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ISSN 2415-3400 (Online)
ISSN 1028-821X (Print)

Microwave radiophysics of unconventional superconductors

Barannik, AА, Gubin, AІ, Lavrinovich, AА, Cherpak, NT
Organization: 

O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Proskura st., Kharkov, 61085, Ukraine

E-mail: al.a.barannik@gmail.com

https://doi.org/10.15407/rej2018.04.015
Language: russian
Abstract: 

The subject and purpose of the work. A review of the main results obtained by the authors in the process of microwave (MW) research of unconventional superconductors and the development of MW devices based on cuprate high-temperature superconductors (HTS) over the past 10–15 years is presented.

Methods and methodology of work. Experimental studies were carried out by the methods of impedance measurements of superconducting samples. To this end, the authors developed two measurement techniques in the mm wavelength range: based on quasi-optical sapphire resonators and using the feature of reflection of a p-polarized wave from the surface of a superconductor at grazing angles of incidence.

The results of the work.. The epitaxial films of the cuprate YBa2Cu3O7–d superconductor and Fe-containing superconductors in the form of single crystals of pnictide Ba (Fe0.926Co0.074)2As2 and epitaxial films of chalcogenide FeSexTe1–x (x = 0.5 and 0.7) are investigated. The results of the MW response of the electrodynamic structures with the samples under study served as the basis for finding the complex conductivity, including fluctuation one, and physical quantities related to it. In general, the results obtained confirm the scenario of d-wave symmetry of the gap function for cuprate superconductors and s±-wave symmetry for Fe superconductors. However, a number of detected features and effects, namely, an unusual frequency dependence of the residual surface resistance in YBa2Cu3O7–d in the form of w3./2, the growth of quasiparticle conductivity with decreasing temperature, starting from the critical one, as well as the avalanche-like transition from the superconducting to the strongly dissipative state in the nonlinear coplanar transmission line, require further study.

New MW devices based on cuprate HTS films in the mm wavelength range have been developed and created: 1) a quasi-optical sapphire resonator with a radial gap and HTS end walls for studying Fe – superconductors in the form of small (1–2 mm in the plane a–b) samples; 2) planar quasi-optical resonator; 3) a band-pass filter with an E-plane insert in a cross-shaped waveguide. The possibility of contactless testing at room temperature of the homogeneity of the properties of massive superconductors is also shown.

Conclusion. The temperature dependence of the complex conductivity of YBa2Cu3O7–d, Ba (Fe0.926Co0.074)2As2 and FeSexTe1–x (x = 0.5 and 0.7) superconductors and physical quantities related with it was obtained, which allows us to judge the confirmation of the corresponding wave symmetry scenarios of gap function function in the investigated superconductors. However, a number of detected features and effects require further study. The previously expressed assessment of the possibility of creating passive HTS-based MW devices with operating frequencies up to 40 GHz has been experimentally confirmed.

Keywords: complex conductivity, microwave surface impedance, nonlinear coplanar transmission line, passive microwave devices, quasioptical sapphire resonator, unconventional superconductors

Manuscript submitted 11.10.2018
PACS: 74.25.nn, 74.70.Xa, 74.78.-w
Radiofiz. elektron. 2018, 23(4): 15-36
Full text  (PDF)

