Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Properties of field induced Josephson junction(s)

77 views

Published on

Field Induced Josephson Junction (FIJJ) is defined as the physical system made by placement of ferromagnetic strip directly or indirectly [insulator layer in-between] on the top of superconducting strip [3, 4, 7]. The analysis conducted in extended Ginzburg-Landau, Bogoliubov-de Gennes and RCSJ [11] models essentially points that the system is in most case a weak-link Josephson junction [2] and sometimes has features of tunneling Josephson junction [1]. Generalization of Field Induced Josephson junctions leads to the case of network of robust coupled field induced Josephson junctions [4] that interact in inductive way. Also the scheme of superconducting Random Access Memory (RAM) for Rapid Single Flux [8, 9] quantum (RSFQ) computer is drawn [6, 10] using the concept of tunneling Josephson junction [1] and Field Induced Josephson junction [3, 4].

The given presentation is also available by YouTube (https://www.youtube.com/watch?v=uIqXqiwDsSM).

Literature
[1]. B.D.Josephson, Possible new effects in superconductive tunnelling, PL, Vol.1, No. 251, 1962
[2]. K.Likharev, Josephson junctions Superconducting weak links, RMP, Vol. 51, No. 101, 1979
[3]. K.Pomorski and P.Prokopow, Possible existence of field induced Josephson junctions, PSS B, Vol.249, No.9, 2012
[4]. K.Pomorski, PhD thesis: Physical description of unconventional Josephson junction, Jagiellonian University, 2015
[4]. K.Pomorski, H.Akaike, A.Fujimaki, Towards robust coupled field induced Josephson junctions, arxiv:1607.05013, 2016
[6]. K.Pomorski, H.Akaike, A.Fujimaki, Relaxation method in description of RAM memory cell in RSFQ computer, Procedings of Applied Conference 2016 (in progress)
[7]. J.Gelhausen and M.Eschrig, Theory of a weak-link superconductor-ferromagnet Josephson structure, PRB, Vol.94, 2016
[8]. K.K. Likharev, Rapid Single Flux Quantum Logic (http://pavel.physics.sunysb.edu/RSFQ/Research/WhatIs/rsfqre2m.html)
[9]. Proceedings of Applied Superconductivity Confence 2016, plenary talk by N.Yoshikawa, Low-energy high-performance computing based on superconducting technology (http://ieeecsc.org/pages/plenary-series-applied-superconductivity-conference-2016-asc-2016#Plenary7)
[10]. A.Y.Herr and Q.P.Herr, Josephson magnetic random access memory system and method, International patent nr:8 270 209 B2, 2012
[11]. J.A.Blackburn, M.Cirillo, N.Gronbech-Jensen, A survey of classical and quantum interpretations of experiments on Josephson junctions at very low temperatures, arXiv:1602.05316v1, 2016

Published in: Science
  • Be the first to comment

  • Be the first to like this

Properties of field induced Josephson junction(s)

  1. 1. Properties of field induced Josephson junctions Krzysztof Pomorski University of Warsaw, Nagoya University kdvpomorski@gmail.com December 14, 2016 Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 1 / 54
  2. 2. Overview 1 Macroscopic quantum states 2 Essence of Josephson effect 3 Concept of simplified FIJJs 4 Generalization of FIJJs 5 Mathematical description of Josephson junctions 6 Numerical method and results Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 2 / 54
  3. 3. Macroscopic quantum states:superconductivity and superfluidity Figure: Transport without dissipation (R → 0) [Onnes 1911], Meissner effect [Wikipedia], movement of liquid without viscosity [Wikipedia]. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 3 / 54
  4. 4. Josephson effect: tunneling junction Figure: Tunneling Josephson junction [Nature 47, J.You and F.Nori, 2011] and its electrical circuit and weak-link Josephson junction. Different of phase of SCOP Θ = ΘR − ΘL determines transport properties. Most simple model assumes ψL = √ ρLeiΘL , ψR = √ ρR eiΘR . H = HL + HR + HT , |ψ = ψL |L + ψR |R (1) H = EL |L L| + ER |R R| + ET (|L R| + |R L|) (2) I(t) = I0 sin(Θ) + 1 R 2e dΘ dt + C 2e d2Θ dt2 (3) Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 4 / 54
