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At least 325 records · Page 18

Thermal conductance enhanced via inelastic phonon transport by atomic vacancies at Cu/Si interfaces

Understanding and controlling heat transfer across interfaces has become an important issue for the performance of micro- and nanoscale electronics, as well as achieving a high figure of merit for thermoelectrics. Intrinsic and extrinsic defects can have a significant impact on thermal transport in bulk materials and across interfaces, but the mechanism is not well understood. Here, nonequilibrium molecular dynamics simulations are used to determine the impact of interfacial atomic vacancies on thermal transport across a Cu/Si junction. In contrast to the reduction in thermal transport typically seen with bulk defects, we find that by introducing atomic vacancies at a concentration of 6.3% near the interface in either or both materials, the interfacial thermal conductance can be increased by up to 76%. By controlling the initial positions of the vacancies and keeping track of their movements and population, we find that interfacial thermal transport is dependent on temperature, vacancy concentration, and distribution, and a positive correlation between the conductance and point defect activities (extent of vacancy migration, rate of Frenkel defect creation and annihilation) is observed. Further calculations based on the phonon density of states and normal mode decomposition reveal that the increase in interfacial thermal conductance originates primarily from high-frequency phonons, supported by enhanced inelastic phonon transport which contributes to more than 60% of the increase. Our findings suggest a practical way to manipulate inelastic phonon conversion through the presence of defects, which provides an alternative perspective on improving thermal transport between materials with a large lattice mismatch.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

GPU-Accelerated Solution of the Bethe–Salpeter Equation for Large and Heterogeneous Systems

We present a massively parallel GPU-accelerated implementation of the Bethe–Salpeter equation (BSE) for the calculation of the vertical excitation energies (VEEs) and optical absorption spectra of condensed and molecular systems, starting from single-particle eigenvalues and eigenvectors obtained with density functional theory. The algorithms adopted here circumvent the slowly converging sums over empty and occupied states and the inversion of large dielectric matrices through a density matrix perturbation theory approach and a low-rank decomposition of the screened Coulomb interaction, respectively. Further computational savings are achieved by exploiting the nearsightedness of the density matrix of semiconductors and insulators to reduce the number of screened Coulomb integrals. We scale our calculations to thousands of GPUs with a hierarchical loop and data distribution strategy. The efficacy of our method is demonstrated by computing the VEEs of several spin defects in wide-band-gap materials, showing that supercells with up to 1000 atoms are necessary to obtain converged results. We discuss the validity of the common approximation that solves the BSE with truncated sums over empty and occupied states. In conclusion, we then apply our GW-BSE implementation to a diamond lattice with 1727 atoms to study the symmetry breaking of triplet states caused by the interaction of a point defect with an extended line defect.

Absorption spectra↗

Evolutionary inverse design of defects at graphene 2D lateral interfaces

Grain boundaries (GBs) in two-dimensional (2D) materials often have a profound impact on various material properties from mechanical to optical to electronic, yet predicting all possible GB formations is a challenge. Here, we introduce a workflow based on an evolutionary algorithm for exploring possible GBs formed at a lateral 2D interface. In a departure from conventional genetic algorithm based structure optimization methods, we perform genetic operations in the near interface region that allow us to be computationally efficient. We benchmark our method using graphene, which is a well-studied 2D material with a wide range of point defects. An empirical potential was used as the surrogate of the evolutionary search. More than 11.5 × 106 structures in total were evaluated for 128 GB orientations, and for each orientation, the ten best structures are recorded. A subset of low energy GBs predicted by empirical potential based search was relaxed by first-principles calculations and used to validate the energetic rank order. With the validated formation energy, we rank-ordered the best 128 GB structures and performed a detailed statistical analysis of primitive rings to find the correlation between the ring distribution and the formation energy. We found that for low energy GBs (below 0.5eV/Å), Stone–Wales defects will dominate, while structures with a higher energy (0.5–1.1eV/Å) show an increasing population of heptagons and nine-membered rings to form seven-nine defect pairs. For structures with energy higher than 1.1eV/Å, the percentage of octagons and nine-membered rings increases, which indicates that these two types of rings are not energetically favorable. Our proposed methodology is broadly applicable to explore defective low dimensional materials and represents a powerful tool that enables a systematic search of GBs of lateral interfaces for 2D materials.

