[1] [1] R.M. Ormerod, Solid oxide fuel cells. Chem. Soc. Rev. 32, 17–28 (2003). 10.1039/b105764m

[2] [2] L. Fan, B. Zhu, P.-C. Su, C. He, Nanomaterials and technologies for low temperature solid oxide fuel cells: recent advances, challenges and opportunities. Nano Energy 45, 148–176 (2018). 10.1016/j.nanoen.2017.12.044

[3] [3] O. Yamamoto, Electrical conductivity of stabilized zirconia with ytterbia and scandia. Solid State Ion. 79, 137–142 (1995). 10.1016/0167-2738(95)00044-7

[4] [4] K.A. Khor, L.-G. Yu, S.H. Chan, X.J. Chen, Densification of plasma sprayed YSZ electrolytes by spark plasma sintering (SPS). J. Eur. Ceram. Soc. 23, 1855–1863 (2003). 10.1016/s0955-2219(02)00421-1

[5] [5] J. Garcia-Barriocanal, A. Rivera-Calzada, M. Varela, Z. Sefrioui, E. Iborra et al., Colossal ionic conductivity at interfaces of epitaxial ZrO2:Y2O3/SrTiO3 heterostructures. Science 321, 676–680 (2008). 10.1126/science.1156393

[6] [6] H. Huang, M. Nakamura, P. Su, R. Fasching, Y. Saito et al., High-performance ultrathin solid oxide fuel cells for low-temperature operation. J. Electrochem. Soc. 154, B20 (2007). 10.1149/1.2372592

[7] [7] D. Pergolesi, E. Fabbri, A. D’Epifanio, E. Di Bartolomeo, A. Tebano et al., High proton conduction in grain-boundary-free yttrium-doped Barium zirconate films grown by pulsed laser deposition. Nat. Mater. 9, 846–852 (2010). 10.1038/nmat2837

[8] [8] K. Kerman, B.-K. Lai, S. Ramanathan, Nanoscale compositionally graded thin-film electrolyte membranes for low-temperature solid oxide fuel cells. Adv. Energy Mater. 2, 656–661 (2012). 10.1002/aenm.201100751

[9] [9] M. Tsuchiya, B.-K. Lai, S. Ramanathan, Scalable nanostructured membranes for solid-oxide fuel cells. Nat. Nanotechnol. 6, 282–286 (2011). 10.1038/nnano.2011.43

[10] [10] P.C. Su, C.C. Chao, J.H. Shim, R. Fasching, F.B. Prinz, Solid oxide fuel cell with corrugated thin film electrolyte. Nano Lett. 8, 2289–2292 (2008). 10.1021/nl800977z

[11] [11] B. Zhu, R. Raza, G. Abbas, M. Singh, An electrolyte-free fuel cell constructed from one homogenous layer with mixed conductivity. Adv. Funct. Mater. 21, 2465–2469 (2011). 10.1002/adfm.201002471

[12] [12] B. Zhu, R. Raza, L. Fan, C. Sun, Solid oxide fuel cells: from electrolyte-based to electrolyte-free devices (John Wiley & Sons, Hoboken, 2020), pp.1–218

[13] [13] M. Afzal, M. Saleemi, B. Wang, C. Xia, W. Zhang et al., Fabrication of novel electrolyte-layer free fuel cell with semi-ionic conductor (Ba0.5Sr0.5Co0.8Fe0.2O3−δ-Sm0.2Ce0.8O1.9) and schottky barrier. J. Power. Sources 328, 136–142 (2016). 10.1016/j.jpowsour.2016.07.093

[14] [14] P. Simon, Y. Gogotsi, Nanoscience and Technology: A Collection of Reviews from Nature Journals, World Scientific. ed. by (Macmillan Publishers, UK, 2010, pp 320–329

[15] [15] V. Dusastre, Materials for sustainable energy: a collection of peer-reviewed research and review articles from nature publishing group (World Scientific, Singapore, 2011), pp.1–327

[16] [16] B. Wang, B. Zhu, S. Yun, W. Zhang, C. Xia et al., Fast ionic conduction in semiconductor CeO2−δ electrolyte fuel cells. npg Asia Mater. 11, 51 (2019). 10.1038/s41427-019-0152-8

[17] [17] C. Xia, Y. Mi, B. Wang, B. Lin, G. Chen et al., Shaping triple-conducting semiconductor BaCo0.4Fe0.4Zr0.1Y0.1O3-δ into an electrolyte for low-temperature solid oxide fuel cells. Nat. Commun. 10, 1707 (2019). 10.1038/s41467-019-09532-z