References: 
  1. Cherpak, N., Barannik, A., He, Y., Sun, L., Zhang, X., Prozorov, R., Tanatar, M., 2018. Microwave Surface Impedance and Complex Conductivity of Ba(Fe0.926Co0.074)2As2 Single Crystals. In: The 12th Int. Conf. Materials and Mechanisms of Superconductivity and High-Temperature Superconductivity (M2S-2018). Abstract Book. Beijing, China, 20–24 August, p. 312.
  2. Kordyuk, A. A., 2018. Electronic band structure of optimal superconductors: from cuprates to ferropnictides and back again. Low Temp. Phys., 44(6), pp. 477–486. DOI: https://doi.org/10.1063/1.5037550
  3. Ma, Y., 2018. Recent progress in the development of Fe-based superconducting wires and tapes. In: The 12th Int. Conf. Materials and Mechanisms of Superconductivity and High-Temperature Superconductivity (M2S-2018). Abstract Book. Beijing, China, 20–24 August, p. 176.
  4. Barannik, A., Cherpak, N., Kirichenko, A., Prokopenko, Y., Vitusevich, S., Yakovenko, V., 2017. Whispering gallery mode resonators in microwave physics and technologies. Int. J. Microw. Wirel. T., 9(4), pp. 781–796. DOI: https://doi.org/10.1017/S1759078716000787
  5. Cherpak, N. T., Barannik, A. A., Prokopenko, Yu. V., Filipov, Yu. F, Vitusevich, S., 2003. Accurate Microwave Technique of Surface Resistance Measurement of Large-area HTS Films using Sapphire Quasioptical Resonator. IEEE Trans. on Appl. Supercon., 13(2), pp. 3570–3573. DOI: http://dx.doi.org/10.1109/TASC. 2003.812400
  6. Barannik, A. A., Bunyaev, S. A., Cherpak, N. T., Prokopenko, Yu. V., Kharchenko, A. A., Vitusevich, S. A., 2010. Whispering gallery mode hemisphere dielectric resonators with impedance plane. IEEE Trans. Microwave Theory Tech., 58(10), pp. 2682–2691. DOI:https:// doi.org/10.1109/TMTT.2010.2065870
  7. Barannik, A. A., Bunyaev, S. A., Cherpak, N. T. and Vitusevich, S. A., 2008. Quasi-Optical Sapphire Resonators in the Form of a Truncated Cone. J. Lightwave Technol., 26(17), pp. 3118–3123. DOI: https://doi.org/ 10.1109/JLT.2008.925039
  8. Barannik, A. A., Cherpak, N. T., Torokhtiy, K. I. and Vitusevich, S., 2011. Slotted-Disk Sapphire Quasi-Optical Resonator with Conducting Endplates. In: Proceedings of the 41st European Microwave Conference (EuMC 2011). Manchester, UK, 12–14 Oct. 2011, pp. 830–833.
  9. Hein, M., 1992. High-Temperature-Superconductor Thin Films at Microwave Frequencies. Berlin: Springer.
  10. Wu, P.H., Min, Q., 1992. Calculations of the microwave conductivity of high-TC superconducting thin films from power transmission measurements. J. Appl. Phys., 71(11), pp. 5550–5553. DOI: https://doi.org/ 10.1063/1.350530
  11. Somal, H. S., Feenstra, B. J., Schützmann, J., Hoon Kim, J., Barber, Z. H., Duijn, V. H., Hien, N. T., Menovsky, A. A., Palumbo, M., van der Marel, D., 1996. Grazing incidence infrared reflectivity of La1.85Sr0.15CuO4 and NbN. Phys. Rev. Lett., 76(9), pp. 1525–1528. DOI: https://doi.org/10.1103/PhysRevLett. 76.1525
  12. Cherpak, N. T., Gubin, A. I., Lavrinovich, A. A., 2001. Microwave Reflectivity of HTS Film. Telecommunications and Radio Engineering, 55(3), pp.81–89. DOI: https://doi.org/10.1615/TelecomRadEng.v55.i3.120
  13. Gubin, A. I., Lavrinovich, A. A., Cherpak, N. T., 2001. Microwave-band reflection coefficient of high-temperature superconductor specimens in E-plane waveguide structures. Tech. Phys. Lett., 27(4), pp. 336–337. DOI: https://doi.org/10.1134/1.1370219
  14. Hein, M., Kaiser, T. and Muller, G., 2000. Surface resistance of epitaxial YBa2Cu3O7−x films on various substrates: Effects of pair condensation and quasipar-ticle scattering. Phys. Rev. B, 61(1), pp. 640–647. DOI: https://doi.org/10.1103/PhysRevB.61.640
