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Kento Nishigomi, Yu Yi, Souren Adhikary, [Kazuhito Tsukagoshi](https://orcid.org/0000-0001-9710-2692), [Katsunori Wakabayashi](https://orcid.org/0000-0002-9147-9939)

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[Strain effects on the electronic properties of cobalt-based coordination nanosheets](https://mdr.nims.go.jp/datasets/bf89800c-1099-4947-9629-baa8260cb308)

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Strain effects on the electronic properties of cobalt-based coordination nanosheetsNanoscaleAdvancesPAPEROpen Access Article. Published on 01 September 2025. Downloaded on 10/26/2025 10:42:42 PM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article OnlineView Journal  | View IssueStrain effects onaDepartment of Nanotechnology for SustaTechnology, Kwansei Gakuin University,Japan. E-mail: waka@kwansei.ac.jp; Fax: +8bResearch Center for Materials NanoarchiMaterials Science (NIMS), Namiki 1-1, TsukcCenter for Spintronics Research Network (C8531, JapanCite this: Nanoscale Adv., 2025, 7,6964Received 21st April 2025Accepted 1st September 2025DOI: 10.1039/d5na00385grsc.li/nanoscale-advances6964 | Nanoscale Adv., 2025, 7, 696the electronic properties ofcobalt-based coordination nanosheetsKento Nishigomi,a Yu Yi,a Souren Adhikary,a Kazuhito Tsukagoshi band Katsunori Wakabayashi *abcWe theoretically study strain effects on the electronic properties of cobalt-based benzenehexathiol(CoBHT) coordination nanosheets using first-principles calculations. Two distinct crystal structures, high-density structure (HDS) and low-density structure (LDS), are explored. Our results reveal that HDSbehaves as a metal, while LDS exhibits semiconducting properties. Spin-polarized electronic bandstructures highlight the presence of energy band structures of the Kagome lattice, and the inclusion ofspin–orbit coupling (SOC) results in band gap openings at high-symmetric K points. Furthermore, weconstruct a tight-binding model to investigate the topological properties of CoBHT, demonstratinganomalous Hall conductivity driven by the intrinsic Berry curvature. The impact of uniaxial strain on theelectronic and magnetic properties of CoBHT is also studied. Strain induces significant modifications inmagnetic moments and density of states, particularly in the HDS. Anomalous Hall conductivity isenhanced under hole-doping conditions, suggesting that strain can be used to tailor the electronicproperties of CoBHT for specific applications. Our findings underscore the potential of CoBHTnanosheets for use in next-generation electronic, optoelectronic, and catalytic devices with tunableproperties through strain engineering.1 IntroductionTwo-dimensional (2D) materials, such as graphene,1–4 boron-nitrides,5,6 transition metal dichalcogenides (TMDCs),7–9 andoxide nanosheets,10 have garnered signicant attention due totheir unique physical and chemical properties, i.e., spin andcharge transport,11–14 ferroelectricity,15–17 magnetism,18,19 andlayer-by-layer oxidation.20,21 Moreover, the nontrivial topologicalproperties of 2D materials give rise to edge and corner statesand optical shi currents, offering promising applications inelectronic, spintronic, and quantum devices.22–29 These mate-rials, oen obtained via top-down exfoliation from bulk-layeredcrystals, exhibit unique physical properties driven by theirreduced dimensionality. However, bottom-up approaches,where nanosheets are synthesized through molecular, ionic, oratomic bonds, offer a complementary method to tailor 2Dmaterial properties and create novel structures. Coordinationnanosheets (CONASHs),30–33 a class of 2Dmaterials composed ofmetal–organic frameworks, represent one such bottom-upinable Energy, School of Science andGakuen-Uegahara 1, Sanda 669-1330,1 79 565 9729; Tel: +81 79 565 9751tectonics (MANA), National Institute foruba 305-0044, JapanSRN), Osaka University, Toyonaka 560-4–6971approach, enabling the design of nanosheets with versatileelectronic, magnetic, and optical characteristics.The material properties of CONASHs can be ne-tuned byselecting different metal centers and ligands, covering a broadrange of the periodic table. The incorporation of transitionmetals into these materials especially enhances their func-tionality. Notable examples include the interfacial synthesis ofsemiconducting nickel bis(dithiolene) (NiBHT) nanosheets,32,34photo-functional bis(dipyrrinato)zinc nanosheets,35 andelectrochromic iron or cobalt bis(terpyridine) nanosheets.36Recent