  5. 5. Weak link Josephson junction systems Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 5 / 54
  6. 6. Tunneling vs weak link Josephson junctions Figure: I-V characteristic of tunneling JJ [left] vs weak-link JJ [C-center] and I-V characteristics in microwave field for weak-link [R-right], [C,R] from L.Gomez. Tunneling vs weak-link Josephson junctions: Two quantum coherent quantum systems interacting in perturbative vs non-pertubative way. sinusoidal vs non-sinusoidal relation between phase difference and electric current. no-current presence vs continous electric current for certain voltageKrzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 6 / 54
  7. 7. Central motivation Figure: Definition of Field Induced Josephson Junctions (FIJJ). Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 7 / 54
  8. 8. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 8 / 54
  9. 9. [PSS B, K.Pomorski and P.Prokopow, 2012] Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 9 / 54
  10. 10. Concept of simplified field induced Josephson junctions Figure: Physical system 1 and its simplification. Figure: Physical system 2 and its simplification [’Towards robust coupled field induced JJs’,Arxiv:1607.05013] Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 10 / 54
  11. 11. Generalization of field induced Josephson junction Figure: Stage I: deformation of sc cable. Stage II: Deformed sc cable + arbitrary shaped polarizing cable [ArXiv:1607.05013]. Figure: Stage III:Coupled sc cables in any net of polarizing cables. Stage IV: hybrid quantum system [ArXiv:1607.05013]. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 11 / 54
  12. 12. Magnetic field entangling superconducting lattice Figure: [Upper figures]: Electrical ways of controlling topologies of magnetic entangler placed in superconducting lattice of cables (BdGe cables). [Picture below]: 2 dim BdGe cables and polarizing cable lattice [ArXiv:1607.05013]. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 12 / 54
  13. 13. Asymptotic states and scattering region in FIJJ/uJJ Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 13 / 54
  14. 14. Analytic formulas for FIJJ with insulator From Ginzburg-Landau we can write the equation for electric current density in the form (c1 > 0) as jx,(y,z)(x, y, z) = −c1Ax,(y,z)(x, y, z)|ψ(x, y, z)|2 . (4) Using Maxwell equation we obtain for time independent vector potential B = × A equation of the following structure × ( × Ax,(y,z)(x, y, z)) = µ0jx,(y,z)(x, y, z) (5) Using the relation a × (b × c) = b(ac) − c(ab) we obtain ×( ×Ax,(y,z)(x, y, z)) = ( Ax,(y,z)(x, y, z))− 2 Ax,(y,z)(x, y, z) (6) that can be written after using Maxwell equation as ( Ax,(y,z)(x, y, z))− 2 Ax,(y,z)(x, y, z) = −c1Ax,(y,z)(x, y, z)|ψ(x, y, z)|2 . (7) Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 14 / 54
  15. 15. ( A1(2)x,(y,z)(x, y, z)) − 2 A1(2)x,(y,z)(x, y, z) = −c1A1(2)x,(y,z)(x, y, z)|ψ0|2 . ( [A1 + A2]x,(y,z)(x, y, z)) − 2 [A1 + A2]x,(y,z)(x, y, z) = −c1[A1 + A2]x,(y,z)(x, y, z)|ψ0|2 . System with translational symmetry has current flow as 2 A1(2)x (y, z) = +c1A1(2)x (y, z)|ψ0|2 . (8) since ( x A1(2)(y, z)x ) = 0. Ax(y) that has translational symmetry is as Ax (y) = a1cosh(k1y) + b1sinh(k1y), where k1 = √ c1|ψ0|,y is from -d to d. I0 = +d −d jx (y)dy = −c1|ψ0|2 +d −d (a1cosh(k1y) + b1sinh(k1y))dy Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 15 / 54
  16. 16. Class of structures to be considered Figure: Important message: FIJJs has built-in shielding current what implies that they are α Josephson junctions so CPR is shifted by arbitrary phase. In general they are weak-links and non-sinusoidal Josephson junctions. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 16 / 54
