Revista UIS Ingenierías

Vol. 22 No. 2 (2023): Revista UIS Ingenierías
Articles

Application of the Klein-Gordon and Bogoliubov-deGennes theories to Nickelates

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  • Jose Jose Barba Ortega,
  • Cristian Aguirre ,
  • Julián Faundez
Jose Jose Barba Ortega
Universidad Nacional de Colombia
Cristian Aguirre
Universidade Federal de Mato-Grosso
Julián Faundez
Temple University
DOI: https://doi.org/10.18273/revuin.v22n2-2023011

Published 2023-06-11

Keywords

  • Teoría Cuántica,
  • Segunda cuantización,
  • Transformación de segundo orden,
  • Bogoliubov-deGennes,
  • Superconductividad

How to Cite

Barba Ortega, J. J., Aguirre , C. ., & Faundez, J. . (2023). Application of the Klein-Gordon and Bogoliubov-deGennes theories to Nickelates. Revista UIS Ingenierías, 22(2), 129–140. https://doi.org/10.18273/revuin.v22n2-2023011

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Abstract

In the present work we show the generalities of the classical field theory (CFT), we study its extension to the quantum field theory (QFT), where as an example of numerical analysis and combination with the field theory technique, we solve a system Klein-Gordon type (KGS) in two space-time dimensions (1+1) studying its stability through the spectral parameter λ(k), principle of convergence due to the parameters of the numerical network and the solution for the field ф (x;t), obtaining novel results. Also, we briefly study the technique of creation and destruction ladder operators from the perspective of the quantum harmonic oscillator, to define some properties and extensions to the problem in canonical quantization. Finally, we apply the topics studied to a problem of unconventional superconductivity in Nickelates compounds by solving the system of Bogoliubov-deGennes (BdG) Equations in the mean expansion of the field, obtaining the superconducting energy band.

