Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Defect tolerance”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Heterogeneous doping via nanoscale coating impacts the mechanics of Li intrusion in brittle solid electrolytes

Lithium dendrite intrusion in solid-state batteries limits fast charging and causes short-circuiting, yet the underlying regulating mechanisms are not well-understood. Here, in this work, we discover that heterogeneous Ag + doping dramatically affects lithium intrusion into Li 6.6 La 3 Zr 1.6 Ta 0.4 O 12 (LLZO), a brittle solid electrolyte. Nanoscale Ag + doping is achieved by thermally annealing a 3-nm-thick metallic coating on LLZO, inducing Ag–Li ion exchange and Ag diffusion into grains and grain boundaries. Density functional theory calculations and experimental characterization show negligible impact on the electronic properties and surface wettability from Ag + incorporation. Mechanically, nanoindentation experiments show a fivefold increase in the mechanical force required to fracture the surface Ag + -doped LLZO, indicating substantial doping-induced surface toughening. Operando microprobe scanning electron microscopy experiments show that the Ag + -doped LLZO surface exhibits improved lithium plating at >250 mA cm −2 and an electroplating diameter that is expanded by over fourfold, even under an extreme indentation stress of 3 GPa. This demonstrates enhanced defect tolerance in LLZO, rather than electronic or adhesion effects. Our study reveals a chemo-mechanical mechanism via surface heterogeneous doping, complementing present bulk design rules to minimize mechanical failures in solid-state batteries.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Detecting ionizing radiation using halide perovskite semiconductors processed through solution and alternative methods

We report the direct detection of high-energy radiation such as X-rays and.-rays by semiconductors at room temperature is a challenging proposition that requires remarkably pure and nearly perfect crystals. The emergence of metal halide perovskites, defect-tolerant semiconductors, is reviving hope for new materials in this field after an almost 20 year hiatus. Metal halide perovskites, which combine exceptional optoelectronic properties, versatile chemistry and simple synthesis, are challenging traditional approaches for the development of novel semiconductors for detecting hard radiation. We discuss the relevant physical properties, promising materials, fabrication techniques and device architectures for high-performance, low-cost detectors by targeting next-generation semiconductors for radiation detection. We also present a perspective on the impact of such advances in future medical imaging applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Data-driven design of novel halide perovskite alloys

The great tunability of the properties of halide perovskites presents new opportunities for optoelectronic applications as well as significant challenges associated with exploring combinatorial chemical spaces. Here, in this work, we develop a framework powered by high-throughput computations and machine learning for the design and prediction of mixed cation halide perovskite alloys. In a chemical space of ABX 3 perovskites with a selected set of options for A, B, and X species, pseudo-cubic structures with B-site mixing are simulated using density functional theory (DFT) and several properties are computed, including stability, lattice constant, band gap, vacancy formation energy, refractive index, and optical absorption spectrum, using both semi-local and hybrid functionals. Neural networks (NN) are used to train predictive models for every property using tabulated elemental properties of A, B, and X site species as descriptors. Starting from a DFT dataset of 229 points, we use the trained NN models to predict the structural, energetic, electronic, and optical properties of an extensive dataset of 17955 compounds, and perform high-throughput screening in terms of stability, band gap, and defect tolerance, to obtain 392 promising compounds that are ranked as potential absorbers according to their photovoltaic figure of merit. Compositional trends in the screened set of attractive mixed cation halide perovskites are revealed and additional computations are performed on selected compounds. The data-driven design framework developed here is promising for designing novel mixed compositions and can be extended to a wider perovskite chemical space in terms of A, B, and X species, different kinds of mixing at the A, B, or X sites, non-cubic phases, and other properties of interest.