[18] [18] M. Li, M.J. Pietrowski, R.A. De Souza, H. Zhang, I.M. Reaney et al., A family of oxide ion conductors based on the ferroelectric perovskite Na0.5Bi0.5TiO3. Nat. Mater. 13, 31–35 (2014). 10.1038/nmat3782

[19] [19] M. Yousaf, Y. Lu, E. Hu, M. Akbar, M.A.K.Y. Shah et al., Interfacial disordering and heterojunction enabling fast proton conduction. Small Methods 7, e2300450 (2023). 10.1002/smtd.202300450

[20] [20] M.A. Subramanian, D. Li, N. Duan, B.A. Reisner, A.W. Sleight, High dielectric constant in ACu3Ti4O12 and ACu3Ti3FeO12 phases. J. Solid State Chem. 151, 323–325 (2000). 10.1006/jssc.2000.8703

[21] [21] R.K. Pandey, W.A. Stapleton, J. Tate, A.K. Bandyopadhyay, I. Sutanto et al., Applications of CCTO supercapacitor in energy storage and electronics. AIP Adv. 3, 062126 (2013). 10.1063/1.4812709

[22] [22] H.S. Kushwaha, N.A. Madhar, B. Ilahi, P. Thomas, A. Halder et al., Efficient solar energy conversion using CaCu3Ti4O12 photoanode for photocatalysis and photoelectrocatalysis. Sci. Rep. 6, 18557 (2016). 10.1038/srep18557

[23] [23] L.C. Kretly, A.F.L. Almeida, P.B.A. Fechine, R.S. de Oliveira, A.S.B. Sombra, Dielectric permittivity and loss of CaCu3Ti4O12 (CCTO) substrates for microwave devices and antennas. J. Mater. Sci. Mater. Electron. 15, 657–663 (2004). 10.1023/B:JMSE.0000038920.30408.77

[24] [24] K. Sun, L.-F. Xu, C. Mao, X. Feng, J.-Y. Liang et al., Preferential orientation and relaxation behaviors of CaCu3Ti4O12 thin films in a low frequency range. J. Alloys Compd. 704, 676–682 (2017). 10.1016/j.jallcom.2017.02.074

[25] [25] L. He, J. Neaton, M.H. Cohen, D. Vanderbilt, C. Homes, First-principles study of the structure and lattice dielectric response of CaCu3Ti4O12. Phys. Rev. B 65, 214112 (2002). 10.1103/PhysRevB.65.214112

[26] [26] G. Chiodelli, V. Massarotti, D. Capsoni, M. Bini, C.B. Azzoni et al., Electric and dielectric properties of pure and doped CaCu3Ti4O12 perovskite materials. Solid State Commun. 132, 241–246 (2004). 10.1016/j.ssc.2004.07.058

[27] [27] G. Cao, L. Feng, C. Wang, Grain-boundary and subgrain-boundary effects on the dielectric properties of CaCu3Ti4O12 ceramics. J. Phys. D Appl. Phys. 40, 2899–2905 (2007). 10.1088/0022-3727/40/9/035

[28] [28] A.A. Felix, M.O. Orlandi, J.A. Varela, Schottky-type grain boundaries in CCTO ceramics. Solid State Commun. 151, 1377–1381 (2011). 10.1016/j.ssc.2011.06.012

[29] [29] M.H. Braga, N.S. Grundish, A.J. Murchison, J.B. Goodenough, Alternative strategy for a safe rechargeable battery. Energy Environ. Sci. 10, 331–336 (2017). 10.1039/c6ee02888h

[30] [30] M.H. Braga, J.A. Ferreira, A.J. Murchison, J.B. Goodenough, Electric dipoles and ionic conductivity in a Na+ glass electrolyte. J. Electrochem. Soc. 164, A207–A213 (2016). 10.1149/2.0691702jes

[31] [31] M.H. Braga, A.J. Murchison, J.A. Ferreira, P. Singh, J.B. Goodenough, glass-amorphous alkali-ion solid electrolytes and their performance in symmetrical cells. Energy Environ. Sci. 9, 948–954 (2016). 10.1039/c5ee02924d

[32] [32] M. Ahmadipour, M.F. Ain, Z.A. Ahmad, Effects of annealing temperature on the structural, morphology, optical properties and resistivity of sputtered CCTO thin film. J. Mater. Sci. Mater. Electron. 28, 12458–12466 (2017). 10.1007/s10854-017-7067-3