  17. 17. Simple FIJJ system in Ginzburg-Landau formalism Figure: [Left]: Simplest case of FIJJ. [Right]: Case on FIJJs network. London relation gives jx = I0 = −c1Ax (x)|ψ(x)|2 = constants and Az(x) = k1Ip (x2+a2 0)1/2 since A(r ) ≈ j(r)dr/|r − r’|. Ginzburg-Landau equation has the structure [|ψ0| = −α β for bulk sc]: α(x)ψ(x, t) + β|ψ(x, t)|2ψ(x, t) + 1 2m ( i d dx − 2e c Ax )2ψ(x, t) = γ d dt ψ(x, t) . Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 17 / 54
  18. 18. View of FIJJs in Ginzburg-Landau formalism We introduce two functions f1(x) and f2(x) that we can engineer. f1(x) = (Ay (x)2 + Az(x)2 ), f2(x) = (∆y d dx Ay (x) + ∆z d dx Az(x)), (9) so effective α(x) = α + 1 2m (2e c )2f1(x) − 2 2m a2 0f2(x)2 and effective GL equations becomes modified and real-valued for f (x) = |ψ(x)|-superconducting order parameter. where (a1, a2, a3, a4) are positive constants so GL is extended −( d2f dx2 ) + βf 3 + α1(x) + a1f1(x) − a2(f2(x))2 f + a3f2(x) I0 f + a4 I2 0 f 3 = 0(10) Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 18 / 54
  19. 19. Mathematical description of FIJJs-time dependent case TDGL-Time Dependent Ginzburg-Landaua equation is considered. We have a time dependent vector potential fields Ax (x, y0, z0, t), Ay (x, y0, z0, t), Az(x, y0, z0, t) and I0(t). We need to calculate γ d dt |ψ| + V (x, t)|ψ| + ia0( x x0 d dt Ax (x , y, z, t)dx + (∆y d dt Ay (x, y, z, t) + ∆z d dt Az (x, y, z, t)))|ψ| = = (α + β|ψ| 2 )|ψ| + e −i(Θx +Θy +Θz ) 1 2m ( i d dx − 2e c Ax ) 2 (|ψ|e i(Θx +Θy +Θz ) + 1 2m ( 2e c ) 2 (A 2 y + A 2 z )|ψ| (11) and I0(t) = dAx (x, y0, z0, t) dt σ − c1Ax (x, y0, z0, t)|ψ(x, y0, z0, t)|2 (12) and Ex (x, y0, z0, t) = − dAx (x, y0, z0, t) dt σ − φ(x, y0, z0, t) (13) where V (x, t) = x x1 Ex (x , y0, z0, t)dx . Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 19 / 54
  20. 20. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 20 / 54
  21. 21. Scheme of relaxation method Gradient method is basing on the following iterations xn+1 i = xn i − i dF(x) dxn i |x=(xn 1 ,...,xn k ), (14) where i are constants and vector (xn 1 , ..., xn k ) gives value of physical fields in n-th steps. Relaxation method is basing on the following iteration scheme δ δXi F[Xi (x)] = ηi dXi (x) dt . (15) In discretized form we have Xi (tn+1) = ∆tn ηi δ δXi F[Xi (tn)] + Xi (tn), (16) where ηi are constants. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 21 / 54
  22. 22. Figure: SCOP obtained by the relaxation method [left] and assumed distribution of α coefficient [right]. Figure: Free energy functional F [left] and average error with iterations [right]. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 22 / 54
  23. 23. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 22 / 54
  24. 24. Ginzburga-Landaua model-thermodynamical derivation Figure: Superconducting order parameter and minimization of functional F. F[ψ, A] = 1 2m |( i d dx − 2e c Ax (x))ψ(x)|2 + α 2 |ψ(x)|2 + β 4 |ψ(x)|4 , (17) Setting functional derivatives δ δXi F = 0 to zero with respect to Xi = (ψ, A) we have the following equations of motion 0 = 1 2m ( i d dx − 2e c Ax (x))2 ψ(x) + αψ(x) + β|ψ(x)|2 ψ(x), j(r) = e m (ψ† (r)( i d dx − 2e c Ax (x)) + c.c). Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 23 / 54
  25. 25. Boundary conditions in GL theory ( i d dx − 2e c Ax )ψ(x) = 0 (18) ( i d dx − 2e c Ax )ψ(x) = 1 b(y) ψ(x) (19) (bases for non-abrupt uJJ). ’Boundary conditions on the GL eqns for anisotropic superconductors’, E.A.Shapoval, Sov. Phys. JETP 61, 1985 ’General boundary conditions for quasiclassical theory of Superconductivity in the diffusive limit:application to strongly spin-polarized systems’ Eschrig et al. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 24 / 54
  26. 26. Concept of unconventional Josephson junction. Figure: Distribution of SCOP ψ(x, y, 1 2 (zmax + zmin)). Geometrical dimension Lx : Ly : Lz = 0.4(0.6) : 20 : 20, in terms of units of superconducting coherence lenght. [PSS B, K.Pomorski and P.Prokopow, 2012] Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 25 / 54
  27. 27. Cylindrical/spherical uJJ(FIJJ) [Perspective on basic architectures and properties of unconventional and field induced Josephson junction devices, K.Pomorski, P.Prokopow, 2013, International Journal of Microelectronics and Computer Science] Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 26 / 54