36 MATERIALS SCIENCE↗
DOE OSTI2025

High-throughput and data-driven search for stable optoelectronic AMSe 3 materials

The rapid advancement in emerging optoelectronic technologies demands highly efficient, affordable, and ecofriendly materials. In this context, ternary chalcogenides, especially ternary selenides, show early promise as a material class due to their stability and remarkable electronic, optical, and transport properties. In this work, we integrate first-principles-based high-throughput computations with machine learning (ML) techniques to predict the thermodynamic stability and optoelectronic properties of 920 valency-satisfied selenide compounds. Through investigating polymorphism, our study reveals the edge-sharing orthorhombic Pnma phase (NH 4 CdCl 3 -type) as the most stable structure for most ternary selenides. High-fidelity supervised ML models are trained and tested to accelerate stability and band gap predictions. These data-driven models pin down the most influential features that dominantly control key material characteristics. The multistep high-throughput computations identify the ternary selenides with optimal direct band gaps, light carrier masses, and strong optical absorption edges. The extensive materials screening considering phase stability, toxicity, and defect tolerance, finally identifies the seven most suitable candidates for photovoltaic applications. Two of these final compounds, SrZrSe 3 and SrHfSe 3 , have already been synthesized in a single-phase form, with the latter showing an optically suitable band gap, aligning well with our findings. The non-adiabatic molecular dynamics reveal sufficiently long photoexcited charge carrier lifetimes (on the order of nanoseconds) in some of these selected selenide materials, indicating their exciting characteristics. Overall, our study suggests a robust in silico framework that can be extended to screen large datasets of various material classes for identifying promising photoactive candidates.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Chapter 4: Perovskite Solar Cells

In the following sections of this chapter, we first discuss the structural and optoelectronic properties as well as the defect tolerance of halide perovskites for solar cell applications. We then compare the various common device architectures for PSCs and discuss several perovskite fabrication strategies, including solution deposition and vacuum processes, that are key to preparing high -quality perovskite thin films for high-performance PSCs. Many research and development (R&D) challenges exist that must be addressed to ready PSCs for practical applications. We review key issues on stability (moisture, thermal, light, and chemical compatibility), material toxicity (Pb and Pb-free PSCs), and scaling up (material, device architecture, and coating approach selection). A key focus area for further PSC development is characterization. Since perovskite behaves differently than conventional semiconductors, specific characterization protocols must be established to reliably evaluate the progress among different research groups. Stability characterization needs special attention given the complexity of perovskite in response to various external stress factors. Finally, we provide an outlook on the research trends in PSC development toward commercialization.

coating approach selection↗
DOE OSTI2020

Surface and grain boundary carbon heterogeneity in CH 3 NH 3 PbI 3 perovskites and its impact on optoelectronic properties

Rivaling state-of-the-art crystalline silicon, organic-inorganic hybrid perovskites have been intensely studied in recent years. Surface and interfacial engineering have been a focus for performance improvement. Even though significant progress has been made during the last decade in terms of the diversity and capability of perovskite-based devices, the structure-property relationship, particularly at the surface, which governs the real-world performance of these applications, is still unresolved. In the article, this issue was addressed by employing synchrotron-related experimental measurements, and a mechanism that correlates microstructure with surface chemistry was resolved. As a powerful and highly sensitive spectromicroscopy, soft x ray photoemission electron microscopy (X-PEEM) was used to probe the surface of perovskite films varying in post solvent annealing. Furthermore, static and in situ grazing incidence hard x ray diffraction (GIXD) was used to track the grain growth dynamics during the film formation process. It was found that the nature of the surfaces was dictated by the local chemistry that varied due to mass flow during the development of the microstructure. Combining optical and electronic characterizations, it was confirmed that a more homogenous chemistry, i.e., uniform chemical components and properties, along with reduced strain and grain boundary energies, yielded more defect-tolerant films. Grain boundaries were more favorable for screening carriers than those in the control film. Our findings underscore the importance of the uniformity in the surface for developing a chemistry-structure-property relationship in perovskite materials, as well as engineering local chemistry toward high-performance and stable devices.

