Alex Gurevich, It is shown that multilayer coating can screen the applied field above the superheating fields of both the superconducting layers and the Nb substrate. There is an optimum multilayer thickness for which the breakdown field at which the multilayer remains in the vortex-free Meissner reaches maximum. It is shown that a dirty layer about the London penetration depth thick at the non-structured Nb surface can increase the superheating field of up to 290 mT. Growing optimized multilayer structures of Nb3Sn or iron pnictides or forming a dirty layer at the surface of the Nb resonator cavities for particle accelerators offer opportunities to increase the peak accelerating electric fields above 100 MV/m.

1. Maximum screening field and the
optimum parameters of superconductivity
multilayers for resonator cavities
Alex Gurevich
Old Dominion University,
Department of Physics and Center for Accelerator Science,
Norfolk, VA 23529, USA
Supported by the US Department of Energy, HEP under grant No. DE-SC0010081
The Sixth International Workshop on THIN FILMS AND NEW IDEAS FOR SRF
October 6 –8, 2014 Legnaro National Laboratories (Padua) ITALY

2. Multilayer coating
Nb
higher-TcSC: NbN,
Nb3Sn, etc
insulating layers
Multilayer coating of SC cavities:
alternating SC and I layers with d < 
Magnetic screening of the Nb
cavity without vortex penetration
No thermodynamically stable parallel
vortices due to the enhancement of Hc1
in thin films with d <  (Abrikosov, 1964)

 


 d
d
2
0
 ln  0.07
 
Hc
1  

2
The breakdown field could be increased up to
the superheating field Hs of the coating:
450 mT for Nb3Sn
AG, APL. 88, 012511 (2006)
The idea has caused a lot of excitement and
misinterpretations (Hc1 = 0, Hc1 is not important,
Hs is reduced not increased, “unmanageable”
dissipation, etc, S. Posen et al., 2014)

3. Recent progress
 Experimental evidences of the enhancement of the parallel Hc1 in thin films
L. Civale, T.K. Worthington, A. Gupta, Phys. Rev. B 48, 7576 (1993).
C. Antoine, et al Phys. Rev. ST-AB 13, 121001 (2010).
T. Tajima, et al. J. Phys. Conf. Ser. 234, 012043 (2010); AIP Conf. Proc. 1435, 297 (2012).
DB Beringer, C Clavero, T Tan, XX Xi, WM Roach, RA Lukaszew IEEE Trans. Appl. Supercond. 23, (2013)
 Increasing the high-field performance and reduction of surface resistance by a
NbN overlayer
C.Z. Antoine, J.-C. Villegier, G. Martinet, APL 102, 102603 (2013).
WM Roach, DB Beringer, Z Li, C Clavero, RA Lukaszew, IEEE Trans. Appl. Supercond. 23 (2013)
What’s next?
 Is there an optimum thickness of layers which maximizes the breakdown field? ✔
 If yes, how far can the maximum screening field Hm be increase by multilayers?
Can the optimized Hm exceed the superheating field of the layer? ✔
 Do we know how to select is the best layer material?
Can we just use a dirty Nb
✔ Are the insulating layers really necessary to protect the cavity and to suppress
strong dissipation caused by local penetration of vortices at defects? ✔

4. Outline
 There is an optimum thickness of multilayers at which it can screen the magnetic field
exceeding the superheating field of both Nb and the layer material.
 ML provide best protection of cavities against surface defects which lower the Bean-
Livingston barrier and open gates for local penetration of vortices.
 Dielectric layers are instrumental to suppress vortex dissipation and dendritic
thermomagnetic avalanches which trigger the cavity quench.
 Implementation of the optimized Nb3Sn or NbN multilayers could double the
maximum accelerating gradient, pushing it above 100 MV/m.
 Pnictides could potentially quadruple the accelerating gradient.
 New opportunities of using dirty Nb multilayers to push Hm up to 280-300 mT

5. GL superheating field

 Meissner state can only exist below the superheating field H < Hs
 Periodic vortex instability as the current density Js = H/ at the
surface reaches the depairing current density Jd = Hs/
Hernandez and Dominguez, PRB 65, 144529 (2002)
 GL calculations of Hs
(Matricon and Saint-James, 1967, Chapman 1995)
Bs »1.2Bc, k @1,
Bs » 0.745Bc, k >>1
 Bs decreases as the surface gets
dirtier and κ = λ/ξ increases.
Nb
At H = Hs the magnetic surface
barrier for penetration of
vortices vanishes

