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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Spatiotemporal Reaction Dynamics Control in Two‐Photon Polymerization for Enhancing Writing Characteristics

Since 2001, 3D microfabrication based on two‐photon polymerization (TPP) has drawn extensive attention and interest in biology, optics, photonics, material science, and high‐energy physics. The in‐volume fabrication capability due to the threshold behavior of two‐photon absorption enables TPP higher flexibility compared with other nanofabrication techniques. However, as determined by the in‐volume fabrication feature as well as various reaction dynamics, the writing characteristics of TPP, such as throughput, accuracy, surface quality, and fabrication capability, are still limited. Herein, a comprehensive study is performed on the spatiotemporal behavior of reaction dynamics during TPP fabrication, mainly focusing on spatiotemporal characteristics of radical diffusion, photothermal effect, microscale mechanics, and voxel stacking process. Based on the study, a nonsequential fabrication method is established to simultaneously improve key writing characteristics of TPP and realize sharp features, high speeds, large overhang structure, and smooth surfaces. The method established in this work can be applied to improve the performance of functional devices for various fields.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Enhanced CO 2 Methanation Activity of Sm 0.25 Ce 0.75 O 2-δ –Ni by Modulating the Chelating Agents-to-Metal Cation Ratio and Tuning Metal–Support Interactions

Highly active and selective CO 2 methanation catalysts are critical to CO 2 upgrading, synthetic natural gas production, and CO 2 emission reduction. Wet impregnation is widely used to synthesize oxide-supported metallic nanoparticles as the catalyst for CO 2 methanation. However, as the reagents cannot be homogeneously mixed at an atomic level, it is challenging to modulate the microstructure, crystal structure, chemical composition, and electronic structure of catalysts via wet impregnation. In this work, a scalable and straightforward catalyst fabrication approach has been designed and validated to produce Sm 0.25 Ce 0.75 O 2-δ -supported Ni (SDC–Ni) as the CO 2 methanation catalyst. By varying the chelating agents-to-total metal cations ratio (C/I ratio) during the catalyst synthesis, we can readily and simultaneously modulate the microstructure, metallic surface area, crystal structure, chemical composition, and electronic structure of SDC–Ni, consequently fine-tuning the oxide–support interactions and CO 2 methanation activity. The optimal C/I ratio (0.1) leads to an SDC–Ni catalyst that facilitates C–O bond cleavage and significantly improves CO 2 conversion at 250 °C. A CO 2 -to-CH 4 yield of >73% has been achieved at 250 °C. Furthermore, a stable operation of >1500 hours has been demonstrated, and no degradation is observed. Extensive characterizations were performed to fundamentally understand how to tune and enhance CO 2 methanation activity of SDC–Ni by modulating the C/I ratio. The correlation of physical, chemical, and catalytic properties of SDC–Ni with the C/I ratio is established and thoroughly elaborated in this work. This study could be applied to tune the oxide–support interactions of various catalysts for enhancing the catalytic activity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Understanding the effect of density functional choice and van der Waals treatment on predicting the binding configuration, loading, and stability of amine-grafted metal organic frameworks

Metal organic frameworks (MOFs) are crystalline, three-dimensional structures with high surface areas and tunable porosities. Made from metal nodes connected by organic linkers, the exact properties of a given MOF are determined by node and linker choice. MOFs hold promise for numerous applications, including gas capture and storage. M2(4,4′-dioxidobiphenyl-3,3′-dicarboxylate)—henceforth simply M2(dobpdc), with M = Mg, Mn, Fe, Co, Ni, Cu, or Zn—is regarded as one of the most promising structures for CO2 capture applications. Further modification of the MOF with diamines or tetramines can significantly boost gas species selectivity, a necessity for the ultra-dilute CO2 concentrations in the direct-air capture of CO2. There are countless potential diamines and tetramines, paving the way for a vast number of potential sorbents to be probed for CO2 adsorption properties. The number of amines and their configuration in the MOF pore are key drivers of CO2 adsorption capacity and kinetics, and so a validation of computational prediction of these quantities is required to suitably use computational methods in the discovery and screening of amine-functionalized sorbents. In this work, we study the predictive accuracy of density functional theory and related calculations on amine loading and configuration for one diamine and two tetramines. In particular, we explore the Perdew–Burke–Ernzerhof (PBE) functional and its formulation for solids (PBEsol) with and without the Grimme-D2 and Grimme-D3 pairwise corrections (PBE+D2/3 and PBEsol+D2/3), two revised PBE functionals with the Grimme-D2 and Grimme-D3 pairwise corrections (RPBE+D2/3 and revPBE+D2/3), and the nonlocal van der Waals correlation (vdW-DF2) functional. We also investigate a universal graph deep learning interatomic potential’s (M3GNet) predictive accuracy for loading and configuration. These results allow us to identify a useful screening procedure for configuration prediction that has a coarse component for quick evaluation and a higher accuracy component for detailed analysis. Our general observation is that the neural network-based potential can be used as a high-level and rapid screening tool, whereas PBEsol+D3 gives a completely qualitatively predictive picture across all systems studied, and can thus be used for high accuracy motif predictions. We close by briefly exploring the predictions of relative thermal stability for the different functionals and dispersion corrections.