Zhang, Jianan↗

Size-dependent radiation damage mechanisms in nanowires and nanoporous structures

Nanostructures with a high density of interfaces, such as in nanoporous materials and nanowires, resist radiation damage by promoting the annihilation and migration of defects. This study details the size effect and origins of the radiation damage mechanisms in nanowires and nanoporous structures in model face-centered (gold) and body-centered (niobium) cubic nanostructures using accelerated multi-cascade atomistic simulations and in-situ ion irradiation experiments. Our results reveal three different size-dependent mechanisms of damage accumulation in irradiated nanowires and nanoporous structures: sputtering for very small nanowires and ligaments, the formation and accumulation of point defects and dislocation loops in larger nanowires, and a face-centered-cubic to hexagonal-close-packed phase transformation for a narrow range of wire diameters in the case of gold nanowires. Smaller nanowires and ligaments have a net effect of lowering the radiation damage as compared to larger wires that can be traced back to the fact that smaller nanowires transition from a rapid accumulation of defects to a saturation and annihilation mechanism at a lower dose than larger nanowires. These irradiation damage mechanisms are accompanied with radiation-induced surface roughening resulting from defect-surface interactions. Comparisons between nanowires and nanoporous structures show that the various mechanisms seen in nanowires provide adequate bounds for the defect accumulation mechanisms in nanoporous structures with the difference attributed to the role of nodes connecting ligaments in nanoporous structures. Altogether, our results shed light on the compounded, size-dependent mechanisms leading to the radiation resistance of nanowires and nanoporous structures.

36 MATERIALS SCIENCE↗

Role of mechanical stress localizations on the radiation hardness of AlGaN/GaN high electron mobility transistors

Multi-material, multi-layered systems such as AlGaN/GaN high electron mobility transistors (HEMTs) contain residual mechanical stresses that arise from sharp contrasts in device geometry and materials parameters. These stresses, which can be either tensile or compressive, are difficult to detect and eliminate because of their highly localized nature. We propose that their high-stored internal energy makes potential sites for defect nucleation sites under radiation, particularly if their locations coincide with the electrically sensitive regions of a transistor. In this study, we validate this hypothesis with molecular dynamic simulation and experiments exposing both pristine and annealed HEMTS to 2.8 MeV Au +3 irradiation. Our unique annealing process uses mechanical momentum of electrons, also known as the electron wind force (EWF) to mitigate the residual stress at room temperature. High-resolution transmission electron microscopy and cathodoluminescence spectra reveal the reduction of point defects and dislocations near the two-dimensional electron gas region of EWF-treated devices compared to pristine devices. The EWF-treated HEMTs showed relatively higher resilience with approximately 10% less degradation of drain saturation current and ON-resistance and 5% less degradation of peak transconductance. Both mobility and carrier concentration of the EWF-treated devices were less impacted compared to the pristine devices. Our results suggest that the lower density of nanoscale stress localization contributed to the improved radiation tolerance of the EWF-treated devices. Intriguingly, the EWF is found to modulate the defect distribution by moving the defects to electrically less sensitive regions in the form of dislocation networks, which act as sinks for the radiation induced defects and this assisted faster dynamic annealing.

AlGaN/GaN HEMTs↗

High Thermoelectric Performance through Crystal Symmetry Enhancement in Triply Doped Diamondoid Compound Cu 2 SnSe 3