studies by Clough et al. further revealed the potential oftransition-metal dithiolene complex coordination polymers inhydrogen evolution catalysis.37 Theoretical work by Liu et al. haspredicted that single-layer NiBHT could function as a 2D topo-logical insulator.38In this paper, using density functional theory we studyelectronic properties of cobalt-based coordination nanosheets(CoBHT),39 constructed from cobalt, sulfur, and carbon atoms.Since CoBHT is a 2D thin lm, applying uniaxial strain isconsidered to signicantly modify the electronic propertiesowing to the mechanical exibility, similar to that observed inTMDCs, i.e., so-called strain engineering.40–45 Thus, in thispaper, we study the effect of external strain on the electronicproperties of CoBHT. As previously reported, other transitionmetal-based BHT compounds have been experimentallysynthesized in two crystal phases: high-density structure (HDS)and low-density structure (LDS), via a liquid–liquid interfacial© 2025 The Author(s). Published by the Royal Society of Chemistryhttp://crossmark.crossref.org/dialog/?doi=10.1039/d5na00385g&domain=pdf&date_stamp=2025-10-19http://orcid.org/0000-0001-9710-2692http://orcid.org/0000-0002-9147-9939http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d5na00385ghttps://pubs.rsc.org/en/journals/journal/NAhttps://pubs.rsc.org/en/journals/journal/NA?issueid=NA007021Paper Nanoscale AdvancesOpen Access Article. Published on 01 September 2025. Downloaded on 10/26/2025 10:42:42 PM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinereaction. CuBHT and FeBHT have been realized in the HDSphase,46–48 whereas NiBHT has been realized in the LDS phase.32Based on these experimental observations, we investigate thepossibility that CoBHT could exist in both HDS and LDS phases,as both exhibit a D6h symmetry with a periodic arrangement ofdithiolene groups. Clough et al. have reported Fourier-transform infrared (FTIR) spectra of CoBHT in the LDSphase37 and Li et al. theoretically reported the HDS phase.49However, the precise crystal structure of CoBHT has not yetbeen experimentally conrmed. Here we explore the electronicand topological properties of these two different crystal struc-tures using rst-principles calculations to identify the suitablecrystal structure. Additionally, we investigate how externalstrain inuences the electronic and magnetic behavior ofCoBHT, offering insights into the tunability of these propertiesfor practical applications.In Sec. II, we present the details of the crystal structure ofCoBHT, and study the electronic states for both HDS and LDSusing rst-principles calculations. It will be shown that HDSbecomes a spin-polarized metallic state. However, LDS becomesa spin-polarized semiconductor which is similar to NiBHT.38Energetically LDS is slightly more stable than HDS. Since Coatoms form the Kagome lattice structure, the energy bandstructures have Dirac cones and at bands. It is also pointed outthat the spin–orbit interactions cause a small opening of theenergy band gap at Dirac cones. In Sec. III, we deduce aneffective tight-binding model by constructing maximally local-ized Wannier functions50,51 for CoBHT. Since HDS has localmagnetic moments originating from Co atoms, it shows ananomalous Hall effect (AHE) owing to the nite Berry curvature.In Sec. IV, we study the external strain effect on the electronicstates of CoBHT. The DOS for HDS near the Fermi energy isshown to be sensitive to the external strain; however, there isalmost no change for LDS due to its semiconducting nature. InSec. V, we provide the summary of the paper. In the SI, weprovide strain effects of CoBHT on electronic band structuresbeyond 5% and a simple tight-binding analysis of the chargedensity prole of CoBHT.Fig. 1 Crystal structures of CoBHT: (a) high-density structure (HDS) and (bconsists of Co (blue), S (yellow), and C (gray) atoms. Here, a1 = (a, 0) andFor HDS and LDS, a = 8.45 and 14.52 Å, respectivelb1 ¼ 2pa�1; � 1ffiffiffi3p�and b2 ¼ 2pa�0;2ffiffiffi3p�:© 2025 The Author(s). Published by the Royal Society of Chemistry2 Electronic states of CoBHTCoBHT is a newly synthesized coordination nanosheetcomposed of cobalt, sulfur, and carbon atoms. Two crystalstructures have been proposed for CoBHT, as shown in Fig. 1(a)and (b): HDS and LDS, respectively. Both structures exhibita periodic arrangement of dithiolene groups and possess D6hsymmetry. It should be noted that the Co atoms form a Kagomelattice structure in both cases. The gray region represents theunit cell, and