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SUMMARY:A current density dependence on phase differences in layered super
 conducting structures of SISIS type
DTSTART;VALUE=DATE-TIME:20181205T102500Z
DTEND;VALUE=DATE-TIME:20181205T104500Z
DTSTAMP;VALUE=DATE-TIME:20260316T192957Z
UID:indico-contribution-13@indico.bitp.kiev.ua
DESCRIPTION:Speakers: Arsen Shutovskyi (Lesya Ukrainka Eastern European Na
 tional University)\nThe explored layered superconducting structure contain
 s three massive superconductors separated by two thin insulator films. Wit
 hout loss of generality we may consider that the superconductors are diffe
 rent. An insulator film is mathematically expressed via the Dirac delta fu
 nction [1]. An order parameter and a current density depend on an applicat
 e\, because we have a one dimensional problem.\nAccording to the supercond
 uctivity theory every physical quantity can be calculated using the Green 
 function method [2]. The Green functions satisfy the closed system of line
 ar differential equations. The mentioned equations have the second derivat
 ive in the configuration representation. Using the Fourier transform we ha
 ve constructed the closed system of linear matrix differential equations i
 n the t-representation [3]. The obtained equations have only the first der
 ivative. Since a momentum is close to the Fermi momentum our calculations 
 become rather simplified. Solving the linear matrix differential equations
  in the t-representation we have introduced the undefined integration cons
 tants. These constants can be defined through application of Green functio
 n continuity. This means that we need to have a boundary condition. An ord
 er parameter as a complex function is usually defined by magnitude and pha
 se. The model with a piecewise constant order parameter allows to suppose 
 that the outside superconductors have equal order parameter magnitudes and
  unequal order parameter phases. The inside superconductor has a zero orde
 r parameter phase. The order parameter magnitude of the inside superconduc
 tor is not necessary equal to the order parameter magnitudes of the outsid
 e superconductors.\nSubstituting the obtained integration constants into t
 he Green functions we have obtained the current density dependence on an a
 pplicate. Calculating the current density on the junction we have obtained
  the current density expression as a phase difference function.\n\n[1] С
 відзинський А. В. Математичні методи тео
 ретичної фізики. У 2-х т. – Вид. 4-те\, допов
 н. і переробл. – К.: І-нт теорет. фізики ім.
  М. М. Боголюбова\, 2009.\n[2] Свидзинский А. В. 
 Пространственно-неоднородные задачи те
 ории сверхпроводимости. – М.: Наука\, 1982. 
 – 310 с.\n[3] Свідзинський А. В. Мікроскопічн
 а теорія надпровідності: монографія. – Л
 уцьк: ВНУ ім. Лесі Українки\, 2011. – 422 с.\n\nht
 tps://indico.bitp.kiev.ua/event/2/contributions/13/
LOCATION:
URL:https://indico.bitp.kiev.ua/event/2/contributions/13/
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