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References

  1. H. Goldstein, J. L. Safko, C. P. Poole, Classical Mechanics: Pearson New International Edition. Pearson Education, 2014. [Online]. Available: https://books.google.com.co/books?id=Xr-pBwAAQBAJ
  2. F. Scheck, Mechanics: From Newton’s Laws to Deterministic Chaos. World Publishing Corporation, 1990. [Online]. Available: https://books.google.com.co/books?id=TgfyAAAAMAAJ
  3. S. T. Thornton, J. B. Marion, Classical Dynamics of Particles and Systems. Brooks/Cole, 2007. [Online]. Available: https://books.google.com.co/books?id=30rWGAAACAAJ
  4. E. T. Whittaker, A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. Cambridge University Press, 1988. [Online]. Available: https://books.google.com.co/books?id=epH1hCB7N2MC
  5. R. Weinstock, Calculus of Variations: With Applications to Physics and Engineering. Dover Publications, 1974. [Online]. Available: https://books.google.com.co/books?id=6wSVuWH1PrsC
  6. R. Courant, D. Hilbert, Methods of Mathematical Physics. 1991.
  7. A. Zee, Quantum Field Theory in a Nutshell. Princeton University Press, 2003.
  8. W. F. Ammes, Numerical Methods for Partial Differential Equations. 2014.
  9. J. Kiusalaas, Numerical Methods in Engineering with MATLAB. Cambridge University Press, 2015.
  10. J. H. Mathews, K. D. Fink, Numerical Methods Using MATLAB. Prentice Hall, 1999. [Online]. Available: https://books.google.com.co/books?id=F1sZAQAAIAAJ
  11. S. C. Chapra, Applied Numerical Methods with MATLAB for Engineers and Scientists.
  12. J. A. Trangenstein, Numerical Solution of Hyperbolic Partial Differential Equations. Cambridge University Press, 2009. [Online]. Available: https://books.google.com.co/books?id=%5C_nlbj1cUgZgC
  13. S. Larsson, V. Thomee, Partial Differential Equations with Numerical Methods. Springer, 2003. [Online]. Available: https://books.google.com.co/books?id=mrmxylxQlPUC
  14. Y. Zhu, B. Guo, Numerical methods for partial differential equations: proceedings of a conference held in Shanghai, PR China, March 25-29, 1987, vol. 1297. Springer, 2006.
  15. T,Roubíček, Nonlinear Partial Differential Equations with Applications, vol. 153. Basel: Birkhäuser-Verlag, 2005. doi: https://doi.org/10.1007/3-7643-7397-0
  16. M. Dehghan, A. Shokri, “Numerical solution of the nonlinear Klein–Gordon equation using radial basis functions,” J. Comput. Appl. Math., vol. 230, no. 2, pp. 400–410, 2009, doi: https://doi.org/10.1016/j.cam.2008.12.011
  17. D. Huang, G. Zou, L. W. Zhang, “Numerical Approximation of Nonlinear Klein-Gordon Equation Using an Element-Free Approach,” Math. Probl. Eng., vol. 2015, p. 548905, 2015, doi: https://doi.org/10.1155/2015/548905
  18. A. M. Wazwaz, “Compactons, solitons and periodic solutions for some forms of nonlinear Klein–Gordon equations,” Chaos, Solitons & Fractals, vol. 28, no. 4, pp. 1005–1013, 2006, doi: https://doi.org/10.1016/j.chaos.2005.08.145
  19. A. S. Botana, F. Bernardini, A. Cano, “Nickelate Superconductors: An Ongoing Dialog between Theory and Experiments,” J. Exp. Theor. Phys., vol. 132, no. 4, pp. 618–627, 2021, doi: https://doi.org/10.1134/S1063776121040026
  20. V. M. Katukuri, N. A. Bogdanov, O. Weser, J. van den Brink, A. Alavi, “Electronic correlations and magnetic interactions in infinite-layer NdNiO2,” Phys. Rev. B, vol. 102, no. 24, p. 241112, 2020, doi: https://doi.org/10.1103/PhysRevB.102.241112
  21. J. G. Bednorz, K. A. Müller, “Possible highTc superconductivity in the Ba−La−Cu−O system,” Zeitschrift für Phys. B Condens. Matter, vol. 64, no. 2, pp. 189–193, 1986, doi: https://doi.org/10.1007/BF01303701
  22. V. I. Anisimov, D. Bukhvalov, T. M. Rice, “Electronic structure of possible nickelate analogs to the cuprates,” Phys. Rev. B, vol. 59, no. 12, pp. 7901–7906, Mar. 1999, doi: https://doi.org/10.1103/PhysRevB.59.7901
  23. K. W. Lee and W. E. Pickett, “Infinite-layer LaNiO2:Ni1+ is notCu2+,” Phys. Rev. B, vol. 70, no. 16, p. 165109, 2004, doi: https://doi.org/10.1103/PhysRevB.70.165109
  24. M. Sarboland, A. Aminataei, “Numerical Solution of the Nonlinear Klein-Gordon Equation Using Multiquadric Quasi-interpolation Scheme,” Universal Journal of Applied Mathematics, 2015, doi: https://doi.org/10.13189/ujam.2015.030302
  25. C. J. Pethick, D. Pines, “Transport processes in heavy-fermion superconductors,” Phys. Rev. Lett., vol. 57, no. 1, pp. 118–121, 1986, doi: https://doi.org/10.1103/PhysRevLett.57.118
  26. Y. Gu, S. Zhu, X. Wang, J. Hu, H. Chen, “A substantial hybridization between correlated Ni-d orbital and itinerant electrons in infinite-layer nickelates,” Commun. Phys., vol. 3, no. 1, p. 84, 2020, doi: https://doi.org/10.1038/s42005-020-0347-x
  27. E. M. Nica, J. Krishna, R. Yu, Q. Si, A. S. Botana, O. Erten, “Theoretical investigation of superconductivity in trilayer square-planar nickelates,” Phys. Rev. B, vol. 102, no. 2, p. 20504, 2020, doi: https://doi.org/10.1103/PhysRevB.102.020504
  28. S. W. Zeng et al., “Observation of perfect diamagnetism and interfacial effect on the electronic structures in infinite layer Nd(0.8)Sr(0.2)NiO(2) superconductors.,” Nat. Commun., vol. 13, no. 1, p. 743, 2022, doi: https://doi.org/10.1038/s41467-022-28390-w
  29. D. Ferenc Segedin et al., “Limits to the strain engineering of layered square-planar nickelate thin films,” Nat. Commun., vol. 14, no. 1, p. 1468, 2023, doi: https://doi.org/10.1038/s41467-023-37117-4
  30. C. A. Aguirre, M. Joya, J. Barba-Ortega, “Dimer structure as topological pinning center in a superconducting sample,” Rev. UIS Ing., vol. 19, no. 1, pp. 109–115, 2020, doi: https://doi.org/10.18273/revuin.v19n1-2020011
  31. C. Aguirre-Tellez, M. Rincón-Joya, J. J. Barba-Ortega, “Released power in a vortex-antivortex pairs annihilation process,” Rev. UIS Ing., vol. 20, no. 1, 2020, doi: https://doi.org/10.18273/revuin.v20n1-2021014
  32. C. A. Aguirre-Tellez, E. D. Valbuena-Niño, J. J. Barba-Ortega, “Estado de vórtices en un cuadrado superconductor de dos-orbitales con condiciones de contorno mixtas,” Rev. Ingenio, vol. 15, no. 1, pp. 38–43, 2018, doi: https://doi.org/10.22463/2011642X.3118
  33. N. B. Kopnin, T. T. Heikkilä, G. E. Volovik, “High-temperature surface superconductivity in topological flat-band systems,” Phys. Rev. B, vol. 83, no. 22, p. 220503, 2011, doi: https://doi.org/10.1103/PhysRevB.83.220503
  34. V. J. Kauppila, F. Aikebaier, T. T. Heikkilä, “Flat-band superconductivity in strained Dirac materials,” Phys. Rev. B, vol. 93, no. 21, p. 214505, 2016, doi: https://doi.org/10.1103/PhysRevB.93.214505
  35. V. Peri, Z.-D. Song, B. A. Bernevig, S. D. Huber, “Fragile Topology and Flat-Band Superconductivity in the Strong-Coupling Regime,” Phys. Rev. Lett., vol. 126, no. 2, p. 27002, 2021, doi: https://doi.org/10.1103/PhysRevLett.126.027002
  36. V. I. Iglovikov, F. Hébert, B. Grémaud, G. G. Batrouni, R. T. Scalettar, “Superconducting transitions in flat-band systems,” Phys. Rev. B, vol. 90, no. 9, p. 94506, 2014, doi: https://doi.org/10.1103/PhysRevB.90.094506
  37. Z. S. Yang, A. M. Ferrenti, R. J. Cava, “Testing whether flat bands in the calculated electronic density of states are good predictors of superconducting materials,” J. Phys. Chem. Solids, vol. 151, p. 109912, 2021, doi: https://doi.org/10.1016/j.jpcs.2020.109912