6. Superheating field at T << Tc
GL is not applicable. Calculation of
Hs requires solution of microscopic
BCS/Eilenberger equations
clean limit (bad):
gap vanishes at H < Hs
dirty limit (good):
gap remains finite
at H = Hs
Lin and Gurevich,
PRB 85, 054513 2012
clean
dirty
Only Hs(0) = 0.84Hc at κ >> 1 has been calculated
in the clean limit (Galaiko 1966, Catelani and Sethna, 2008)
and for arbitrary impurity concentration
(Lin and Gurevich, 2012)

7. Possible multilayer materials
Materi
al
Tc (K) Hc [T] Hc1
[mT]
Hc2[T] [nm] 
[meV]
Nb 9.2 0.2 170 0.4 40 1.5
pnictid
es
30-55 0.5-0.9 30 >100 200 10-20
Nb3Sn 18 0.54 50 30 85 3.1
NbN 16.2 0.23 20 15 200 2.6
MgB2 40 0.43 30 3.5-60 140 2.3;
7.1
YBCO 93 1.4 10 >100 150 20
Large gap Δ (good for SRF) is usually accompanied by
low Hc1 (bad for SRF)
Very small surface
resistance at H < Hc1
(Q = 1010-1011)
Q drop due to vortex
dissipation at H > Hc1
Nb has the highest Hc1
but not Hc:
Raise RF critical field
above H(Nb) using
c1
higher Hc materials which
have low Hc1

8. London screening of parallel field
 London equation for the magnetic field h(x)eiωt
in a multilayer on a thick SC substrate in the
external field Heiωt
 Boundary conditions: continuity of the magnetic and electric field at x = d:
continuity of magnetic field continuity of electric field
The rf electric field is:
T. Kubo, Y. Iwashita, and T. Saeki,
APL 104, 032603 (2014).
AG, 2014 unpublished

9. London Solutions
 Solutions for the screening filed at di << ds:
where c and b are given by:
 Important parameters
for the SC substrate (Nb)
with λ0 < λ,
both c and k are positive
J(x)/J(0)
Breakdown of the Meissner state
occurs at the surface of either
ML or Nb where the current
densities J(0) = h’(0) and
J(d) = h’(d) are maximum

10. Current counterflow induced by the substrate
 Current density in the layer J(x) = - h’(x):
 Current density at the surface J(0) is reduced by the substrate with λ0 < λ:
The conterflow induced by the substrate reduces the current density at the ML
surface, allowing the Meissner state in the ML to survive up to fields exceeding
the superheating field Hs for a semi-infinite SC
For a thick ML with d >> λ, the maximum field Hm is limited by Hs:
optimum thickness dm at which Hm exceeds both Hs and Hs0
AG, unpublished, 2014

11. Optimum thickness
 The Meissner state is stable if the screening current densitity at the surface of
both the ML and the substrate is smaller than the depairing limit:
J(0) < Jd = Hs/λ and J(d) < Jd0 = Hs0/λ0
for Hs = 2Hs0 and k = ½,
dc = ln[μ + (μ2 – k)1/2 ]
The Meissner state is below both blue and red lines.
The crossing point defines the optimum thickness dm
for maximum Hm which exceeds the superheating
fields of both the layers and the substrate
The assumption that the breakdown of the Neissner state is caused by the rf field but not
current (T. Kubo, Y. Iwashita, and T. Saeki, APL 104, 032603 (2014)) underestimates Hm

12. Maximum screening field
 The maximum screening field Hm corresponds to d = dm for which
Hm at the optimum thickness exceeds the bulk superheating fields of both Nb and
the layer material. For λ >> λ0, practically for λ > 160 nm for a SC layer on the Nb
cavity with λ0 = 40 nm, Hm approaches the limit
Let us evaluate Hm for a ML on clean Nb with λ0 = 40 nm and Hs0 = 1.2Hc = 240 mT
(the GL result for clean Nb) and different layer materials, such as Nb3Sn, NbN,
pnictides, and also dirty Nb
AG, unpublished, 2014

13. Estimates of Hm and dm
 Nb3Sn: Hs = 0.84Hc = 454 mT and λ = 120 nm (moderately dirty):
Hm = 507 mT, dm = 1.1λ = 132 nm
doubles the superheating field of clean Nb
 Ba0.6K0.4Fe2As2, Tc = 38 K, Hc = 0.9T, Hs =756 mT, λ = 200 nm
Hm = 930 mT, dm = 1.78λ = 356 nm.
almost quadruples the superheating field of clean Nb
 dirty Nb layer: Hc = 200 mT, Hs = 170 mT, l = 2 nm, and λ =λ(ξ0 /l)1/2 = 180 nm
Hm = 288 mT, dm = 0.44λ = 79 nm.
20% gain as compared to Hs = 240 mT of clean Nb

14. Surface barrier and vortex penetration at H > Hc1
 Meissner current pushes the vortex in the bulk
 Attraction of the vortex to its antivortex image pushes
the vortex out of the superconductor