  15. Hensen, S., Müller, G., Rick, C. T. and Shamberg, K., 1997. In-plane surface impedance of epitaxial YBa2Cu3O7−d films: Comparison of experimental data taken at 87 GHz with d- and s-wave models of superconductivity Phys. Rev. B, 56(10), pp. 6237–6264. DOI: https://doi.org/10.1103/PhysRevB.56.6237
  16. Pan, V. M., Kalenyuk, O. A., Kasatkin, O. L., Komash-ko, V. A., Ivanyuta, O. M. and Melkov, G. A., 2006. Microwave response of single crystal YBa2Cu3O7−d films as a probe for pairing symmetry. Low Temp. Phys., 32(4), pp. 497–504. DOI: https://doi.org/10.1063/ 1.2199453
  17. Harris, R., Turner, P. J., Kamal Saeid, Hosseimi, A. R., Dosaujh, P., Mullins, G. K., Bobowski, J. S., Bidinosti, C. P., Broun, D. M., Liang Ruixing, Hardy, W. V. and Bonn, D. A., 2006. Phenomenology of a-axis and b-axis charge dynamics from microwave spectroscopy of highly ordered YBa2Cu3O6.50 and YBa2Cu3O6.993. Phys. Rev. B, 74(10), pp. 104508(16 p.). DOI: https://doi.org/10.1103/ PhysRevB.74.104508
  18. Trunin, M. R., Nefyodov, Y. A. and Fink, H. J., 2000. Phenomenological description of the microwave surface impedance and complex conductivity of high-Tc single crystals. J. Exp. Theor. Phys., 91(4), pp. 801–816. DOI: https://doi.org/10.1134/1.1326973
  19. Barannik, A. A., Bunyaev, S. A., Cherpak, N. T., 2008. On the low-temperature microwave response of a YBa2Cu3O7−d epitaxial film determined by a new measurement technique. Low Temp. Phys., 34(12), pp. 977–981. DOI: https://doi.org/10.1063/1.3029749
  20. Hosseini, A., Harris, R., Kamal, S., Dosanjh, P., Preston, J., Liang, R., Hardy, W. N. and Bonn, D. A., 1999. Microwave spectroscopy of thermally excited quasiparticles in YBa2Cu3O6.99. Phys. Rev. B, 60(2), pp. 1349–1359. DOI: https://doi.org/10.1103/PhysRevB. 60.1349
  21. Harris, R., Hosseini, A., Kamal, S., Dosanjh, P., Liang, R., Hardy, W. N. and Bonn, D. A., 2001. Microwave spectroscopy of quasiparticle transport in the b̂ direction of YBa2Cu3O6.993. Phys. Rev. B, 64(6), p. 064509. DOI: https://doi.org/10.1103/PhysRevB.64. 064509
  22. Klein, N., 2000. Electrodynamic properties of oxide super-conductors. Berichte des Forschungzentrums Jülich. Juel-3773. P. 101.
  23. Barannik, A. A., Cherpak, N. T., Kharchenko, M. S., Semerad, R., Vitusevich, S., 2013. Surface impedance of YBa2Cu3O7−d films grown on MgO substrate as a function of film thickness. J. Supercond. Novel Magn., 26(1), pp. 43–48. DOI: https://doi.org/10.1007/s10948-012-1695-x
  24. Barannik, A. A, Cherpak, N. T., Tanatar, M. A., Vitusevich, S., Skresanov, V., Canfield, P. C. and Prozorov, R., 2013. Millimeter-wave surface impedance of optimally-doped Ba(Fe1−xCox)2As2 single crystals. Phys. Rev. B, 87(1), pp. 014506 (7 p.). DOI: https://doi.org/10.1103/PhysRevB.87.014506
  25. Cherpak, N. T., Barannik, A. A., Prozorov, R., Tanatar, M. A., Velichko, A. V., 2013. On the determination of the quasiparticle scattering rate in unconventional superconductors by microwave surface impedance. Low Temp. Phys., 39(12), pp. 1110–1112. DOI: https:// doi.org/10.1063/1.4830422
  26. Valdés Aguilar, R., Bilbro, L. S., Lee, S., Bark, C. W., Jiang, J., Weiss, J. D., Hellstrom, E. E., Larbalestier, D. C., Eom, C. B. and Armitage, N. P., 2010. Pair-breaking effects and coherence peak in the terahertz conductivity of superconducting BaFe2−2xCo2xAs2 thin films. Phys. Rev. B, 82(18), pp. 180514 (4 p.). DOI: https://doi.org/ 10.1103/PhysRevB.82.180514