42 ENGINEERING↗
DOE OSTI2025

Defect modeling in semiconductors: the role of first principles simulations and machine learning

Abstract Point defects in semiconductors dictate their electronic and optical properties. Vacancies, interstitials, substitutional defects, and defect complexes can form in the semiconductor lattice and significantly impact its performance in applications such as solar absorption, light emission, electronics, and catalysis. Understanding the nature and energetics of point defects is essential for the design and optimization of next-generation semiconductor technologies. Here, we provide a comprehensive overview of the current state of research on point defects in semiconductors, focusing on the application of density functional theory (DFT) and machine learning (ML) in accelerating the prediction and understanding of defect properties. DFT has been instrumental in accurately calculating defect formation energies, charge transition levels, and other defect-related properties such as carrier recombination rates and lifetimes, and ion migration barriers. ML techniques, particularly neural networks, have emerged as powerful tools for enabling rapid prediction of defect properties at DFT-accuracy in order to overcome the expense of using large supercells and advanced functionals. We begin this article with a discussion of different types of point defects and complexes, their impact on semiconductor properties, and the experimental and DFT approaches typically used for their characterization. Through multiple case studies, we explore how DFT has been successfully applied to understand defect behavior across a variety of semiconductors, and how ML approaches integrated with DFT can efficiently predict defect properties and facilitate the discovery of new materials with tailored defect behavior. Overall, the advent of ‘DFT+ML’ promises to drive advancements in semiconductor technology, catalysis, and renewable energy applications, paving the way for the development of high-performance semiconductors which are defect-tolerant or have desirable dopability.

Rahman, Md Habibur (ORCID:000000027705984X)↗
DOE OSTI2020

Regulating off-centering distortion maximizes photoluminescence in halide perovskites

Abstract Metal halide perovskites possess unique atomic and electronic configurations that endow them with high defect tolerance and enable high-performance photovoltaics and optoelectronics. Perovskite light-emitting diodes have achieved an external quantum efficiency of over 20%. Despite tremendous progress, fundamental questions remain, such as how structural distortion affects the optical properties. Addressing their relationships is considerably challenging due to the scarcity of effective diagnostic tools during structural and property tuning as well as the limited tunability achievable by conventional methods. Here, using pressure and chemical methods to regulate the metal off-centering distortion, we demonstrate the giant tunability of photoluminescence (PL) in both the intensity (>20 times) and wavelength (>180 nm/GPa) in the highly distorted halide perovskites [CH3NH3GeI3, HC(NH2)2GeI3, and CsGeI3]. Using advanced in situ high-pressure probes and first-principles calculations, we quantitatively reveal a universal relationship whereby regulating the level of off-centering distortion towards 0.2 leads to the best PL performance in the halide perovskites. By applying this principle, intense PL can still be induced by substituting CH3NH3+ with Cs+ to control the distortion in (CH3NH3)1-xCsxGeI3, where the chemical substitution plays a similar role as external pressure. The compression of a fully substituted sample of CsGeI3 further tunes the distortion to the optimal value at 0.7 GPa, which maximizes the emission with a 10-fold enhancement. This work not only demonstrates a quantitative relationship between structural distortion and PL property of the halide perovskites but also illustrates the use of knowledge gained from high-pressure research to achieve the desired properties by ambient methods.

halide perovskites↗
DOE OSTI2021

Chiral Topological Surface States on a Finite Square Photonic Crystal Bounded by Air

Chiral, topologically protected, photonic surface states can be found at the boundary between gyrotropic photonic crystals where a changing magnetic field induces different topology across the interface. Typically, photonic crystals with either a suitable band structure on both sides of the interface to provide a band gap and evanescent decay of the surface states away from the interface, or an outer layer with engineered material properties is required. In this paper, we show the emergence of topological, unidirectional surface states at the termination of finite gyrotropic photonic crystals with a simple square lattice and C 4 rotational symmetry bounded by a vacuum, eliminating the need for an outside layer to enable chiral surface modes. Here, we start from an infinite, time-reversal-symmetry-breaking photonic crystal with a band gap associated with bands with nonzero Chern numbers, different from all-zero Chern numbers in air. We then modify the photonic crystal to move this band gap below the light line, while maintaining the Chern-number discontinuities. Band-structure calculations for a supercell approximating a photonic crystal finite in the direction normal to the surface demonstrate the existence, dispersion, and chirality of the surface mode. Extensive direct scattering calculations for a point source and spatial Fourier analysis further reveal a unidirectional free-space topological surface state, which propagates counterclockwise around the surface of a finite photonic crystal, providing a nearly foolproof way to cross-check the surface-mode band structure unaffected by backscattering from local defects. Additionally, scattering simulations allow an independent characterization of the state dispersion and unveil the robustness of the topological plasmonic mode propagation around the 90° bends of the structure, being due to only radiation leakage. In contrast to buried topological surface states, the observed surface modes at the photonic crystal–air interface have the advantage of being accessible to the outside world, allowing one to take advantage of the defect-tolerant backscattering-free surface modes to engineer emission from photonic crystal surfaces into arbitrary free-space beam shapes and directions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Increased light-emission efficiency in disordered (In, Ga)N through the correlated reduction of recombination rates