The presence of high crystallographic symmetry and nanoscale defects are favorable for thermoelectrics. With proper electronic structures, a highly symmetric crystal tends to possess multiple carrier channels and promote electrical conductivity without sacrificing Seebeck coefficient. In addition, nanoscale defects can effectively scatter acoustic phonons to suppress thermal conductivity. Here, we report that the triple doping of Cu 2 SnSe 3 leads to a high ZT value of 1.6 at 823 K for Cu 1.85 Ag 0.15 (Sn 0.88 Ga 0.1 Na 0.02 )Se 3 , and a decent average ZT (ZT ave ) value of 0.7 is also achieved for Cu 1.85 Ag 0.15 (Sn 0.93 Mg 0.06 Na 0.01 )Se 3 from 475 to 823 K. Our study reveals: (1) Ag doping on Cu sites generates numerous point defects and greatly decreases lattice thermal conductivity. (2) Doping Mg or Ga converts the monoclinic Cu 2 SnSe 3 into a cubic structure. This symmetry enhancing leads to increase in the effective mass from 0.8 m e to 2.6 m e (m e , free electron mass) and the power factor from 4.3 μW/cm –1 K –2 for Cu 2 SnSe 3 to 11.6 μW/cm –1 K –2 . (3) Na doping creates dense dislocation arrays and nanoprecipitates, which strengthens the phonon scattering. (4) Pair distribution function analysis shows localized symmetry breakdwon in the cubic Cu 1.85 Ag 0.15 (Sn 0.88 Ga 0.1 Na 0.02 )Se 3 . Furthermore, the present work provides a standpoint to design promising thermoelectric materials by synergistically manipulating crystal symmetry and nanoscale defects.

36 MATERIALS SCIENCE↗

Thermal diffusivity recovery and defect annealing kinetics of self-ion implanted tungsten probed by insitu transient grating spectroscopy

Tungsten is a promising candidate material for plasma-facing armour components in future fusion reactors. A key concern is irradiation-induced degradation of its normally excellent thermal transport properties. In this comprehensive study, thermal diffusivity degradation in ion-implanted tungsten and its evolution from room temperature (RT) to 1073 K is considered. Five samples were exposed to 20 MeV self-ions at RT to achieve damage levels ranging from 3.2 x 10 -4 to 3.2 displacements per atom (dpa). Transient grating spectroscopy with in-situ heating was then used to study thermal diffusivity evolution as a function of temperature. Using a kinetic theory model, an equivalent point defect density is estimated from the measured thermal diffusivity. The results showed a prominent recovery of thermal diffusivity between 450 K and 650 K, which coincides with the onset of mono-vacancy mobility. After 1073 K annealing samples with initial damage of 3.2 x 10 -3 dpa or less recover close to the pristine value of thermal diffusivity. For doses of 3.2 x 10 -2 dpa or higher, on the other hand, a residual reduction in thermal diffusivity remains even after 1073 K annealing. Transmission electron microscopy reveals that this is associated with extended, irradiation-induced dislocation structures that are retained after annealing. A sensitivity analysis shows that thermal diffusivity provides an efficient tool for the assessing total defect content in tungsten up to 1000 K.

36 MATERIALS SCIENCE↗

Plasmonic Energetic Electrons Drive CO 2 Reduction on Defective Cu 2 O

Plasmonic photoreduction of CO 2 is valuable for decarbonization and producing value-added chemicals. However, insights into the mechanisms of this reaction remain elusive, particularly regarding the roles of structural defects and their interplay with the nonequilibrium charge carriers. Here, we report density functional theory calculations on Cu 2 O, a prototype photocatalyst, through which we investigate CO 2 reduction over three defected facets to reveal the interfacial charge transfer and bond dynamics under plasmonic excitation. We find that the activation barrier of C–O bond cleavage decreases from 3.2 to about 1 eV, assisted by oxygen vacancies, and that the remaining barrier can be further reduced or eliminated at the plasmon-excited states when Cu 2 O is integrated with plasmonic metals. The regeneration of oxygen vacancies (by H 2 to form water) on Cu 2 O to complete the catalysis cycle is feasible and not affected by the energetic electrons. Furthermore, our calculations thus show the important synergistic effect of energetic electrons and point defects to promote CO 2 reduction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Origins of the change in mechanical strength of silicon/gold nanocomposites during irradiation

Abstract Silicon-based layered nanocomposites, comprised of covalent-metal interfaces, have demonstrated elevated resistance to radiation. The amorphization of the crystalline silicon sublayer during irradiation and/or heating can provide an additional mechanism for accommodating irradiation-induced defects. In this study, we investigated the mechanical strength of irradiated Si-based nanocomposites using atomistic modeling. We first examined dose effects on the defect evolution mechanisms near silicon-gold crystalline and amorphous interfaces. Our simulations reveal the growth of an emergent amorphous interfacial layer with increasing dose, a dominant factor mitigating radiation damage. We then examined the effect of radiation on the mechanical strength of silicon-gold multilayers by constructing yield surfaces. These results demonstrate a rapid onset strength loss with dose. Nearly identical behavior is observed in bulk gold, a phenomenon that can be rooted to the formation of radiation-induced stacking fault tetrahedra which dominate the dislocation emission mechanism during mechanical loading. Taken together, these results advance our understanding of the interaction between radiation-induced point defects and metal-covalent interfaces.