  27. Fischer, T., Pronin, A. V., Wosnitza, J., Iida, K., Kurth, F., Haindl, S., Schultz, L., Holzapfel, B. and Schachinger, E., 2010. Highly anisotropic energy gap in supercon-ducting Ba(Fe0.9Co0.1)2As2 from optical conductivity measurements. Phys. Rev. B, 82(22), p. 224507. DOI: https://doi.org/10.1103/PhysRevB.82.224507
  28. Ghigo G., Gerbaldo R., Gozzelino L., Laviano F. and Tamegai T. 2016. Penetration Depth and Quasiparticle Conductivity of Co- and K-Doped BaFe2As2Crystals, Investigated by a Microwave Coplanar Resonator Technique. IEEE Trans. Appl. Surercond., 26(3), artic le 7300104. DOI: https://doi.org/10.1103/PhysRevB. 82.224507
  29. Barannik, A. A., Cherpak, N. T., Ni, N., Tanatar, M. A., Vitusevich, S. A., Skresanov V. N., Canfield P. C., Prozorov R., Glamazdin V. V. and Torokhtii K. I., 2011. Millimeter-wave study of London penetration depth temperature dependence in Ba(Fe0.926Co0.074)2As2 single crystal. Low Temp. Phys., 37(11). p. 725–728. DOI: https://doi.org/10.1063/1.3660321
  30. Cherpak, N. T., Barannik, A. A., He, Y.-S., Prozorov, R. and Tanatar, M., 2013. Microwave response, complex conductivity and effect of order parameter symmetry in Fe-based superconductors. In: Proc. of the Int. Kharkov Symp. Physics and Engineering of Microwaves, Millimeter and Sub-Millimeter waves (MSMW-2013). Kharkiv, Ukraine, 23–28 June 2013, pp. 163–168. DOI: https://doi.org/10.1109/MSMW.2013.6622174
  31. Prozorov, R., Kogan, V. G., 2011. London penetration depth in iron-based superconductors. Rep. Prog. Phys., 74(12), pp. 124505 (20 p.). DOI: http://dx.doi.org/ 10.1088/0034-4885/74/12/124505
  32. Barannik, A. A., Cherpak, N. T., Kharchenko, M. S., Wu, Yun, Luo, Sheng, He, Yusheng and Porch, A., 2014. Unusual microwave response and bulk conductivity of very thin FeSe0.3Te0.7 films as a function of temperature. Low Temp. Phys., 40(7), pp. 492–504. DOI: http://dx.doi.org/10.1063/1.4881178
  33. Cherpak, N. (M.) T., Barannik, A. A., He, Y.-S., Sun, L., Zhang, X., Ma, Y., Bian, Y. and Li, G., 2018. On Nature of Microwave Response of the Resonator with Thin FeSe1–xTex Film near Critical Temperature. IEEE Trans. Appl. Supercond., 28(4), pp. 1501104. DOI: https://doi.org/10.1109/TASC.2018.2804095
  34. Barannik, A. A., Cherpak, N. T., He, Y.-S., Sun, L., Zhang, X., Vovnyuk, M. V., Wu, Y., 2018. Microwave response of cavity resonator with thin superconductor film depending on film temperature and orientation. Low Temp. Phys., 44(3), p. 247–251. DOI: https:// doi.org/10.1063/1.5024545
  35. Cherpak, N. T., Gubin, A. I, Lavrinovich, A. A., 2007. Rectangular microwaveguide with high-TC superconducting wall. In: Proc. Int. Kharkov Symp. Physics and Engineering of Millimeter and Sub-millimeter Waves (MSMW-2007). Kharkov, Ukraine, 25–30 Jun. 2007, pp. 392–394. IEEE. DOI: https://doi.org/10.1109/ MSMW.2007.4294673
  36. Silva, E., Marcon, R., Sarti., Fastampa, R., Giura, M., Cucolo, A. M., 2002. Microwave fluctuational conductivity in YBa2Cu3O7–d . Eur. Phys. J. B, 37(3), pp. 277–284. DOI: https://doi.org/10.1140/epjb/e2004-00057-5
  37. Silva, E., Marcon, R., Fastampa, R., Giura, M., Sarti, S., 2003. High-Frequency Fluctuational Conductivity in YBa2Cu3O7–d . J. Low Temp. Phys., 131(5–6), pp. 831–835. DOI: https://doi.org/10.1023/A:1023479010670
  38. Gubin, A. I., Cherpak, N. T., Lavrinovich, A. A., Oganisian, K. V., 2007. Temperature dependence of the microwave conductivity of a YBCuO film in the normal state. Low Temp. Phys., 33(10), pp. 818–820. DOI: https://doi.org/10.1063/1.2746852