Experiments have shown that the light-emission efficiency of indium gallium nitride (InGaN) lightemitting diodes improves with increasing indium concentration. It is widely thought that compositional fluctuations due to indium incorporation suppress diffusion of carriers to non-radiative centers, thus leading to defect-insensitive emission. However, recent experiments have challenged this hypothesis by revealing unexpectedly long diffusion lengths at room temperature. Here, we demonstrate an alternative mechanism involving the correlated reduction in radiative and nonradiative recombination rates that explains the increase in light-emission efficiency of InGaN with increasing indium concentration, without invoking the suppression of carrier diffusion. Furthermore, our analysis challenges the notion that carrier localization gives rise to defect tolerance in InGaN.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Coherent band-edge oscillations and dynamic longitudinal-optical phonon mode splitting as evidence for polarons in perovskites

The coherence of collective modes, such as phonons and polarons, and their modulation of electronic states is long sought in complex systems, which is a crosscutting issue in photovoltaics and quantum electronics. In photovoltaic cells and lasers based on metal halide perovskites, the presence of polarons, i.e., photocarriers dressed by the macroscopic motion of charged lattice, assisted by terahertz (THz) longitudinal-optical (LO) phonons, has been intensely studied yet is still debated. This may be key for explaining the remarkable properties of the perovskite materials, e.g., defect tolerance, long charge lifetimes, and diffusion lengths. In this work we use the intense single-cycle THz pulse with peak electric field up to E THz = 1000 kV/cm to drive coherent polaronic band-edge oscillations at room temperature in CH 3 NH 3 PbI 3 (MAPbI 3 ). We reveal the oscillatory behavior is dominated by a specific quantized lattice vibration mode at $ω$ LO ~ 4 THz, which is both dipole and momentum forbidden. THz-driven coherent polaron dynamics exhibits distinguishing features: room temperature coherent oscillations at ω LO longer than 1 ps in both single crystals and thin films, mode-selective modulation of different band-edge states assisted by electron-phonon interaction, and dynamic mode splitting at low temperature due to entropy and anharmonicity of organic cations. Our results demonstrate intense THz-driven coherent band-edge modulation is a powerful probe of electron-lattice coupling phenomena and polaronic quantum control in perovskites.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Temporally decoherent and spatially coherent vibrations in metal halide perovskites

The long carrier lifetime and defect tolerance in metal halide perovskites (MHPs) are major contributors to the superb performance of MHP optoelectronic devices. Large polarons were reported to be responsible for the long carrier lifetime. Yet microscopic mechanisms of the large polaron formation, including the so-called phonon melting, are still under debate. In this study, time-of-flight inelastic neutron scattering experiments and first-principles density-functional theory calculations were employed to investigate the lattice vibrations (or phonon dynamics) in methylammonium lead iodide, a prototypical example of MHPs. Our findings are that optical phonons lose temporal coherence gradually with increasing temperature which vanishes at the orthorhombic-to-tetragonal structural phase transition. Surprisingly, however, we found that the spatial coherence is still retained throughout the decoherence process. We argue that the temporally decoherent and spatially coherent vibrations contribute to the formation of large polarons in this metal halide perovskite.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Cation Dynamics in Hybrid Halide Perovskites