  28. 28. Extended Ginzburg-Landaua formalism F = Fs + FM + Fs−M, FM = dr(a(T)|M(r)|2 + b(T) 2 |M(r)|4 + C| M(r)|2 ), (20) Fs = dr( α 2 |ψ|2 + β 4 |ψ|4 + 1 2m |( i − 2e c A)ψ|2 + (curlA)2 4π ) (21) Fs,M = dr(γ|ψ(r)|2 |M(r)|2 + (| M(r)|2 |ψ(r)|2 ) + µ 2m |( i − 2e c A)ψ(r)|2 |M(r)|2 + curl(A)M) (22) It is quite essential to tract K.Kubokiego and K.Yano derivation of GL from extended Hubbard model [Journal of the Physical Society of Japan, ’Microscopic Derivation of Ginzburg-Landau Equations for Coexistent States of Superconductivity and Magnetism’, 2013]. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 27 / 54
  29. 29. Figure: Transition between tunneling Josephson junction and weak-link JJ obtained by extended GL model [PSSB, K.Pomorski, P.Prokopow, 2012]. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 28 / 54
  30. 30. Bogoliubov-de Gennes equations (BdGe) Hamiltonian H of free particle [no superconducting order parameter] H = 1 2m i d dx − 2e c Ax (x, y, z) 2 + i d dy − 2e c Ay (x, y, z) 2 + 1 2m i d dz − 2e c Az (x, y, z) 2 + V (x, y, z). From BCS theory we have +Hun(x, y, z) + ∆(x, y, z)vn(x, y, z) = nun(x, y, z) −H† vn(x, y, z) + ∆(x, y, z)† un(x, y, z) = nvn(x, y, z) ∆(x, y, z) = −V1 n un(x, y, z)v† n (x, y, z)(1 − 2f ( n)), Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 29 / 54
  31. 31. Local density of states (LDOS) for uJJ Figure: Local density of state (LDOS) for different temperatures T1 and T2 (T1 < T2), [K.Pomorski et al., PSSB 2012] N(r, E) = − n (f ( n − E)|un(r)|2 + f ( n + E)|vn(r)|2 ) (23) Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 30 / 54
  32. 32. Topological defects in Sc-Fe system Both Abrikosov and Josephson vortices can be induced in FIJJ as given in [K.P EJTP 2010, K.P. PhD thesis 2015, G. Carapella et al, Nature 2016 ]. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 31 / 54
  33. 33. Triangle and tunability of FIJJ properties: critical current, CPR, α continuous shift in CPR, Density of States, heat capacity, transmission coefficient, conversion between singlet and triplet current [EJTP, KP 2010] Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 32 / 54
  34. 34. Andreev reflection at interface between normal and superconducting state Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 33 / 54
  35. 35. Andreev bound states in JJ Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 34 / 54
  36. 36. Andreev reflection in 2 dimensions Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 35 / 54
  37. 37. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 36 / 54
  38. 38. Full Counting Statistics (FCS) for FIJJs/uJJs Figure: Effective reflection coefficient can be determined so Full Counting Statistics can be determined. In such case we can obtain the scattering matrix tunned by properties of uJJ/FIJJ and tune its properties in continous way. Having scattering matrix we can get cummulant generating function F(χ) and use Lesovik-Levitov formula for getting cummulants of noise. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 37 / 54
  39. 39. RCSJ in description of uJJ (FIJJ) Figure: We are biasing guJJ (granular unconventional Josephson junction) via V(t) between A i B or electric current I(t). (I20,I21): s=(I0,I0), s1 = (I21 = 0.6I0), s2 = (I21 = 0.1I0), s3=(I20 = 0.1I0 = I21). Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 38 / 54
  40. 40. Figure: (I20,I21): s=(I0,I0), s1 = (I21 = 0.6I0), s2 = (I21 = 0.1I0), s3=(I20 = 0.1I0 = I21), C = 0, basing by electric current. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 39 / 54
  41. 41. Figure: Vortices in short Josephson junction:no-self field effects Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 40 / 54