  39. Cherpak, N. T., Velichko, A. V., 2000. High-Temperature Superconductor in microwave technique (review). Successes of modern radioelectronics., 4, pp. 3–47 (in Russian).
  40. Vendik, I. O., Vendik, O. G. 1997. High-Temperature Superconductor Devices for Microwave Signal Processing. St.-Petersburg, ТОО Skladen Publ. Part 1.
  41. Oates, O. D. E., Agassi, D., Wong, E., Leese de Escobar, A., Irgmaier, K., 2008. Nonlinear Meissner effect in a high-temperature superconductor: Local versus nonlocal electrodynamics. Phys. Rev. B, 77(21), P. 214521 (8 p.). DOI: http://dx.doi.org/10.1103/PhysRevB. 77.214521
  42. Halbritter, J., 1970. Change of eigenstate in a superconducting RF cavity due to a nonlinear response. J. Appl. Phys., 41(11), pp. 4581–4588. DOI: https://doi.org/ 10.1063/1.1658500
  43. Hartwig, W. H., 1973. Superconducting resonator and devices. Proc. IEEE, 61(1), pp. 58–69. DOI: https:// doi.org/10.1109/PROC.1973.8971
  44. Velichko, A. V., Cherpak, N. T., 1998. Response of high-temperature superconductors to electromagnetic radiation: (A Review). Low Temp. Phys., 24(5), pp. 297–323. DOI: https://doi.org/10.1063/1.593592
  45. Gaidukov, M. M., Vendik, O. G., Kolesov, S. G., 1990. Microwave power limiter based on high Tc superconducting film. Electron. Lett., 26(16), pp. 1229–1230. DOI:https://doi.org/10.1049/el:19900792
  46. Bondarenko, I. N., Lavrinovich, А. А., 2006. Thing film high temperature superconductivity coplanar line investigation. In: V. M. Yakovenko, ed. 2006. Radiofizika i elektronika. Kharkov: IRE NAS of Ukraine Publ. 11(2), pp. 318–322 (in Russian).
  47. Lavrinovich, A. A., Khramota, E. V., Cherpak, N. T., 2009. Study of microwave superconducting transmission line in the strong electromagnetic fields. In: V. M. Yakovenko, ed. 2009. Radiofizika i elektronika. Kharkov: IRE NAS of Ukraine Publ. 14(1), pp. 64–68 (in Russian).
  48. Cherpak, N. T., Lavrinovich, A. A., Kalenyuk, A. A., Pan, V. M., Gubin, A. I., Khramota, E. V., Kurakin, A. A., Vitusevich, S. A., 2010. DC-biased coplanar waveguide on the basis of high-Tc superconducting thin film with nonlinear impedance. Telecommunications and Radio Engineering, 69(15), pp. 1357–1364. DOI: https://doi.org/10.1615/TelecomRadEng.v69.i15.40
  49. Booth, J. C., Rudman, D. A., Ono, R. H., 2003. A Self-Attenuating Superconducting Transmission Line for Use as a Microwave Power Limiter. IEEE Trans. Appl. Supercond., 13(2), pp. 305–310. DOI: https://doi.org/ 10.1109/TASC.2003.813716
  50. Cherpak, N. T., Lavrinovich, A. A., Gubin, A. I., and Vitusevich, S. A., 2014. Direct-current-assisted microwave quenching of YBa2Cu3O7–d coplanar waveguide to a highly dissipative state. Appl. Phys. Lett., 105(2), pp. 022601 (3 p.). DOI: https://doi.org/10.1063/1.4890123
  51. Cherpak, N. T., Gubin, A. I., Lavrinovich, A. A., Vitu-sevich, S. A., 2016. Microwave quenching in DC-biased coplanar waveguide based on YBa2Cu3O7–d thin film. IEEE Trans. on Appl. Supercond., 26(3), pp. 1501204. DOI: https://doi.org/10.1109/TASC.2016. 2537138
  52. Ruibal, M., Ferro, G., Osorio, M. R., Maza, J., Veira, J. A., Vidal, F., 2007. Size effects on the quenching to the normal state of YBa2Cu3O7–d thin-film superconductors. Phys. Rev. B, 75(1), pp. 012504 (4 p.). DOI: https://doi.org/10.1103/PhysRevB.75.012504
  53. Wu, Y., Cui, B., Luo, S., Jiang, X., Zhou, F., Bian, Y., He, Y., Barannik, A. A., Cherpak, N. T. and Skresa-nov, V. N., 2013. A Unique Ka-Band Measurement System Based on Quasi-Optical Dielectric Resonator Technology for Studying Small Superconducting Samples. IEEE Trans. on Appl. Supercond., 23(3), pp. 9000204. DOI: https://doi.org/10.1109/TASC.2012.2233836