the primitive lattice vectors for both structures area1 = (1, 0)a and a2 ¼ að1=2; ffiffiffi3p=2Þ; with lattice constants of a =8.45 Å for HDS and a = 14.52 Å for LDS. The correspondingprimitive vectors in reciprocal space are given asb1 ¼ 2pa�1; � 1ffiffiffi3p�and b2 ¼ 2pa�0;2ffiffiffi3p�: Therefore, thecorresponding rst Brillouin zone (BZ) is shown in Fig. 1(c).In this paper, electronic structure calculations were per-formed with a density functional theory (DFT)-based QuantumEspresso package using the projector augmented wavepseudopotential method.52 The exchange correlation functionwas considered using the generalized gradient approximation(GGA) by the Perdew–Burke–Ernzerhof (PBE) method.53 Weperformed structural optimization of CoBHT using a variablecell relaxation procedure. For structural optimization, thekinetic energy cut off was set to 85 Ry and the Brillouin zone wassampled using a 12 × 12 × 1 grid based on a G-centered Mon-khorst–Pack mesh.54 The convergence threshold for the forceson each atom was set below 10−5 Ry Å−1, and the convergencecriterion for the energy was set to 10−13 Ry.Fig. 2(a) and (b) show the spin density plots within the unit cellfor HDS and LDS, respectively. Both HDS and LDS exhibit nitemagnetic moments, which originate from the cobalt atoms. Theground state of both systems exhibits ferromagnetic ordering. Toverify this, we have compared the total energies of the systems ina ferromagnetic conguration and an antiferromagnetic cong-uration (in which one of the Co atoms is aligned oppositely to theother two). We have found that the ferromagnetic congurationhas a lower total energy. The magnitudes of these magneticmoments are 1.85 mB for HDS and 4.07 mB for LDS. The difference) low-density structure (LDS). The gray rhombus is the unit cell. CoBHTa2 ¼ að1=2; ffiffiffi3p=2Þ are primitive vectors, where a is the lattice constant.y. (c) The corresponding 1st Brillouin zone (BZ). Here,Nanoscale Adv., 2025, 7, 6964–6971 | 6965http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d5na00385gNanoscale Advances PaperOpen Access Article. Published on 01 September 2025. Downloaded on 10/26/2025 10:42:42 PM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinein the magnitude of magnetic moments between the HDS andLDS phases can be attributed to the role of the ligand, i.e., thedifferent structural connectivity of Co atoms in the two phases(see Fig. 1(a) and (b)). To conrm this, we calculate the Badercharges on each Co atom in both systems.55 We nd that theaverage Bader charge on a Co atom is 8.29 (in arbitrary unit) inthe HDS system and 8.25 (in arbitrary unit) in the LDS system. Asa result, the magnitude of the magnetic moment differs betweenthe two systems. It is also worth comparing the binding energy,DE, between HDS and LDS. The binding energy is calculatedusing the following equation:DE ¼Etotal �PiNiEiPiNi: (1)Here, the summation index i represents the Co, C and S atoms.Etotal is the total energy of CoBHT for either HDS or LDS. Ni andEi denote the total number and total energy of the i atom,respectively. The calculated values of DE are −0.5165 Ry peratom for LDS and −0.5065 Ry per atom for HDS, indicating thatboth HDS and LDS are energetically stable. Moreover, LDS isslightly more stable than HDS by 0.0010 Ry per atom. Further,we evaluated the thermodynamic stability using moleculardynamics simulations at 300 K, with the results presented in theSI.56 We observed that both phases of CoBHT remained intact,preserving their hexagonal congurations and planaritycompared to the 0 K structures. These ndings conrm thethermal stability of both phases.Fig. 2(c) and (d) show the spin-polarized electronic energyband structure for HDS and LDS, respectively. The red and bluelines indicate the spin-up and spin-down states, respectively.Fig. 2 Spin density plots of CoBHT in the unit cell for (a) HDS and (b) LDSatoms. The magnetic moment of HDS is 1.85 mB, while that of LDS is 4.07respectively. Red and blue lines represent up and down spin states, resdensity of states (DOS) considering SOC for HDS and LDS, respectively. TDOS plots, the blue lines represent the cobalt atoms, yellow lines reprerepresent the total DOS. LDS exhibits semiconductor behavior with a ba6966 | Nanoscale Adv., 2025, 7, 6964–6971The electronic energy band structure is calculated along highlysymmetric directions in the rst BZ. HDS is metallic. However,LDS becomes a semiconductor with a band gap of 0.265 eV.Both structures exhibit linear dispersion at the K point andfeature