Chemistry↗
DOE OSTI2024

Composition and in situ structure of the Methanospirillum hungatei cell envelope and surface layer

Archaea share genomic similarities with Eukarya and cellular architectural similarities with Bacteria, though archaeal and bacterial surface layers (S-layers) differ. Using cellular cryo–electron tomography, we visualized the S-layer lattice surroundingMethanospirillum hungatei, a methanogenic archaeon. Though more compact than known structures,M. hungatei’s S-layer is a flexible hexagonal lattice of dome-shaped tiles, uniformly spaced from both the overlying cell sheath and the underlying cell membrane. Subtomogram averaging resolved the S-layer hexamer tile at 6.4-angstrom resolution. By fitting an AlphaFold model into hexamer tiles in flat and curved conformations, we uncover intra- and intertile interactions that contribute to the S-layer’s cylindrical and flexible architecture, along with a spacer extension for cell membrane attachment.M. hungateicell’s end plug structure, likely composed of S-layer isoforms, further highlights the uniqueness of this archaeal cell. These structural features offer advantages for methane release and reflect divergent evolutionary adaptations to environmental pressures during early microbial emergence.

Science & Technology - Other Topics↗
DOE OSTI2020

Controlled removal of hydrogen atoms from H-terminated silicon surfaces

The controlled formation of dangling bond structures on a H-terminated silicon surface is the first step in an atomically precise method of fabrication of silicon quantum electronic devices. An ultrahigh vacuum scanning tunneling microscope (STM) tip is used to selectively desorb hydrogen atoms from a Si(100)-2x1:H surface by injecting electrons with the sample held at a positive bias voltage. The authors propose a lithography method that allows the STM to operate under negative bias imaging conditions and simultaneously desorb H atoms as required. A high frequency signal is added to the negative bias voltage to deliver the required energy for hydrogen removal. The resulting current at this frequency and its harmonics are filtered to minimize their effect on the operation of the STM’s feedback control loop. The authors show that the chance of tip-sample crash during the lithography process is reduced by employing this method. They also demonstrate that this approach offers a significant potential for controlled and precise removal of H atoms from a H-terminated silicon surface and thus may be used for the fabrication of practical silicon-based atomic-scale devices.

42 ENGINEERING↗
DOE OSTI2020

Reduction of uranyl and uranyl-organic complexes mediated by magnetite and ilmenite: A combined electrochemical AFM and DFT study