36 MATERIALS SCIENCE↗

Improving the laser performance of ion beam sputtered dielectric thin films through the suppression of nanoscale defects by employing a xenon sputtering gas

Laser damage-prone precursors in high index materials such as hafnia are believed to be the primary limiter in the performance of dielectric multilayer films to advance ultra-high power and energy laser applications. Removing or suppressing these precursors is the key to fabricating laser damage resistant thin films for the enabling technologies. Early work has revealed that nanobubbles formed by entrapped argon (Ar) working gas in ion beam sputtering (IBS) produced hafnia films are primarily responsible for the onset of laser damage upon exposure to UV, ns-laser pulses. In this study, we demonstrate that the UV ns-laser damage onset of IBS produced hafnia films can be improved to 3.1 +/- 0.2 J/cm 2 by substituting the conventional Ar working gas with xenon (Xe), a nearly 1 J/cm 2 increase from that of the Ar produced hafnia films. In addition to the suppression of the overall point-defect density of the hafnia films, the reduction of the Xe entrapment eliminates the nanobubbles and the generation of plasmas that initiates the laser damage. The defect suppression and its correlation to the increase in laser damage threshold is revealed by the combined analysis of Rutherford backscattering spectroscopy, electron paramagnetic resonance spectroscopy, transmission electron microscopy, and laser damage testing. Monte Carlo simulations suggest a much smaller entrapment of Xe gas by comparison to Ar, which is attributed to the significant difference in the energy of the reflected neutrals (3X) which are likely to be implanted. These results provide an effective process route with a fundamental understanding for producing high laser damage resistant dielectric films for high power and high energy laser applications.

36 MATERIALS SCIENCE↗

Quantum Mechanical Evaluation of CZTS Properties for Photovoltaic Applications

As a quaternary semiconductor, CZTS (Cu 2 ZnSnS 4 ) shows promise as a thin-film solar cell material. The constituent elements in CZTS are abundant and non-toxic, and CZTS has an ideal band gap (~1.5 eV) for solar cell applications, which produces a large absorption coefficient. Unfortunately, the low efficiencies and difficulties in synthesizing the desired crystallographic phase (kesterite) and the associated formation of antisite defects limit its deployment. Using theoretical and computational tools, we investigated these current limitations, explored strategies to resolve these issues, and developed design guidelines to improve the efficiency of CZTS-based sunlight absorbers. We first sought to understand the challenges associated with synthesizing the kesterite phase and proposed ways to favor kesterite growth, thus adding to the understanding of CZTS photovoltaics. We also analyzed the major limitations at the atomic scale lowering the efficiency of CZTS: the low open-circuit voltage (V oc ) and the short carrier lifetime, thus addressing the technical effectiveness of CZTS photovoltaics. We believe the latter is due to Shockley-Read-Hall (SRH) recombination centers associated with point defects. We also studied the electronic structure of interfaces and defects introducing such recombination centers, and explored doping strategies to reduce SRH recombination. Ultimately, these efforts will benefit the public by contributing to the development of cheap and efficient solar energy conversion technologies made from abundant, non-toxic materials.

14 SOLAR ENERGY↗

Spectral quadrature for the first principles study of crystal defects: Application to magnesium

In this work, we present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing non-local pseudopotentials, local reformulation of electrostatics, and truncation of the spatial Kohn-Sham Hamiltonian, and the Linear Scaling Spectral Quadrature method to solve for the pointwise electronic fields in real-space and the non-local component of the atomic force, we develop a parallel finite difference framework suitable for distributed memory computing architectures to simulate non-periodic systems embedded in a bulk environment. Choosing examples from magnesium-aluminum alloys, we first demonstrate the convergence of energies and forces with respect to spectral quadrature polynomial order, and the width of the spatially truncated Hamiltonian. Next, we demonstrate the parallel scaling of our framework, and show that the computation time and memory scale linearly with respect to the number of atoms. Next, we use the developed framework to simulate isolated point defects and their interactions in magnesium-aluminum alloys. Our findings conclude that the binding energies of divacancies, Al solute-vacancy and two Al solute atoms are anisotropic and are dependent on cell size. Furthermore, the binding is favorable in all three cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Atomistic modeling of meso -timescale processes with $\mathrm{SEAKMC}$: A perspective and recent developments