Hybrid halide perovskite semiconductors exhibit complex, dynamical disorder while also harboring properties ideal for optoelectronic applications that include photovoltaics. However, these materials are structurally and compositionally distinct from traditional compound semiconductors composed of tetrahedrally coordinated elements with an average valence electron count of silicon. The additional dynamic degrees of freedom of hybrid halide perovskites underlie many of their potentially transformative physical properties. Neutron scattering and spectroscopy studies of the atomic dynamics of these materials have yielded significant insights into their functional properties. Specifically, inelastic neutron scattering has been used to elucidate the phonon band structure, and quasi-elastic neutron scattering has revealed the nature of the uncorrelated dynamics pertaining to molecular reorientations. Understanding the dynamics of these complex semiconductors has elucidated the temperature-dependent phase stability and origins of defect-tolerant electronic transport from the highly polarizable dielectric response. Furthermore, the dynamic degrees of freedom of the hybrid perovskites provide additional opportunities for application engineering and innovation.

Materials Science↗
DOE OSTI2020

Integrated dispersion compensated mode-locked quantum dot laser

Quantum dot lasers are excellent on-chip light sources, offering high defect tolerance, low threshold, low temperature variation, and high feedback insensitivity. Yet a monolithic integration technique combining epitaxial quantum dot lasers with passive waveguides has not been demonstrated and is needed for complex photonic integrated circuits. We present here, for the first time to our knowledge, a monolithc offset quantum dot integration platform that permits formation of a laser cavity utilizing both the robust quantum dot active region and the versatility of passive GaAs waveguide structures. This platform is substrate agnostic and therefore compatible with the quantum dot lasers directly grown on Si. As an illustration of the potential of this platform, we designed and fabricated a 20 GHz mode-locked laser with a dispersion-engineered on-chip waveguide mirror. Due to the dispersion compensation effect of the waveguide mirror, the pulse width of the mode-locked laser is reduced by a factor of 2.8.

Zhang, Zeyu (ORCID:0000000271576272)↗
DOE OSTI2020

The underappreciated lone pair in halide perovskites underpins their unusual properties

The presence of 6s 2 (5s 2 ) lone-pair electrons on the B-site Pb (Sn) in all-inorganic and hybrid halide ABX 3 perovskites distinguishes these materials from the familiar tetrahedral semiconductors traditionally employed in optoelectronics and is key to many of their appealing properties. These electrons are stereochemically active, albeit often in a hidden fashion, resulting in unusual and highly anharmonic lattice dynamics that are linked to many of the special optoelectronic properties displayed by this material class. This article describes the connections between this atypical electronic configuration and the electronic structure and lattice dynamics of these compounds. We illustrate how the lone pair leads to favorable bandwidths and band alignments, mobile holes, large ionic dielectric response, large positive thermal expansion, and even possibly defect-tolerant electronic transport. Taken together, the evidence suggests that other high-performing semiconductors may be found among compounds with lone-pair-bearing cations in high symmetry environments and a high degree of connectivity between atoms.

36 MATERIALS SCIENCE↗
DOE OSTI2022

In-situ Characterizations of Microstructural Degradation of Perovskite Solar Cells