[33] [33] S.-Y. Chung, I.-D. Kim, S.-J.L. Kang, Strong nonlinear current–voltage behaviour in perovskite-derivative calcium copper titanate. Nat. Mater. 3, 774–778 (2004). 10.1038/nmat1238

[34] [34] Y.-H. Lin, J. Cai, M. Li, C.-W. Nan, J. He, High dielectric and nonlinear electrical behaviors in TiO2-rich CaCu3Ti4O12 ceramics. Appl. Phys. Lett. 88, 172902 (2006). 10.1063/1.2198479

[35] [35] G. Kresse, J. Hafner, Ab initio molecular dynamics for liquid metals. Phys. Rev. B Condens. Matter 47, 558–561 (1993). 10.1103/physrevb.47.558

[36] [36] G. Kresse, J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996). 10.1016/0927-0256(96)00008-0

[37] [37] J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996). 10.1103/physrevlett.77.3865

[38] [38] G. Kresse, D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999). 10.1103/physrevb.59.1758

[39] [39] S.L. Dudarev, G.A. Botton, S.Y. Savrasov, C.J. Humphreys, A.P. Sutton, Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study. Phys. Rev. B 57, 1505–1509 (1998). 10.1103/physrevb.57.1505

[40] [40] S. Gražulis, D. Chateigner, R.T. Downs, A.F.T. Yokochi, M. Quirós et al., Crystallography open database–an open-access collection of crystal structures. J. Appl. Crystallogr. 42, 726–729 (2009). 10.1107/s0021889809016690

[41] [41] S. Grimme, Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 27, 1787–1799 (2006). 10.1002/jcc.20495

[42] [42] H.J. Monkhorst, J.D. Pack, Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976). 10.1103/physrevb.13.5188

[43] [43] V. Wang, N. Xu, J.-C. Liu, G. Tang, W.-T. Geng, VASPKIT: a user-friendly interface facilitating high-throughput computing and analysis using VASP code. Comput. Phys. Commun. 267, 108033 (2021). 10.1016/j.cpc.2021.108033

[44] [44] B. Zhu, P.D. Lund, R. Raza, Y. Ma, L. Fan et al., Schottky junction effect on high performance fuel cells based on nanocomposite materials. Adv. Energy Mater. 5, 1401895 (2015). 10.1002/aenm.201401895

[45] [45] L. Li, Single-layer Ga2O3/graphene heterogeneous structure with optical switching effect. Carbon Trends 7, 100153 (2022). 10.1016/j.cartre.2022.100153

[46] [46] Z. Wang, Q. Chen, J. Wang, Electronic structure of twisted bilayers of graphene/MoS2 and MoS2/MoS2. J. Phys. Chem. C 119, 4752–4758 (2015). 10.1021/jp507751p

[47] [47] N. Hadi, F. Abdi, T.-E. Lamcharfi, A. Belaaraj, S. Kassou et al., Study of the dielectric, optical and microstructure properties of CaCu3Ti4O12PbZr0.48Ti0.52O3 ceramic system with different compositions. Mediterr. J. Chem. 8, 245 (2019). 10.13171/10.13171/mjc8319052212nh

[48] [48] M. Guilmard, C. Pouillerie, L. Croguennec, C. Delmas, Structural and electrochemical properties of LiNi0.70Co0.15Al0.15O2. Solid State Ion. 160, 39–50 (2003). 10.1016/S0167-2738(03)00106-1

[49] [49] F. Izumi, T. Ikeda, A rietveld-analysis programm RIETAN-98 and its applications to zeolites. Mater. Sci. Forum 321–324, 198–205 (2000). 10.4028/www.scientific.net/msf.321-324.198

[50] [50] N. Mushtaq, C. Xia, W. Dong, B. Wang, R. Raza et al., Tuning the energy band structure at interfaces of the SrFe0.75Ti0.25O3–δ–Sm0.25Ce0.75O2–δ heterostructure for fast ionic transport. ACS Appl. Mater. Interfaces 11, 38737–38745 (2019). 10.1021/acsami.9b13044

[51] [51] N. Mushtaq, Y. Lu, C. Xia, W. Dong, B. Wang et al., Promoted electrocatalytic activity and ionic transport simultaneously in dual functional Ba0.5Sr0.5Fe0.8Sb0.2O3-δ-Sm0.2Ce0.8O2−δ heterostructure. Appl. Catal. B Environ. 298, 120503 (2021). 10.1016/j.apcatb.2021.120503

