosity,
diffusion and stiffness. Predicted
diffusion agrees with compacted Na-bentonite measurements.
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All authors Yalda Pedram, Yaoting Zhang, Laurent Brochard, Chang Seok Kim, Laurent Karim Béland
Materials Science
First-principles theory of phonon renormalization from nonlinear electron-phonon interactions
Florian Kluibenschedl, Matthew Houtput, Jacques Tempere et al. (+3 more)
Electron-
phonon interactions renormalize
phonon frequencies and lifetimes and are central to the dynamical properties of solids. While these effects are usually described within linear electron-
phonon coupling, the role of nonlinear electron-
phonon interactions for
phonon properties remains largely unexplored. In this work, we study
phonon renormalization arising from the long-range linear one-electron-one-
phonon and the nonlinear one-electron-two-
phonon interactions within a diagrammatic framework. We derive the corresponding self-energy diagrams, which depend on the chemical potential and temperature, and evaluate them from first principles for the two polar
semiconductors LiF and KTaO$_3$. In both materials, the two interaction channels renormalize the
phonon spectrum in qualitatively distinct ways. The linear contribution is sharply localized near the Brillouin-zone center, whereas the nonlinear process couples an incoming
phonon to other branches throughout the spectrum. As a result, it renormalizes
phonons across the entire Brillouin-zone, with a pronounced temperature dependence governed by the thermal occupation of those branches. This behavior provides a clean experimental signature of the one-electron-two-
phonon coupling. While the nonlinear
phonon renormalization is small in LiF, it is somewhat larger in KTaO$_3$, which we attribute to its greater number of thermally populated
phonon branches at room temperature. Our results establish a general framework to assess nonlinear electron-
phonon effects on the
phonon properties in materials with stronger
lattice fluctuations, including soft
semiconductors such as lead-halide perovskites.
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All authors Florian Kluibenschedl, Matthew Houtput, Jacques Tempere, Cesare Franchini, Mikhail Lemeshko, Ragheed Alhyder
Materials Science
Spin-Lattice Dynamics and Interactions in Magnonic Spinels
Hari Paudyal, Yuri Suzuki, Michael E. Flatté et al. (+1 more)
Minimizing
magnetic damping while understanding
spin-
lattice interactions remains a key challenge for magnonics. We show site-specific Al/Li ordering in spinel ferrites drives a ferrimagnetic insulating state, quenching the Fermi-level density of states. Ab initio calculations reveal collective acoustic modes alongside sub-
lattice-selective optical modes on tetrahedral and octahedral networks, providing a microscopic understanding of substitution-driven
spin dynamics. Crucially, the low-frequency
magnon and acoustic
phonon modes intersect, driving strong hybridization for low-loss technologies.
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All authors Hari Paudyal, Yuri Suzuki, Michael E. Flatté, Durga Paudyal
Materials Science
Magnon-Phonon Dynamics in Multidimensional Antiferromagnetic Oxides
Yogendra Limbu, Michael E. Flatté and Durga Paudyal
Antiferromagnetic oxides offer a compelling paradigm for magnonics. Combining ab initio and
spin Hamiltonian modeling, we map Cr2O3 from bulk to monolayer limits, verifying stability via
phonon spectra. Contrary to previously predicted half-metallic ferromagnetic monolayer phases, we conclusively demonstrate that monolayer and bilayer configurations preserve an antiferromagnetic
semiconductor ground state despite systematic gap narrowing. Intersecting
magnon and
phonon branches drive strong hybridization, establishing low-dimensional Cr2O3 as an ideal platform for
quantum spintronics.
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Materials Science · Cross-listed from cond-mat.str-el
Multiconfigurational Analysis of Local Electronic Structure of $\mathrm{RuO_2}$ Using Relativistic Embedded Clusters
Zhosan I. A., Lomachuk Yu. V., Maltsev D. A. et al. (+2 more)
We present a multiconfigurational, relativistic embedded-cluster study of the local electronic structure of ruthenium dioxide ($\mathrm{RuO_2}$), a candidate altermagnetic material. Starting from free $\mathrm{Ru}$ ions, we progressively build up the local environment through a $\mathrm{Ru+Q_6}$ electrostatic model, a bare $\mathrm{[RuO_6]^{8-}}$ ligand model, and finally a high-accuracy $\mathrm{RuO_6}$@CTEP embedded cluster that reproduces the crystalline surroundings. All systems are treated at the SA-CASSCF and NEVPT2+SOC levels of theory to capture strong electron correlation and
spin-orbit coupling on an equal footing. While the formal local site
symmetry of the $\mathrm{Ru}$ sites in $\mathrm{RuO_2}$ is orthorhombic ($D_{2h}$), we find that the calculated $4d$-orbital energy spectrum and its splitting pattern behave much closer to the higher tetragonal ($D_{4h}$)
symmetry, preserving a strong quasi-degeneracy among the relevant $4d$ orbitals. Since the local $xy$ quadrupolar order responsible for altermagnetic
spin splitting in independent-particle models relies on this
symmetry reduction, its suppression by orbital quasi-degeneracy offers a natural explanation for why altermagnetism is not observed in bulk $\mathrm{RuO_2}$ experiments, in contrast to the robust altermagnetic signatures reported in strained thin films.