On-the-fly kinetic Monte Carlo (kMC) methods have recently garnered significant attentions after successful applications to various atomic-scale problems using a timescale outside the reach of classical molecular dynamics. These methods play a critical role in modeling atomistic meso-timescale processes, and it is therefore essential to further improve their capabilities. In this report we review one of the on-the-fly kMC methods, Self-Evolving Atomistic kinetic Monte Carlo (SEAKMC) and propose two schemes that considerably enhance the efficiency of saddle point searches (SPSs) during the simulations. The performance of these schemes is tested using the diffusion of point defects in bcc Fe. In addition, we discuss approaches to significantly mitigate limitations of these schemes, which further improves their efficiencies. Importantly, these schemes improve the SPS efficiency not only for SEAKMC but also for other on-the-fly kMC methods, broadening the applications of on-the-fly kMC simulations to complex meso-timescale problems.

36 MATERIALS SCIENCE↗

Band gap and electronic structure of defects in the ternary nitride BP 3 N 6 : experiment and theory

Recent advances in methods to access nitride systems by a high-pressure high-temperature approach have made possible the one-step synthesis of mixed ternary non-metal nitrides. As a prerequisite to use in a practical device, it is important to understand important bulk electronic properties, such as the band gap, as well as characterizing the presence and effect of defects that are present. In this work, the novel ternary nitride BP 3 N 6 is studied using techniques sensitive to the partial electronic density of states, specifically X-ray absorption spectroscopy and X-ray emission spectroscopy. Complementary full-potential all-electron density functional theory (DFT) calculations allow important bulk electronic parameters, such as the band gap, to be elucidated. The band gap of BP 3 N 6 has been determined to be 3.9 ± 0.2 eV and 4.1 ± 0.4 eV at the B K- and N K-edges, respectively. This is close to a theoretical value of 4.3 eV predicted by the PBEsol exchange–correlation functional and considerably less than a value of 5.8 eV predicted by the modified Becke–Johnson exchange–correlation functional. X-Ray excited optical luminescence (XEOL) measurements are performed to interrogate the presence of point defects in this system. Together with DFT calculations, these measurements reveal the presence of nitrogen vacancies which lead to multiple mid-gap trap states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Energy migration and scintillation kinetics in compositionally complex (Gd 1/4 Y 1/4 Tb 1/4 Lu 1/4 ) 3 Al 5 O 12 :Ce single crystal scintillator

It is well-established that compositional tuning through binary admixture can improve scintillation performance in several materials systems, including Ce-activated garnets. Although recent work on ternary or quaternary cation admixture shows promise, the impact of this increased compositional complexity on thermal stability and carrier-defect dynamics has not been addressed. Here, we investigate a compositionally complex garnet, (Gd 1/4 Y 1/4 Tb 1/4 Lu 1/4 ) 3 Al 5 O 12 :Ce (GYTLAG), grown by the Czochralski method using temperature-dependent photoluminescence (PL), PL decay, and thermoluminescence (TL). PL and PL decay measurements support a thermally activated Tb 3+ -Ce 3+ energy transfer, where Tb 3+ emission dominates below 60 K, but Ce 3+ emission increases from 20-300 K. Thermal quenching of Ce 3+ emission occurs around T 50 = 508 K, with an activation energy of 0.6 eV. TL and wavelength-resolved TL spectra from 20–500 K show that GYTLAG contains similar trap groups to LuAG but with a broader distribution of glow peaks below room temperature, possibly caused by quaternary cation mixing. A combination of dose dependence, partial cleaning and initial rise, and glow curve fitting to a first order continuous Gaussian distribution model are used to understand the contribution of electronic point defects to scintillation decay and afterglow at room temperature. Furthermore, these results inform how increased compositional complexity influences recombination dynamics in garnet scintillators.