Reduction of mobile aqueous uranyl complexes can be hindered by the strength of the uranyl-ligand complex and the resistivity of the complexes to electron transfer. Semiconducting solids, such as magnetite (Fe 3 O 4 ) and ilmenite (FeTiO 3 ), can facilitate otherwise-slow electron transfer between the reductant and oxidant, especially if these species are adsorbed on their surfaces as inner-sphere complexes. Electrons can then be shuttled through the surface or the structure. This process can be facilitated by either finding a new electron transfer path or by weakening or destroying the ligand-uranyl complex. Using in situ electrochemical atomic force microscopy (EC-AFM), we imaged reduction products of uranyl as mediated by magnetite and ilmenite in the absence or presence of the organic ligands, ethylenediaminetetraacetate (EDTA) and oxalate. In situ images of uranyl reduction show gradual nucleation and growth of reduced uranium on the mineral surfaces with decreasing reduction potentials. X-ray photoelectron spectroscopy (XPS) measurements indicate pentavalent uranium as the dominant uranium species resulting from uranyl reduction mediated by magnetite and ilmenite. The reduction potentials of uranyl-organic species relevant to our reaction system, (U VI O 2 ∙oxalate) 0 and (U VI O 2 ∙HEDTA) - , are derived using quantum–mechanical modeling and compared with the midpoint potentials obtained from cyclic voltammetry measurements. The spectroscopic, electrochemical, and computational data suggest that the catalysis of Fe-bearing minerals facilitates the reduction of uranyl-organic complexes. U(VI)-oxalate complexes are redox-active and participate directly in the reduction mediated by magnetite. In the presence of EDTA, reduction of uranyl may proceed in concert with ligand exchange between metals (i.e., U and Fe) on the mineral surface. Finally, the proposed mechanism is the breaking of uranyl-organic bonds upon interaction with the mineral surface followed by the formation of Fe-organic bonds, thereby allowing the reduction of hexavalent uranyl to pentavalent one.

58 GEOSCIENCES↗
DOE OSTI2022

KCo 2 As 2 : A new portal for the physics of high-purity metals

High-quality single crystals of KCo 2 As 2 with the body-centered tetragonal ThCr 2 Si 2 structure were grown using KAs self flux. Structural, magnetic, thermal, and electrical transport properties were investigated. No clear evidence for any phase transitions was found in the temperature range 2–300 K. The in-plane electrical resistivity ρ versus temperature T is highly unusual, showing a T 4 behavior below 30 K and an anomalous positive curvature up to 300 K, which is different from the linear behavior expected from the Bloch-Grüneisen theory for electron scattering by acoustic phonons. This positive curvature has been previously observed in the in-plane resistivity of high-conductivity layered delafossites such as PdCoO 2 and PtCoO 2 . The in-plane ρ(T → 0) = 0.36μΩ cm of KCo 2 As 2 is exceptionally small for this class of compounds. The material also exhibits a magnetoresistance at low T which attains a value of about 40% at T = 2 K and magnetic field H = 80 kOe. The magnetic susceptibility χ of KCo 2 As 2 is isotropic and about an order of magnitude smaller than the values for the related compounds SrCo 2 As 2 and BaCo 2 As 2 . The χ increases above 100 K, which is found from our first-principles calculations to arise from a sharp peak in the electronic density of states just above the Fermi energy E F . Heat capacity C p (T) data at low T yield an electronic density of states N(E F ) that is about 36% larger than predicted by the first-principles theory. The C p (T) data near room temperature suggest the presence of excited optic vibration modes, which may also be the source of the positive curvature in ρ(T). Angle-resolved photoemission spectroscopy measurements are compared with the theoretical predictions of the band structure and Fermi surfaces. In conclusion, our results show that KCo 2 As 2 provides a new avenue for investigating the physics of high-purity metals.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Geometry of the charge density wave in the kagome metal A V 3 Sb 5

Kagome lattice is a fertile platform for topological and intertwined electronic excitations. Recently, experimental evidence of an unconventional charge density wave (CDW) is observed in a Z 2 kagome metal AV 3 Sb 5 (A=K, Cs, Rb). This observation triggers wide interest in the interplay between frustrated crystal structure and Fermi surface instabilities. Here, we analyze the lattice effect and its impact on CDW in AV 3 Sb 5 . Based on published experimental data, we show that the 2×2×2 CDW breaks the sixfold rotational symmetry of the crystal due to the phase shift between kagome layers and can explain the twofold symmetric CDW peak intensity observed by scanning tunneling spectroscopy. The coupling between the lattice and electronic degrees of freedom yields a weak first-order structural transition without continuous change of lattice dynamics. Our result emphasizes the fundamental role of lattice geometry in proper understanding of unconventional electronic orders in AV 3 Sb 5 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Reformed Mesoporous Ge for Substrate Reuse in III-V Solar Cells

Mesoporous Ge was generated by bipolar electrochemical etching of (100) Ge. Through high-temperature annealing experiments, we found that the mesoporous Ge microstructure produces pore coalescence deep in the structure rather than at the surface. III-V epitaxy on annealed porous Ge with subsurface coalescence and coral-like structures on the surface produced shunted photovoltaic devices. The roughness of the annealed porous Ge film was reduced by a pre-annealing HBr treatment and a post-annealing ultrasonic DI water dip. A smoother reformed surface was obtained, on which a GaInAs upright device with an efficiency of 5.7% was grown, demonstrating a first step towards technical viability.