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All authors Zhosan I. A., Lomachuk Yu. V., Maltsev D. A., Moiseev I. A., Andreev O. Yu
Materials Science · Cross-listed from physics.chem-ph
Truncated automatic sparse differentiation for machine learning interatomic potentials
Marcel F. Langer, Adrian Hill and Michele Ceriotti
Machine learning interatomic potentials (MLIPs) learn the mapping from atomic positions to potential energy. The forces, the negative gradient of this energy, drive molecular dynamics and are readily obtained using automatic differentiation. Higher-order derivatives, most notably the Hessian, describe collective motion and allow the direct prediction of experimental observables, but are considered computationally inaccessible for large systems. We suggest a solution: in physical systems, interactions decay with distance, and most MLIPs build on this locality through message passing up to a finite receptive field. This implies both sparsity of higher-order derivatives and their decay with distance. This structure can be exploited using automatic sparse differentiation (ASD). We explain how to compute the sparsity pattern for MLIP derivatives and demonstrate that, for multiple foundation MLIPs, ASD computes full Hessians of large porous materials exactly, but with modest speedups at best. The larger gains come from truncated ASD: discarding small, but nonzero, Hessian entries between distant atoms yields order-of-magnitude speedups with negligible impact on predicted observables.
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Materials Science
Strain-Induced Metal-to-Insulator Transition in Antiferromagnetic SrCrO$_3$ Thin Films
S. Jöhr, A. Carta, J. Moreno et al. (+11 more)
Antiferromagnetic (AF) metals are rare, yet they combine properties attractive for spintronic devices like robustness against stray fields and electrical readout. Among AF metal oxide candidates, SrCrO$_3$ remains largely unexplored due to its notoriously difficult synthesis. In this paper, we demonstrate the growth of high-quality SrCrO$_3$ thin films by magnetron sputtering on substrates that impose a wide range of tensile and compressive strains.
Muon spin relaxation experiments, supported by x-ray
magnetic dichroism, unveil the emergence of an AF phase with dilute
magnetic disorder at low temperatures, while resistivity measurements confirm the simultaneous metallic ground state of SrCrO$_3$ under low strain. As both compressive and tensile strain increase, a metal-to-
insulator transition is induced in the films, while the onset of the
magnetic transition temperature remains unchanged. Moreover, an intriguing resistivity upturn, accompanied by a change in the dominant charge-carrier type, occurs at a temperature that correlates with strain. These observations suggest a complex strain-dependent band structure, with strain-induced Jahn-Teller distortions or tilting of the CrO$_6$ octahedra that emerge depending on the sign of the strain, as inferred from density functional theory calculations.
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All authors S. Jöhr, A. Carta, J. Moreno, A. Suter, Z. Salman, A. Panda, J. Spring, G. De Luca, J. Herrero-Martin, B. Mundet, C. Piamonteze, M. Gabay, C. Ederer, M. Gibert
Materials Science
Tuning the Coercive Field in Ferroelectric Hf0.5Zr0.5O2-Al2O3 Heterostructures via Interfacial Charge Dynamics
Marshall B. Frye, Chanyoung Kim, Jeong-Woo Sun et al. (+8 more)
Interleaving dielectric layers into ferroelectric Hf0.5Zr0.5O2 (HZO) films increases the
memory window (MW) beyond what is accounted for by the dielectric constants. Determining the physical mechanisms behind these MW improvements is critical to reaching the full potential of HZO FeNAND. Here, we show that MW improvements stem from the interfacial charge dynamics enabled by oxygen vacancies at the interlayer interface. X-ray photoelectron spectroscopy(XPS) etching experiments demonstrate increased off-stoichiometry at the interface, with a 2.3x increase in oxygen vacancies. Polarization-dependent XPS and first-order reversal curves(FORC) show that tunneling between interfacial defect states causes a bidirectional internal bias of 0.56MV/cm. The impact of defects is further corroborated through phase-field modeling(PFM), which only recreates the coercive fields, FORC, and internal bias for defect densities and tunneling barrier heights that are consistent with experiment, quantitatively capturing an internal electric field of 0.55 MV/cm. The phase field models are then used to simulate 36 devices with varied charge densities and dielectric thickness to provide a predictive framework for further improvements in the MW of interlayer HZO. These findings redefine the role of defects in ferroelectric HZO from deleterious to engineerable and provide critical insights into how to tune ferroelectric device architectures for improved
memory.
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All authors Marshall B. Frye, Chanyoung Kim, Jeong-Woo Sun, John Wellington-Johnson, Lance Fernandes, Prasanna Venkatesan Ravindran, Bogdan Dryzhakov, TaeYoung Song, Mengkun Tian, Asif I. Khan, Lauren M. Garten
Materials Science · Cross-listed from cond-mat.mes-hall
Disorder-induced modulation of the nonlinear Hall effect in Weyl semimetals
Juan A. Cañas, Daniel A. Bonilla and A. Martín-Ruiz
We study the effects of impurity scattering on the nonlinear Hall response of Weyl semimetals within the semiclassical Boltzmann approach. We derive the rectified and second-harmonic conductivity tensors for a general momentum-dependent transport relaxation time and evaluate this quantity microscopically for short-range, Gaussian, screened Coulomb, and
magnetic impurities. For scalar disorder, the relaxation time is isotropic and chirality independent. The nonlinear Hall response is then determined by the anomalous velocity associated with the Berry
curvature, and a finite net response requires energetically inequivalent Weyl nodes to avoid cancellation between opposite chiralities. Polarized
magnetic impurities lead to a qualitatively different behavior. We find that interference between the first- and second-order Born amplitudes generates a helicity-dependent anisotropic correction to the relaxation time. This anisotropy changes the tensor structure of the nonlinear Hall conductivity and gives rise to a finite second-harmonic current for suitable orientations of the electric field relative to the impurity polarization. For representative parameters, however, the anisotropic contribution is several orders of magnitude smaller than the dominant isotropic response. These results establish how the microscopic form of impurity scattering enters the nonlinear Hall response of Weyl semimetals through the transport relaxation time.
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