Compositionally complex↗

Trap characterization of high-growth-rate laser-assisted MOCVD GaN

A detailed study comparing defect incorporation between laser-assisted metal-organic chemical vapor deposition (MOCVD)-grown GaN and conventional low- and high-growth-rate MOCVD GaN was conducted. Using deep-level transient and optical spectroscopy, traps throughout the bandgap were characterized where traps were found at EC-0.25 eV, EC-0.57 eV, EC-0.72 eV, EC-0.9 eV, EC-1.35 eV, EC-2.6 eV, and EC-3.28 eV in all three samples. This indicates no new traps were observed in the laser-assisted MOCVD GaN sample. Overall, the trap concentrations in the laser-assisted MOCVD sample were ∼2× higher than the optimal low-growth-rate sample, but this is primarily due to the increase in gallium vacancy EC-2.6 eV and carbon-related EC-3.28 eV trap concentrations. The EC-0.9 eV trap concentration was ∼2× higher in the laser-assisted sample, so proton irradiation experiments were conducted to identify the physical source of this level. The results indicated this was a native point defect likely related to gallium interstitials. Overall, this study shows that the laser-assisted MOCVD growth method is promising for future thick, high-quality GaN epilayers after further growth optimizations.

Physics↗

Impact of metal diffusion, lattice distortions, native defects, and ambient on dielectric breakdown in Ni–Ga 2 O 3 Schottky diodes

Ga 2 O 3 unipolar devices are of high interest due to their ~8 MV/cm predicted breakdown fields, which have not yet been achieved due to premature device failure. Pre- and post-failure defect analysis of Ni–Ga 2 O 3 Schottky diodes in ultrahigh vacuum (UHV) and air were performed using depth-resolved cathodoluminescence, high angle annular dark field scanning transmission electron microscopy, and energy dispersive x-ray analysis to understand the physical mechanisms that precede premature breakdown. The breakdown voltage in UHV was dramatically reduced by nearly 40% compared with the breakdown in air. This reduction in the breakdown voltage correlated with post-breakdown differences in Ni distribution, indicating that the coordination and bonding of Ni contribute strongly to electrical behavior in Ni–Ga 2 O 3 Schottky diodes. Breakdown studies in UHV revealed that Ni diffuses away more from the metal–semiconductor interface than with air breakdown, where Ni localizes more near the interface, indicative of the preferential formation of a Ni oxide under O-poor conditions. These measurements also identified the formation of divacancy-interstitial complexes and their characteristic luminescence signature ~150 nm from the interface, the densities of which correlated with breakdown fields. These findings show that electric-field-induced degradation occurs via the rearrangement of native point defects, which act as an additional precursor to device failure. Macroscopically, they show the impact of both vacuum conditions and metal reactivity on Ga 2 O 3 device fabrication.

36 MATERIALS SCIENCE↗

Imaging the Breakdown and Restoration of Topological Protection in Magnetic Topological Insulator MnBi 2 Te 4

Quantum anomalous Hall (QAH) insulators transport charge without resistance along topologically protected chiral 1D edge states. Yet, in magnetic topological insulators to date, topological protection is far from robust, with zero-magnetic field QAH effect only realized at temperatures an order of magnitude below the Néel temperature T N , though small magnetic fields can stabilize QAH effect. Understanding why topological protection breaks down is therefore essential to realizing QAH effect at higher temperatures. Here a scanning tunneling microscope is used to directly map the size of exchange gap (E g,ex ) and its spatial fluctuation in the QAH insulator 5-layer MnBi 2 Te 4 . Long-range fluctuations of E g,ex are observed, with values ranging between 0 (gapless) and 70 meV, appearing to be uncorrelated to individual surface point defects. The breakdown of topological protection is directly imaged, showing that the gapless edge state, the hallmark signature of a QAH insulator, hybridizes with extended gapless regions in the bulk. Finally, it is unambiguously demonstrated that the gapless regions originate from magnetic disorder, by demonstrating that a small magnetic field restores E g,ex in these regions, explaining the recovery of topological protection in magnetic fields. The results indicate that overcoming magnetic disorder is the key to exploiting the unique properties of QAH insulators.

36 MATERIALS SCIENCE↗