14 SOLAR ENERGY↗
DOE OSTI2022

Investigation of the Electrode-Electrolyte Interphase in Ester-Based Electrolytes in NCM523/Graphite Cells

The use of methyl acetate (MA) and methyl propionate (MP) as co-solvents in carbonate/LiPF 6 electrolytes have been investigated in LiNi 0.5 Co 0.2 Mn 0.3 O 2 (NCM523)/graphite cells to improve electrochemical performance at low temperature (−20 °C). Consistent with previous investigations, improved low temperature performance was observed with all electrolyte formulations containing esters. Detailed ex situ surface analysis of the surface films generated with the ester-based electrolytes containing electrolyte additives reveal significant changes to the SEI on graphite upon cycling at moderately elevated temperature (45 °C). In the presence of vinylene carbonate (VC) lithium plating is observed upon cycling at low temperature (−20 °C) which leads to a thicker solid electrolyte interface (SEI) upon cycling at 45 °C. Incorporation of fluoroethylene carbonate (FEC) as an electrolyte additive results in the generation of a thin SEI and alters the structure of the surface film on the NCM523 cathode resulting in stable cycling over a wide temperature range.

Rodrigo, Nuwanthi D. (ORCID:0000000343129536)↗
DOE OSTI2020

Understanding Microstructural Effects on Dynamic Performance Towards the Development of Shock Metamaterials

With the recent advances in additive manufacturing (AM), long-range periodic lattice assemblies are being developed for vibration and shock mitigation components in aerospace and military applications with unique geometric and topological structures. There has been extensive work in understanding the static properties associated with varying topology of these lattice architectures, but there is almost no understanding of microstructural affects in such structures under high-strain rate dynamic loading conditions. Here we report the shock behavior of lattices with varying intrinsic grain structures achieved by post process annealing. High resolution 316L stainless steel lattices were 3D printed by a laser-powder bed fusion machine and characterized by computed tomography. Subsequent annealing resulted in stress-relieved and recrystallized lattices. Overall the lattices had strong cubic texture aligning with the x-, y- and z-directions of the build with a preference outside the build direction (z). The recrystallized sample had more equiaxed polygonal grains and a layer of BCC ferrite at the surface of the structure approximately 1 grain thick. Upon dynamic compression the as-deposited lattice showed steady compaction behavior while the heat-treated lattices exhibit negative velocity behavior indicative of failure. We attribute this to the stiffer BCC ferrite in the annealed lattices becoming damaged and fragmenting during compression.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Efficient black silicon photovoltaic devices with enhanced blue response

A photovoltaic (PV) device with improved blue response. The PV device includes a silicon substrate with an emitter layer on a light receiving side. The emitter layer has a low opant level such that it has sheet resistance of 90 to 170 ohm/sq. Anti-reflection in the PV device is provided solely by a nano-structured or black silicon surface on the light-receiving surface, through which the emitter is formed by diffusion. The nano structures of the black silicon are formed in a manner that does not result in gold or another high-recombination metal being left in the black silicon such as with metal-assisted etching using silver. The black silicon is further processed to widen these pores so as to provide larger nanostructures with lateral dimensions in the range of 65 to 150 nanometers so as to reduce surface area and also to etch away a highly doped portion of the emitter.

Oh, Jihun↗
DOE OSTI2021

A universal method to fabricating porous carbon for Li-O 2 battery

The main bottleneck in the application of biomass-based carbon material in energy field is the development of an economical, nanoscale controllable and universal fabrication method. Herein, we demonstrate that a biomass-derived carbon consisting of loose carbon nanosphere clusters could serve as an ideal cathode material for high performance Li-O 2 batteries. The carbon nanomaterial can be prepared from both biomass derivatives and crude biomass by a low cost, facile and nanoscale controllable method. The open slit-shaped hierarchical pore structure endows the electrode sufficient active surface sites and mass transport channels that are not easily asphyxiated by the discharge products. The concentration of oxygenic groups and structure defects on the surface of obtained carbon materials is very low, which minimizes the side reactions associated with carbon decomposition. Finally, the unique pore structure and surface properties of the carbon electrode give rise to a superhigh specific capacity of 20,300 mA h g -1 and an extremely long cycle life which a cyclic capacity retention of 100% is maintained for 543 cycles with current density of 0.2 mA cm -2 at controlled discharge-charge depths of 500 mA h g -1 .