[52] [52] Y. Xing, S. Rauf, H. Cai, Z. Tayyab, B. Wang et al., Designing p-n heterostructure of LSCF-CeO2 material for ionic transportation as an electrolyte for semiconductor ion membrane fuel cell. Int. J. Hydrog. Energy 50, 428–440 (2024). 10.1016/j.ijhydene.2023.08.204

[53] [53] A. Yadav, R. Pyare, J.B. Goodenough, P. Singh, KTa1–x–yTixGeyO3−δ: A high κ relaxor dielectric and superior oxide-ion electrolyte for it-sofc. ACS Appl. Energy Mater. 3, 3205–3211 (2020). 10.1021/acsaem.0c00466

[54] [54] L.-F. Xu, C. Mao, V.V. Marchenkov, K. Sun, T.V. Dyachkova et al., Influence of sintering atmosphere and thermobaric treatment (TBT) on dielectric behaviors of CaCu3Ti4O12 ceramics. Phys. Lett. A 382, 2861–2867 (2018). 10.1016/j.physleta.2018.06.018

[55] [55] M. Li, D.C. Sinclair, A.R. West, Extrinsic origins of the apparent relaxorlike behavior in CaCu3Ti4O12 ceramics at high temperatures: a cautionary tale. J. Appl. Phys. 109, 084106 (2011). 10.1063/1.3572256

[56] [56] E. Fabbri, D. Pergolesi, E. Traversa, Ionic conductivity in oxide heterostructures: the role of interfaces. Sci. Technol. Adv. Mater. 11, 054503 (2010). 10.1088/1468-6996/11/5/054503

[57] [57] N. Akbar, S. Paydar, M.A.K.Y. Shah, N. Mushtaq, M. Yousaf et al., Space charge polarization effect in surface-coated BaTiO3 electrolyte for low-temperature ceramic fuel cell. ACS Appl. Energy Mater. 7, 1128–1135 (2024). 10.1021/acsaem.3c02633

[58] [58] J.L. Zhang, P. Zheng, C.L. Wang, M.L. Zhao, J.C. Li et al., Dielectric dispersion of CaCu3Ti4O12 ceramics at high temperatures. Appl. Phys. Lett. 87, 142901 (2005). 10.1063/1.2077864

[59] [59] L. Chen, C. Chen, Y. Lin, Y. Chen, X. Chen et al., High temperature electrical properties of highly epitaxial CaCu3Ti4O12 thin films on (001) LaAlO3. Appl. Phys. Lett. 82, 2317–2319 (2003). 10.1063/1.1565702

[60] [60] R. Yu, H. Xue, Z. Cao, L. Chen, Z. Xiong, Effect of oxygen sintering atmosphere on the electrical behavior of CCTO ceramics. J. Eur. Ceram. Soc. 32, 1245–1249 (2012). 10.1016/j.jeurceramsoc.2011.11.039

[61] [61] C.-M. Wang, S.-Y. Lin, K.-S. Kao, Y.-C. Chen, S.-C. Weng, Microstructural and electrical properties of CaTiO3–CaCu3Ti4O12 ceramics. J. Alloys Compd. 491, 423–430 (2010). 10.1016/j.jallcom.2009.10.216

[62] [62] C. Xia, B. Wang, Y. Ma, Y. Cai, M. Afzal et al., Industrial-grade rare-earth and perovskite oxide for high-performance electrolyte layer-free fuel cell. J. Power. Sources 307, 270–279 (2016). 10.1016/j.jpowsour.2015.12.086

[63] [63] J. Sugiyama, K. Mukai, Y. Ikedo, P.L. Russo, H. Nozaki et al., Static magnetic order in the triangular lattice of LixNiO2 (x ≤ 1): Muon-spin spectroscopy measurements. Phys. Rev. B. Conden. Matter Mater. Phys. 78, 144412 (2008). 10.1103/PhysRevB.78.144412

[64] [64] G. Wang, X. Wu, Y. Cai, Y. Ji, A. Yaqub et al., Design, fabrication and characterization of a double layer solid oxide fuel cell (DLFC). J. Power. Sources 332, 8–15 (2016). 10.1016/j.jpowsour.2016.09.011

[65] [65] Z. Qiao, C. Xia, Y. Cai, M. Afzal, H. Wang et al., Electrochemical and electrical properties of doped CeO2-ZnO composite for low-temperature solid oxide fuel cell applications. J. Power. Sources 392, 33–40 (2018). 10.1016/j.jpowsour.2018.04.096