  42. 42. Basic concept of Rapid Single Quantum Flux electronics Figure: Way of pushing of magnetic flux out of superconducting loop [left] and concept of Josephson transmission line [right]. The logical gate NOT [left] and its implementation [right] is given below. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 41 / 54
  43. 43. RAM cell for Rapid Single Flux quantum electronics Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 42 / 54
  44. 44. Scattering vector potential Ay (x, y), Az(x, y) in RAM cell Figure: Vector potential in Scenario (I, II)[Ay], I[Az] in states(up—down=1—0). Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 43 / 54
  45. 45. Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 44 / 54
  46. 46. References [1]. B.D.Josephson, Possible new effects in superconductive tunnelling, PL, Vol.1, No. 251, 1962 [2]. K.Likharev, Josephson junctions Superconducting weak links, RMP, Vol. 51, No. 101, 1979 [3]. K.Pomorski and P.Prokopow, Possible existence of field induced Josephson junctions, PSS B, Vol.249, No.9, 2012 [4]. K.Pomorski, PhD thesis: Physical description of unconventional Josephson junction, Jagiellonian University, 2015 [5]. K.Pomorski, H.Akaike, A.Fujimaki, Towards robust coupled field induced Josephson junctions, arxiv:1607.05013, 2016 [6]. K.Pomorski, H.Akaike, A.Fujimaki, Relaxation method in description of RAM memory cell in RSFQ computer, Procedings of Applied Conference 2016 (in progress) [7]. J.Gelhausen and M.Eschrig, Theory of a weak-link superconductor-ferromagnet Josephson structure, PRB, Vol.94, 2016 [8]. K.K. Likharev, Rapid Single Flux Quantum Logic (http://pavel.physics.sunysb.edu/RSFQ/Research/WhatIs/rsfqre2m.html) Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 45 / 54
  47. 47. [9]. Proceedings of Applied Superconductivity Confence 2016, plenary talk by N.Yoshikawa, Low-energy high-performance computing based on superconducting technology [10]. A.Y.Herr and Q.P.Herr, Josephson magnetic random access memory system and method, International patent nr:8 270 209 B2, 2012 [11]. J.A.Blackburn, M.Cirillo, N.Gronbech-Jensen, A survey of classical and quantum interpretations of experiments on Josephson junctions at very low temperatures, arXiv:1602.05316v1, 2016 [12]. Current driven transition from Abrikosov-Josephson to Josephson-like vortex in mesoscopic lateral S/S/S superconducting weak links, G. Carapella, P. Sabatino, C. Barone, S. Pagano and M. Gombos, Nature, 2016 [13].Fluxon Propagation on a Josephson Transmission Line, A. Matsuda and T. Kawakami Phys. Rev. Lett. 51, 694,1983 Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 46 / 54
  48. 48. Publikacje wlasne 1 K.Pomorski, P.Prokopow, International Journal of Microelectronics and Computer Science (2013), Vol.4, No.3, strony: 110-115, Perspective on basic architecture and properties of unconventional and field induced Josephson junction devices 2 K.Pomorski, P.Prokopow, Physica status solidi B 249, No 9 (2012), strony: 1805-183, Possible existence of field induced Josephson junctions + backover 3 K.Pomorski, P.Prokopow, Electronic Journal of Theoretical Physics (2010), Vol.7, No. 23, strony 85-121, Towards the determination of properties of the unconventional Josephson junction made by putting non-superconducting strip on the top of superconducting strip 4 K.Pomorski, P.Prokopow, Bulletin de la societe et des sciences et des lettres de Lodz, Recherches sur les deformations (2012), Numerical solutions of nearly time independent Ginzburg-Landau equations for various superconducting structures, part I 5 K.Pomorski, P.Prokopow, Bulletin de la societe et des sciences et des lettres de Lodz, Recherches sur les deformations (2013), Numerical solutions of nearly time independent Ginzburg-Landau equations for various superconducting structures, part II 6 K.Pomorski, P.Prokopow, Bulletin de la societe et des sciences et des lettres de Lodz, Recherches sur les deformations (2011), vol. LXI, no. 2, Numerical solutions of time-dependent Ginzburg-Landau equations for various superconducting structures 7 K.Pomorski, M.Zubert, P.Prokopow, Transport properties of dirty unconventional Josephson junction devices in RCSJ model, pierwsze miejsce na konferencji ICSM2014 8 K.Pomorski, M.Zubert, P.Prokopow, Numerical solutions of nearly time-independent Ginzburg-Landau equation for various superconducting structures: III. Analytical solutions and improvement of relaxation method, Bulletin de la societe et des sciences et des lettres de Lodz, Recherches sur les deformations Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 47 / 54