25 ENERGY STORAGE↗
DOE OSTI2020

Steam-Induced Coarsening of Single-Unit-Cell MFI Zeolite Nanosheets and Its Effect on External Surface Brønsted Acid Catalysis

Commonly used methods to assess crystallinity, micro-/mesoporosity, Brønsted acid site density and distribution (in micro- vs. mesopores), and catalytic activity suggest nearly invariant structure and function for aluminosilicate zeolite MFI two-dimensional nanosheets before and after superheated steam treatment. Yet, pronounced reaction rate decrease for benzyl alcohol alkylation with mesitylene, a reaction that cannot take place in the zeolite micropores, is observed. Transmission electron microscopy images reveal pronounced changes in nanosheet thickness, aspect ratio and roughness indicating that nanosheet coarsening and the associated changes in the external (mesoporous) surface structure are responsible for the changes in the external surface catalytic activity. Finally, superheated steam treatment of hierarchical zeolites can be used to alter nanosheet morphology and regulate external surface catalytic activity while preserving micro- and mesoporosity, and micropore reaction rates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

An Experimental and Numerical Study of Plasma Treatment Effects on Adhesive Joints of Metals, CFRTPs, and Metal–CFRTP Combinations

This work investigates the effects of plasma surface treatment on both the local adherend–adhesive interfacial strength and the global lap shear strength (LSS) of adhesively-bonded joints composed of metals, CFRTPs, and metal-CFRTP combinations, using AA6061 and CFRPPA as representative examples. Experimental and computational results show that plasma treatment improved the ratio of CFRPPA–adhesive interfacial normal strength to adhesive tensile strength (sint,n/scri,t,adhesive) from 0.59–1.00 to 0.91–1.73, leading to an average 90% increase in LSS for CFRPPA-related joints. In contrast, the LSS and sint,n/scri,t,adhesive values of AA6061–AA6061 joints (>=2.27) remained nearly unchanged after plasma treatment. The enhanced joint bonding was further supported by post-failure surface morphologies from three-dimensional profilometry and simulations, showing a transition from dominant interfacial failure to mixed modes involving interfacial, cohesive, and slight fiber-peeling failures. The LSS evolution with respect to sint,n/scri,t,adhesive was numerically established until the saturation of the LSS of various joints, and the behavior of AA6061–CFRPPA T-joints with varying interfacial strengths was also modeled. This study highlights the importance of local interfacial bonding strength, rather than global LSS, for understanding and optimizing the mechanical performance of adhesively-bonded composite–metal and composite-composite structures via different surface modification strategies.

Qiao, Yao (ORCID:0000000265867604)↗
DOE OSTI2023

Development of ultralow-background cryogenic calorimeters for the measurement of surface α contamination

Next-generation experiments searching for rare events must satisfy increasingly stringent requirements on the bulk and surface radioactive contamination of their active and structural materials. The measurement of surface contamination is particularly challenging, as no existing technology is capable of separately measuring parts of the 232 Th and 238 U decay chains that are commonly found to be out of secular equilibrium. We will present the results obtained with a detector prototype consisting of 8 silicon wafers of 150mm diameter instrumented as bolometers and operated in a low-background dilution refrigerator at the Gran Sasso Underground Laboratory of INFN, Italy. Furthermore, the prototype was characterized by a baseline energy resolution of few keV and a background <100nBq/cm 2 in the full range of α energies, obtained with simple procedures for cleaning of all employed materials and no specific measures to prevent recontamination. Such performance, together with the modularity of the detector design, demonstrate the possibility to realize an alpha detector capable of separately measuring all alpha emitters of the 232 Th and 238 U chains, possibly reaching a sensitivity of few nBq/cm 2 .