a band structure resembling the Kagome lattice(Kagome-like band). Additionally, we have calculated the elec-tronic band structures by including an on-site Coulomb inter-action (DFT + U) on each Co atom for both systems and presentthe results in the SI. We nd no changes in their magneticground state and electronic band dispersion. This result isconsistent with a previous theoretical study.57 In the SI,considering the simple tight-binding model of the Kagomelattice, we compare the charge density plots obtained from DFTwith those obtained from the simple tight-binding model.Since CoBHT contains cobalt atoms, which induce relativelylarge intrinsic spin–orbit interactions into the system, here wehave taken spin–orbit coupling (SOC) into account. Fig. 2(e) and(f) depict the electronic energy band structures with SOC,together with the partial density of states (PDOS) for HDS andLDS, respectively. In both structures, nite SOC opens theenergy band gap at the K point (as marked by the red ellipses).Furthermore, from the PDOS near the Fermi energy, it is evidentthat in HDS the contribution of cobalt electrons is predomi-nant, while in the LDS, there is a contribution not only fromcobalt electrons but also from sulfur and carbon electrons.3 Tight-binding model and BerrycurvatureIn order to analyze the topological properties of CoBHT, weshall construct an effective tight-binding model of HDS using, respectively. CoBHT has finite magnetic moments originating from ComB. Spin-polarized electronic band structures for (c) HDS and (d) LDS,pectively. Figures (e) and (f) depict the electronic band structures andhe band gap openings at the K point are marked by red ellipses. In thesent sulfur atoms, gray lines represent carbon atoms, and black linesnd gap of 0.265 eV.© 2025 The Author(s). Published by the Royal Society of Chemistryhttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d5na00385gFig. 3 (a) Comparison of the band structures of CoBHT for HDS with SOC as calculated by DFT (the black line) and the WTB Hamiltonian (theblue circles). The WTB Hamiltonian consists of all d-orbitals of the cobalt atoms. (b) Contour plot of Berry curvature (−Uzk) in the first BZ. (c)Energy band structure and corresponding Berry curvature (−Uzk) along the path through the high-symmetric points in the first BZ. (d) Fermienergy dependence of the anomalous Hall conductivity of CoBHT for HDS.Paper Nanoscale AdvancesOpen Access Article. Published on 01 September 2025. Downloaded on 10/26/2025 10:42:42 PM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article OnlineWannier90 (ref. 58) to reproduce the energy band structureobtained by DFT. In HDS, the electronic states near the Fermienergy are predominantly occupied by cobalt electrons.Furthermore, since the d-orbitals of cobalt electrons contributein this energy range, we consider all d orbitals (dxy, dxz, dyz, dz2,dx2−y2) for each of the three cobalt atoms in the unit cell, i.e.,a total of 15 orbitals. The size of the effective tight-bindingHamiltonian is 30 × 30, because the SOC derived from cobaltatoms is also considered.Fig. 3(a) shows the energy band obtained by DFT and theeffective model for HDS obtained byWannier90. The black linesrepresent the energy band dispersion from DFT, while the bluecircles represent the energy band dispersion from the effectivetight-binding model. Thus, the energy band structure of HDS ofCoBHT can be well-described by the d orbitals of cobalt atoms.Since the cobalt atoms form a 2D katome lattice, further anal-ysis using a simple tight-binding model is presented in the SI.Since HDS has a spin-polarized metallic state owing to thelocal magnetic moment of Co atoms, it is expected that HDSexhibits AHE,59–65 i.e., nite Hall conductivity without anexternal magnetic eld. It is known that there are two mainmechanisms for AHE, i.e., extrinsic and intrinsic mechanisms.The extrinsic one is attributed to the skew scattering63,64 or side-jump65 from disorder. The intrinsic one can be attributed to thetopological properties of bulk wave functions, which occur evenin the perfect crystal. Here, we shall focus on the intrinsic AHE.The anomalous Hall conductivity can be obtained by the k-integration of the Berry curvature in the 1st BZ assxy ¼ �e2ħðBZd3kð2pÞ3Uzk (2)Here Uzk is the summation of Berry curvature up to the Fermienergy, which is given asUzk ¼XnfnUznk; (3)where fn is the Fermi-Dirac distribution function and n is theband index. The Berry curvature for the n-th band can benumerically evaluated through the Kubo