  49. 49. Cytowana literatura 1 K. Kuboki, Microscopic derivation of the Ginzburg-Landau equations for coexistent states of superconductivity and magnetism, arXiv:1102.3329 (2011) 2 A. Maeda, L. Gomez, Experimental Studies to Realize Josephson Junctions and Qubits in Cuprate and Fe-based Superconductors, Journal of Superconductivity and Novel Magnetism 23, (2010). 3 K.K. Likharev, Superconducting weak links, Review of Modern Physics 51, (1979) 4 T. Clinton, Advances in the development of the magnetoquenched superconducting valve: Integrated control lines and a Nb-based device, Journal of Applied Physics 91 (2002) 5 B.D. Josephson,Possible new effects in superconductive tunnelling, Physics Letters 1 (1962) 6 J.S. Reymond, P. SanGiorgio, Tunneling density of states as a function of thickness in superconductor/strong ferromagnet bilayers, Physical Review B 73 (2006) 7 X.B. Xu, H. Fanohr, Vortex dynamics for low-k type superconductors, Physical Review B 84 (2011) 8 M. Thinkham, Introduction to superconductivity, Dover Publications, (2004) 9 J.Q. You, F. Nori, Superconducting Circuits and Quantum Information, Physics today (2005) 10 N. Cassol-Seewald, G. Krein, Numerical simulation of GinzburgLandau-Langevin equations, Brazilian Journal of Physics 37 (2007) 11 J.J.V. Alvarez, C.A. Balseiro, Vortex structure in d-wave superconductors, Physical Review B 58 (1998) Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 48 / 54
  50. 50. Cytowana literatura-metody numeryczne 1. Metoda: Variable link. ’Numerical solution of the time-dependent Ginzburg-Landau equation for a superconducting mesoscopic disk:Link variable method’, J.Barbara-Ortega et al. , IOP, 2008 2. Algorytm relaksacyjny zastosowany w jednym wymiarze dla GL. 3. Metoda wygrzewania (annealing). 4. Split-step method stosowana w r´ownaniu Grossa-Pitaeveskiego (GP). Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 49 / 54
  51. 51. Congratulates Mr. Krzysztof Pomorski, As the presenting author of Transport Properties of Dirty Unconventional Josephson Junction Devices in RCSJ Model For the first place in the “Best Poster Award” To be continued ...!!! Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 50 / 54
  52. 52. Research plan 1 Design of superconducting RAM cell for RSFQ computer of small dimensions 2 Extension and validation of M.Eschrig [PhysRevB.94.104502] results (He cites my PSSB 2012 work) 3 Creation platform supporting last Nature publication on crossover from Abrikosov vortex to Josephson vortices [G. Carapella et al, Nature 2016] 4 Determination of properties of robust field induced Josephson junction 5 Application of canonical quantization procedure to one dimensional field induced Josephson junction [continuation of work with dr hab. Adam Bednorz (FUW),arXiv:1502.00511 and its generalization published in IOP paper by K.P and A.B, 2016] 6 Determination of Current Phase Relation for FIJJs with Fe strip on the top of superconductor with insulator in-between [already some analytical results are known.] 7 Determination of properties of topological Meissner effect 8 Validation of canonical procedure for systems showing topological JJs Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 51 / 54
  53. 53. Research plan Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 52 / 54
  54. 54. Essence of topological Meissner effect Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 53 / 54
  55. 55. Stages of topological Meissner effect Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 54 / 54

×