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2022

Corrosion evaluation of metal foams in eutectic molten salts for high temperature latent heat energy storage application

High-temperature Thermal Energy Storage (TES) has drawn great attention as a technology that can increase the role and profitability of micro nuclear reactors in the decentralized clean energy market. Various research needs have been proposed by Idaho National Laboratory (INL) in "the Integrated Energy Systems: 2020 Roadmap" with the goal of utilizing the high temperature of 550 degrees or more generated in the 4th generation reactor to industrial purposes from the standpoint of integrated energy systems [1]. With the recent development of the 4th generation nuclear power plant, including micro nuclear reactor, there is a great deal of interest in researching how to efficiently couple a heat source to an industrial process through thermal processing. Texas A&M University (TAMU) and INL are currently collaborating to develop a novel latent heat storage design called HITB (Heat pipe-Integrated Thermal Battery). As part of the small-scale experimental demonstration research for HITB, a study for storage medium selection was conducted at TAMU. Eutectic salts have attracted interest as high-temperature heat storage medium for HITB. Especially, chloride molten salts and fluoride molten salts are considered promising candidates due to their high melting temperature, thermal stability, and high latent heat of fusion. Since eutectic salts have poor thermal conductivity in general, it is critical to distribute materials with high thermal conductivity evenly to facilitate the charging and discharging of heat. In this study, metal foam was considered in the HITB system to overcome the poor heat transfer characteristics of eutectic salts. In order to improve heat transfer, it is necessary to study materials with high thermal conductivity, corrosion resistant to molten salts, such as fins, extended surfaces, particles, microcapsulation, or foam structure. Porous structure of copper or aluminum can increase heat transfer area, form a thermal transfer network, and increase the effective thermal conductivity of thermal storage medium [2]. Since the melting temperature is required to be at least 450? in the current HITB design, various eutectic salts are being considered. FLiNaK and FLiBe, which are famous for fluoride salts, are good candidates, but due to the sharp rise in the price of LiF recently, they are excluded for economic reasons to be applied to large-capacity thermal energy storage. On the other hand, chloride salts are very cheap and easy to obtain, have a high melting temperature, and have a high latent heat of fusion, so they are recently in the spotlight as a phase change material. However, because of the hygroscopic nature of chloride salts, HCl gas due to impurity is easy to be released and is particularly vulnerable to corrosion. Chloride eutectic salts have been tested and suggested for metal alloys that are particularly resistant to corrosion, such as SS304, SS316, Hastelloy, Inconel 625, Incoloy 800H, which has low thermal conductivity, and is very expensive [3-6]. Porous materials with high thermal conductivity such as copper and aluminum have been tested for stability in fluids such as paraffin or water as metal foam or metal fin structures, but high temperature corrosion tests were not performed on various eutectic salts yet. Therefore, this study investigated the high temperature corrosion characteristics of metal alloys, such as C10100 foam, C10100 plate, 6101 alloy foam, and SS316 plate, while immersed in the candidate eutectic salts. A total of 20 tests for SS316 coupons and 10 tests for C10100 coupons were performed to ensure the repeatability of the present measurements. Since it is difficult to completely remove the salt inside metal foam due to the complex inner structure of the metal foam, only the surface condition was observed with a microscopy and scanning electron microscopy (SEM) image, except for measuring the corrosion rate and average mass loss.

25 ENERGY STORAGE↗
DOE OSTI2025

Second harmonic generation in topological insulators under quantizing magnetic fields

We theoretically investigate the second harmonic generation (SHG) of topological insulator surface states in a perpendicular magnetic field. Our theory is based on the microscopic expression of the second-order magneto-optical conductivity developed from the density matrix formalism, taking into account hexagonal warping effects on the surface states' band structure. Using numerically exact Landau-level energies and wave functions including hexagonal warping, we calculate the spectrum of SHG conductivities under normal incidence for different values of magnetic field and chemical potential. The imaginary parts of the SHG conductivities show prominent resonant peaks corresponding to one-photon and two-photon inter-Landau-level transitions. Treating the hexagonal warping term perturbatively, these transitions are clarified analytically within a perturbation theory from which approximate selection rules for the allowable optical transitions for SHG are determined. Furthermore, our results show extremely high SHG susceptibility that is easily tunable by magnetic field and doping level for topological surface states in the far-infrared regime, exceeding that of many conventional nonlinear materials. This work highlights the key role of hexagonal warping effects in generating second-order optical responses and provides insights into the nonlinear magneto-optical properties of the topological insulators.

Landau levels↗