Rapid progress has been achieved in perovskite solar cells (PSCs), and their efficiencies have improved from 3.8 % to 24.2 % in less than a decade. With low-cost processing, PSCs have shown exciting photovoltaic (PV) properties, such as effective optical absorption, a long carrier lifetime, and unique defect tolerance. While recent studies demonstrated improved stability up to 100 days, PSC technology is still challenged to meet the stringent industry requirements for commercialization. Despite considerable efforts, the underlying physical mechanisms for the inferior stability of PSCs are not well understood. One reason for this divergence is that many established measurement techniques (e.g., quantum efficiency, photoluminescence) probe the properties on length scales far greater than that of electronic and/or structural inhomogeneity (i.e., < 1 μm near grain boundaries) and therefore characterize convoluted and/or averaged properties. Ion/electron beam-based techniques have been extensively used to access the microstructures of PSCs, enabling atomic/nanoscale structural, chemical, optical, and electrical characterizations. For example, focused ion beam (FIB) milling produces an atomically smooth surface that minimizes the artifacts attributed to the surface roughness. FIB techniques can also create a well-defined cross-section of PSCs without mechanical damage in a physical cleaving sample preparation. While powerful, there are some concerns about possible beam damage of inorganic-organic perovskites via chemical-bond breakage and local heating. This project aims to comprehensively understand how the microstructural/interfacial properties of PSCs (e.g., Methylammonium Lead Iodide [MAPbI 3 ]) are modified under the irradiating ion beams. Specifically, we investigate the sub-surface properties of PSCs before and after Ar-ion beam injections. Kelvin probe force microscopy (KPFM) measures the contact potential differences (CPDs). Photoluminescence (PL) microscopy in conjunction with Finite-Difference Time-Domain (FDTD) simulations infers the formation of a “dead layer” (< 15 nm) on the subsurface of MAPbI 3 during Ar+ milling processes while preserving the initial bulk properties. The x-ray photoemission spectroscopy (XPS) confirms this modified surface is a lead-rich and iodine-deficient surface. We initiate customizing in-situ measurement setup while measuring the local optical and electrical properties of PSC under thermal (cooling, heating) and light stressors. Our results provide in-depth knowledge of the ion-beam impact on metal-halide perovskites and how this modified sub-surface impacts their properties under accelerated stressors of light and heat. Intensive Monte Carlo simulations of an electron beam interacting with PSCs provide the beam energy distribution in PSCs, proposing possible measurement conditions of using e-beam with minimizing beam damage. Our in-situ measurement platform can accommodate the diverse architecture of PSC devices for studying deterioration mechanisms under mixed environmental stressors.

14 SOLAR ENERGY↗
DOE OSTI2020

Defect behavior and radiation tolerance of MAB phases (MoAlB and Fe2AlB2) with comparison to MAX phases

MAB phases are a new class of layered ternary materials that have already shown a number of outstanding properties. Here, we investigate defect evolution and radiation tolerance of two MAB phases, MoAlB and Fe 2 AlB 2 , using a combination of experimental characterization and first-principles calculations. We find that Fe 2 AlB 2 is more tolerant to radiation-induced amorphization than MoAlB, both at 150 °C and at 300 °C. The results can be explained by the fact that the Mo Frenkel pair is unstable in MoAlB and as a result, irradiated MoAlB is expected to have a significant concentration of Mo Al antisites, which are difficult to anneal even at 300 °C. We find that the tolerance to radiation-induced amorphization of MAB phases is lower than in MAX phases, but it is comparable to that of SiC. However, MAB phases do not show radiation-induced cracking which is observed in MAX phases under the same irradiation conditions. This research suggests that MAB phases might be a promising class of materials for applications that involve radiation.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Cross-Cap Defects and Fault-Tolerant Logical Gates in the Surface Code and the Honeycomb Floquet Code

We consider the Z 2 toric code, surface code, and Floquet code defined on a nonorientable surface, which can be considered as families of codes extending Shor’s nine-qubit code. We investigate the fault-tolerant logical gates of the Z 2 toric code in this setup, which corresponds to e ↔ m exchanging symmetry of the underlying Z 2 gauge theory. We find that nonorientable geometry provides a new way for the emergent symmetry to act on the code space, and discover the new realization of the fault-tolerant Hadamard gate of the two-dimensional surface code with a single cross cap connecting the vertices nonlocally along a slit, dubbed a nonorientable surface code. This Hadamard gate can be realized by a constant-depth local unitary circuit modulo nonlocality caused by a cross cap. Via folding, the nonorientable surface code can be turned into a bilayer local quantum code, where the folded cross cap is equivalent to a bilayer twist terminated on a gapped boundary and the logical Hadamard only contains local gates with intralayer couplings when being away from the cross cap, as opposed to the interlayer couplings on each site needed in the case of the folded surface code. We further obtain the complete logical Clifford gate set for a stack of nonorientable surface codes and similarly for codes defined on Klein-bottle geometries. We then construct the honeycomb Floquet code in the presence of a single cross cap, and find that the period of the sequential Pauli measurements acts as a H Z logical gate on the single logical qubit, where the cross cap enriches the dynamics compared with the orientable case. We find that the dynamics of the honeycomb Floquet code is precisely described by a condensation operator of the Z 2 gauge theory, and illustrate the exotic dynamics of our code in terms of a condensation operator supported at a nonorientable surface. Published by the American Physical Society 2024

Physics↗