formula, i.e.,© 2025 The Author(s). Published by the Royal Society of ChemistryUznk ¼ �Xn0sn2ImhJnkjvx���Jn0kEhJnkjvy���Jn0kEðun0 � unÞ2; (4)where vx(y) is the x(y) component of the velocity operators, un =En/ħ.Since CoBHT is ferromagnetic, i.e., a time-reversal brokensystem, the Berry curvature has the property of Uz,k = Uz,−k.Fig. 3(b) shows the contour plot of Berry curvatureUz,k in the 1stBZ. Fig. 3(c) shows the energy band structure of HDS near theFermi energy and the corresponding Berry curvature Uz,k alongthe high symmetric k points of the 1st BZ. The Berry curvatureof HDS clearly exhibits a six-fold rotational symmetry withrespect to the G point. It is clearly seen that the mostpronounced peaks appear at K and K0 points, where Dirac pointsexist owing to the nature of the 2D Kagome lattice. Thus, asshown in Fig. 3(d), the nite anomalous Hall conductivity sxy isobtained for CoBHT, which is a profound value.4 Strain effect on CoBHTIn atomically-thin 2D materials, the electronic states can besignicantly modied by the application of external strain.66–68Here we study the strain effect on the electronic states ofCoBHT. Since CoBHT has D6h hexagonal symmetry, the appli-cation of uniaxial strain breaks the hexagonal crystal symmetry,resulting in the signicant modication of electronic states.Furthermore, recent studies show that the strain can inducetopological transitions in the 2D Kagome lattice.69Fig. 4 shows the energy band structures of HDS under theapplication of external strains of 1.0%, 5.0%, and 10.0%,respectively. Here, the elongation strain is applied. The effect ofcompression strain and weaker strain less than 1.0% is pre-sented in the SI. The upper and lower panels of Fig. 4 corre-spond to the external strain along the x and y axes, respectively.Since applying the strain to HDS breaks the hexagonalsymmetry of the system, a gap opens up in the linear dispersionat the K point.It is also observed that strain induces an anisotropic effect inthe electronic states of CoBHT, which becomes sizable in theNanoscale Adv., 2025, 7, 6964–6971 | 6967http://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d5na00385gFig. 4 Strain effect of CoBHT for HDS on the electronic energy band structures. (Upper panels) Elongation strain along the x-axis with strainvalues of 1.0, 5.0, and 10.0%. (Lower panels) Elongation strain along the y-axis.Nanoscale Advances PaperOpen Access Article. Published on 01 September 2025. Downloaded on 10/26/2025 10:42:42 PM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinerange of 5.0% to 10.0%. However, the following discussion shallfocus on the uniaxial strain up to 0.5%, from an experimentalperspective. In the case of biaxial strain, further large strain canbe achieved using indenting devices.70–72Fig. 5(a) illustrates the strain dependence of the magneticmoment for HDS and LDS of CoBHT at the charge-neutralpoint, i.e., EF = 0. For HDS, the magnetic moment mono-tonically increases with an increase in strain. However, for LDS,the magnetic moment remains nearly unchanged. Thus, theHDS has a stronger strain dependence of magnetic momentsthan the LDS. Since the magnetic moments originate from thed-orbitals of Co atoms, these results indicate that the strainaffects the spin–spin interactions in HDS more than LDS. Thismight be attributed to the fact that the atomic distancesbetween Co atoms differ signicantly between HDS and LDS. Inother words, HDS (LDS) has stronger (weaker) magnetic inter-actions between Co atoms.Fig. 5(b) shows the strain dependence of DOS for HDS atseveral different Fermi energies. The values of DOS areFig. 5 (a) Strain dependence of magnetic moments for (lower) HDS and(b) The strain effect of DOS at EF for HDS is for several different electron oof HDS. (d) Fermi energy dependence of anomalous Hall conductivity fo6968 | Nanoscale Adv., 2025, 7, 6964–6971normalized by the DOS at EF = 0 with no strain. At the chargeneutral point, applying a 0.5% strain results in an approxi-mately 40% increase in the DOS compared to the case withoutstrain. Taking the doped case into consideration, it was foundthat applying a 0.5% strain, especially in the hole-doped case (EF= −0.1 eV), results in an approximately 60% increase. Oneanticipated application of CONASHs is their utilization aselectrode catalyst nanosheets, and the results suggest thepossibility of activating catalytic functions. The LDS has a bandgap of 0.265 eV, so there is no DOS in the range where EF is from−0.1 to 0.1.Fig. 5(c) depicts the anomalous Hall conductivity of HDSobtained by applying strain and calculating it at severaldifferent Fermi energy levels, similar to the procedure employedfor DOS calculations. The calculation of anomalous Hallconductivity was performed using eqn (2) presented in Sect. III.The change in conductivity due to strain is generally small onaverage, but for the hole-doped case with EF = −0.2,(upper) LDS, respectively. Here EF is fixed at 0 eV, i.e., non-doping case.r hole doping cases. (c) Strain effect on the anomalous Hall conductivityr HDS with several different strains.