  54. Skresanov, V. N., Glamazdin, V. V., Cherpak, N. T., 2011. The novel approach to coupled modes parameters recovery from microwave resonator amplitude-frequency response. In: Proceedings of the 41st European Microwave Conference (EuMC 2011). Man-chester, UK, 12–14 Oct. 2011, pp. 830–833. DOI: https://doi.org/10.23919/EuMC.2011.6101922
  55. Surzhenko, A. B., Schauroth, S., Litzkendorf, D., Zeisberger, M., Habisrenther, T., Gawalek, W., 2001. Growth-related profiles of remanent flux in bulk melt-textured YBaCuO crystal magnetized by pulsed fields. Supercond. Sci. Technol. 14(9), pp. 770–775. DOI: https://doi.org/10.1088/0953-2048/14/9/328
  56. Chiang, C. H., Yang, C. W., Hsieh, P. L., Chan, W. C., 2003. Levitation Force Measurement at Different Temperatures for YBCO Superconductor. J. Low Temp. Phys., 131(3–4), pp. 743–746. DOI: https://doi.org/ 10.1023/A:1022925419581
  57. Cherpak, N. T., Gubin, A. I., Lavrinovich, A. A., Gawalek, W., Litzkendorf, D., 2004. Microwave bulk properties of melt-textured high-TC YBa2Cu3O77–dsuperconductors. Supercond. Sci. Technol. 17(4), pp. 645–648. DOI: https://doi.org/10.1088/0953-2048/ 17/4/013
  58. Cherpak, N. T., Gawalek, W., Golubnichaya, G. V., Gubin, A. I., Kirichenko, A. Ya., Lavrinovich, A. A., Litzkendorf, D., Maximchuk I. G., 2002. High-frequency absorption in melt-textured high-Tc YBaCuO superconductors. Physica C, 372-376(pt. 2), pp. 1123–1126. DOI: https://doi.org/10.1016/S0921-4534(02)00864-X
  59. Bunyaev, S. A., Barannik, A. A. and Cherpak, N. T., 2015. Microstrip Whispering-Gallery-Mode Resonator. IEEE Trans. Microwave Theory Tech., 63(9), pp. 2776–2781. DOI: https://doi.org/10.1109/TMTT. 2015.2457898
  60. Sun, L., Cherpak, N., Barannik, A., He, Y., Glamazdin, V., Zhang, X., Wang, J., Zolotaryov, V., 2017. New Type of Microwave High-TcSuperconductor Microstrip Resonator and Its Application Prospects. IEEE Trans. Appl. Supercond., 27(4), pp. 1501304. DOI: https://doi.org/10.1109/TASC.2016.2631882
  61. Skresanov, V. N., Barannik, A. A., Cherpak, N. T., He, Y., Glamazdin, V. V., Zolotaryov, V. A., Shubny, A. I., Sun, L., Wang, J., Wu, Y., 2016. Experience in developing Ka-band waveguide filter with HTS E-plane insert. In: Proc. of the Int. Kharkov Symposium on Physics and Engineering of Microwaves, Millimeter and Sub-Millimeter waves (MSMW-2016). Kharkov, Ukraine, 20–24 June 2016, 4 p. DOI: https://doi.org/ 10.1109/MSMW.2016.7538050
  62. He, Y., Barannik, A., Cherpak, N., Sun, L., Skresanov, V., Bian, Y., Wang, J., Natarov, M., Zolotaryov, V., 2017. Novel Design of Band-Pass Waveguide Filter with HTS E-Plane Insert. IEEE Trans. Appl. Supercond. 27(4), p. 1501604. DOI: https://doi.org/10.1109/TASC. 2017.2654350
  63. Sun L., Wang X., Wang J., Wu Y., He Y., Li H., Huang J., Luo S., Skresanov V., Barannyk O., Glamazdin V., Zolotarev V., Natarov M., Cherpak M., O. Shubnyj. Rectangular band-pass filter having recesses of less than one-quarter wavelength depth dielectric insert with superconductive film within the recesses. U.S. Pat. 9,537,195.
  64. Cherpak N.T. 2004. High-temperature superconductors and MM wave technology: challenge and perspectives. In: Proc. 5th Int. Kharkiv Symp. Physics and Engineering of Microwaves, Millimeter and Sub-Millimeter Waves (MSMW-2004) Kharkov, Ukraine, 21–26 June 2004, 1, pp. 412–414. DOI: https://doi.org/10.1109/ MSMW.2004.1345912