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
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. 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. 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. 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. Weak link Josephson junction systems
Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 5 / 54
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. Central motivation
Figure: Definition of Field Induced Josephson Junctions (FIJJ).
Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 7 / 54
9. [PSS B, K.Pomorski and P.Prokopow, 2012]
Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 9 / 54
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. 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. 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. Asymptotic states and scattering region in FIJJ/uJJ
Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 13 / 54
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. ( 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. 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. 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. 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. 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
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. 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
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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Andreev reflection at interface between normal and
superconducting state
Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 33 / 54
35. Andreev bound states in JJ
Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 34 / 54
36. Andreev reflection in 2 dimensions
Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 35 / 54
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. 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. 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. Figure: Vortices in short Josephson junction:no-self field effects
Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 40 / 54
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. RAM cell for Rapid Single Flux quantum electronics
Krzysztof Pomorski (UW,UN) Properties of FIJJ December 14, 2016 42 / 54
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
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. [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. 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. 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. 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. 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. 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