© 2025 The Author(s). Published by the Royal Society of Chemistryhttp://creativecommons.org/licenses/by/3.0/http://creativecommons.org/licenses/by/3.0/https://doi.org/10.1039/d5na00385gPaper Nanoscale AdvancesOpen Access Article. Published on 01 September 2025. Downloaded on 10/26/2025 10:42:42 PM.  This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.View Article Onlinea signicant increase was observed when applying strain from0.2% to 0.3%.Fig. 5(d) shows graphs for cases where the strain of 0.2% and0.3% was applied, with the horizontal axis representing Fermienergy and the vertical axis indicating conductivity. The bluedashed line shows EF = −0.2. Upon comparing each graph, itcan be observed that when applying strain from 0.2% to 0.3%,the peaks near the blue dashed line precisely overlap. Therefore,when strain is applied at 0.3% or higher, the conductivity takeson signicant values.5 ConclusionsIn this paper, we investigated the electronic structure and straineffects of CoBHT using rst-principles calculations. Our resultsdemonstrate that CoBHT exhibits diverse electronic andmagnetic properties, with the HDS showing metallic behaviorand the LDS functioning as a semiconductor with a band gap of0.265 eV. The inclusion of SOC further reveals a band gapopening at the K points, contributing to the topological prop-erties of the system. We also analyzed the Kagome-like bandstructure and anomalous Hall conductivity using the Wanniertight-binding model, conrming the non-trivial topologicalnature of the HDS.Furthermore, we explored strain effects on the electronicproperties of CoBHT, showing that uniaxial strain can inducesignicant changes in magnetic moments, DOS, and anoma-lous Hall conductivity. These ndings suggest that strain engi-neering could be a viable approach to enhance the electronicfunctionality of CoBHT, particularly in applications requiringtunable electronic, magnetic, and catalytic properties. Thiswork underscores the potential of CoBHT nanosheets for next-generation electronic and optoelectronic devices, as well asadvanced catalytic applications.Author contributionsKento Nishigomi: Formal analysis, investigation, data curation,writing – original dra, visualization, soware. Yu Yi: Investi-gation. Souren Adhikary: Investigation, formal analysis. Kazu-hito Tsukagoshi: Conceptualization, writing – review & editing.Katsunori Wakabayashi: Conceptualization, methodology,project administration, supervision, writing – original dra,writing – review & editing.Conflicts of interestThere are no conicts to declare.Data availabilityAdditional data or computational les are available from thecorresponding author upon reasonable request.All relevant data supporting the ndings of this study areincluded in the article and its SI. See DOI: https://doi.org/10.1039/d5na00385g.© 2025 The Author(s). Published by the Royal Society of ChemistryAcknowledgementsThe authors are grateful to A. Kumatani for helpful discussionsand showing us his experimental data in advance of publica-tion. This work was supported by JSPS KAKENHI (Grants No.JP25K01609, No. JP22H05473, and No. JP21H01019) and JSTCREST (Grant No. JPMJCR19T1). K. W. acknowledges thenancial support for Basic Science Research Projects (Grant No.2401203) from the Sumitomo Foundation.Notes and references1 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang,S. V. Dubonos, I. V. Grigorieva and A. A. Firsov, Science, 2004,306, 666–669.2 K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang,M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos andA. A. Firsov, Nature, 2005, 438, 197.3 K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich,S. Morozov and A. Geim, Proc. Natl. Acad. Sci. U. S. A.,2005, 102, 10451–10453.4 A. K. Geim and K. S. Novoselov, Nat. Mater., 2007, 6, 183–191.5 K. Watanabe, T. Taniguchi and H. Kanda, Nat. Mater., 2004,3, 404–409.6 L. Song, L. Ci, H. Lu, P. B. Sorokin, C. Jin, J. Ni,A. G. 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