[66] [66] S.F. Wang, Y.L. Liao, Y.F. Hsu, P. Jasinski, Effects of LiNi0.8Co0.15Al0.05O2 electrodes on the conduction mechanism of Sm0.2Ce0.8O2−δ electrolyte and performance of low-temperature solid oxide fuel cells. J. Power Sources 546, 231995 (2022). 10.1016/j.jpowsour.2022.231995

[67] [67] S. Chan, K. Khor, Z. Xia, A complete polarization model of a solid oxide fuel cell and its sensitivity to the change of cell component thickness. J. Power Sources 93, 130–140 (2001). 10.1016/S0378-7753(00)00556-5

[68] [68] B. Zhu, B. Wang, Y. Wang, R. Raza, W. Tan et al., Charge separation and transport in La0.6Sr0.4Co0.2Fe0.8O3-δ and ion-doping ceria heterostructure material for new generation fuel cell. Nano Energy 37, 195–202 (2017). 10.1016/j.nanoen.2017.05.003

[69] [69] D. Gao, J. Zhang, J. Zhu, J. Qi, Z. Zhang et al., Vacancy-mediated magnetism in pure copper oxide nanoparticles. Nanoscale Res. Lett. 5, 769–772 (2010). 10.1007/s11671-010-9555-8

[70] [70] G. Xing, J. Yi, J. Tao, T. Liu, L. Wong et al., Comparative study of structural inhomogeneity enhanced room-temperature ferromagnetism in Cu-doped ZnO nanowires. Adv. Mater. 20, 3521 (2008). 10.1002/adma.200703149

[71] [71] S. Rauf, M.B. Hanif, F. Wali, Z. Tayyab, B. Zhu et al., Highly active interfacial sites in SFT-SnO2 heterojunction electrolyte for enhanced fuel cell performance via engineered energy bands: envisioned theoretically and experimentally. Energy Environ. Mater. 7, 12606 (2024). 10.1002/eem2.12606

[72] [72] T. Gao, A. Kumar, Z. Shang, X. Duan, H. Wang et al., Promoting electrochemical conversion of CO2 to formate with rich oxygen vacancies in nanoporous tin oxides. Chin. Chem. Lett. 30, 2274–2278 (2019). 10.1016/j.cclet.2019.07.028

[73] [73] Y. Xing, Y. Wu, L. Li, Q. Shi, J. Shi et al., Proton shuttles in CeO2/CeO2–δ core–shell structure. ACS Energy Lett. 4, 2601–2607 (2019). 10.1021/acsenergylett.9b01829

[74] [74] C. Li, S. Dong, R. Tang, X. Ge, Z. Zhang et al., Heteroatomic interface engineering in MOF-derived carbon heterostructures with built-in electric-field effects for high performance Al-ion batteries. Energy Environ. Sci. 11, 3201–3211 (2018). 10.1039/C8EE01046C

[75] [75] G.-L. Li, Z. Yin, M.-S. Zhang, First-principles study of the electronic and magnetic structures of CaCu3Ti4O12. Phys. Lett. A 344, 238–246 (2005). 10.1016/j.physleta.2005.07.005

[76] [76] A.M. Ganose, A.J. Jackson, D.O. Scanlon, Sumo: Command-line tools for plotting and analysis of periodic ab initio calculations. J. Open Source Softw. 3, 717 (2018). 10.21105/joss.00717

[77] [77] S. Na-Phattalung, M. Smith, K. Kim, M. Du, S. Wei et al., First-principles study of native defects in anatase TiO2. Phys. Rev. B 73, 125205 (2006). 10.1103/PhysRevB.73.125205

[78] [78] B. Zhu, P. Lund, R. Raza, J. Patakangas, Q.-A. Huang et al., A new energy conversion technology based on nano-redox and nano-device processes. Nano Energy 2, 1179–1185 (2013). 10.1016/j.nanoen.2013.05.001

[79] [79] Z. Tayyab, S. Rauf, C. Xia, B. Wang, M.Y. Shah et al., Advanced LT-SOFC based on reconstruction of the energy band structure of the LiNi0.8Co0.15Al0.05O2–Sm0.2Ce0.8O2-δ heterostructure for fast ionic transport. ACS Appl. Energy Mater. 4, 8922–8932 (2021). 10.1021/acsaem.1c01186

[80] [80] B. Zhu, L. Fan, N. Mushtaq, R. Raza, M. Sajid et al., Semiconductor electrochemistry for clean energy conversion and storage. Electrochem. Energy Rev. 4, 757–792 (2021). 10.1007/s41918-021-00112-8