H0
b
J
image
to ensure
J = 0
 
 b /
    0 0 G b H e H b H H v c
( ) [ (2 ) ] 1 0
H < Hc1
H = Hc1
H > Hc1
H = Hc
b
G
Thermodynamic potential G(b) of the vortex:
Meissner Image
Vortices have to overcome the surface barrier
even at H > Hc1 (Bean & Livingston, 1964)
BL barrier at an ideal surface disappears
only at the overheating field H = Hs
Surface materials defects open gates for
local penetration of vortices at H < Hs

15. Penetration of vortices in a thick film
A defect locally weakens
the surface barrier which
vanishes at
J(0) > βJd β < 1
Once a vortex breaks
through a defect, it triggers
a magnetic flux avalanche
in the bulk at H > Hc1
H
λ λ
H
Penetration of many vortices causes heating and a dendritic thermo-magnetic flux jump
Poor thermal conductivity of Nb3Sn: a 2-3 μm thick film doubles the thermal impedance
of the Nb cavity wall, facilitating local overheating and branching vortex avalanches
Thin dielectric layers provide the strongest possible pinning of vortices, blocking
propagation of vortex avalanches

16. Penetration of vortices in a thin multilayer
Parallel Hc1 in a thin film multilayer
is irrelevant (no longer a problem)
I layer intercepts propagating vortex loops,
turning them into two short vortices of
opposite polarity. No propagation in the
bulk if h(d) < Hc1
Great reduction of the RF vortex power q
localized in a thin S layer. Upper limits of
q and the amplitude of V-AV oscillations um
Nb3Sn: ρn = 0.2 μΩm, d/λ = 0.2,
κ = 20, λ = 100 nm, β = 1/2, ν = 2GHz
For Nb3Sn, um ≈ 4 μm, and q ≈ 2 μW
Unlike thick Nb3Sn films (d > 1-2 μm), a thin ML only slightly (by ≈ 5%) increases the thermal
Impedance of the cavity wall. No deterioration of thermal quench stability.

17. Magnetic flux penetration in superconductors
Smooth
flux penetration and
remagnetization in a
Nb single crystal
MgB2
Dendritic flux penetration:
magnetic microavalanches
(mostly at low T)
U. Oslo and UW websites
Vortex sandpile.
Nonlinear magnetic
flux diffusion
Positive feedback
between flux motion
and Joule heating
Thermomagnetic
instability
Dendritic pattern
formation

18. What happens if vortex avalanches are not stopped
(MO image of Nb film by M.Welling and R. Wijngaarden, U. Amsterdam)

19. Looks familiar?
snowflake
 Dendritic instability
during solidification growth
 Viscous liquid fingering
 Diffusion-limited
aggregation
 bacterial “snowflakes”

20. Theory of dendritic flux penetration
 Coupled equations for the temperature T and electric field E
 ( , )
E
J T E
t
  
E
T J T E E
T
t
C




  
( , )
0
2


 

J J c  Two characteristic times:
- tm = 0L2/ - time of magnetic flux diffusion
- th = CL2/ - time of thermal diffusion
 Thermal bistability and nonlocal flux diffusion
 Turring instability in a reaction-diffusion systems
 Nonequilibrium dendritic structures
Aranson, Gurevich, Vinokur, Phys. Rev. Lett. 87, 0976003 (2001); 94, 037002 (2005).
Becomes particularly
violent at low temperatures
< 4 K as the specific heat
C(T) = C0T3 decreases

21. Dendritic flux propagation in a film with surface defects
EM nonlocality
facilitates branching
instability
Giant magnetic avalanche
in the defect free region
Several successive
waves of dendritic
flux propagation
Supersonic propagation
at low temperatures
Aranson, Gurevich, Vinokur,
Phys. Rev. Lett. 87, 94, 037002 (2005).

22. How to protect cavities from vortex avalanches?
βHs
Hc1
Maximum field which satisfies the necessary
stability margin
but now Hs and Hs0 are re-defined as follows
The onset of vortex penetration
reduced by defects (β < 1)
The onset of vortex penetration
reduced by defects (β < 1)
Conservative stability margin: even in the worst case scenario vortex hotspots are
only localized in a thin surface layer and do not propagate in the bulk
Other conservative assumptions, β = ½ and Hc1 = 170 mT for numerical estimates

23. Estimates of Hm and dm for β = ½ and Hs0 = 170 mT
Conservative stability margin against penetration of vortices
 Nb3Sn: Hs = 0.84Hc = 454 mT and λ = 120 nm (moderately dirty):
Hm = 273 mT, dm = 96 nm
20% higher than for thick Nb3Sn
 Ba0.6K0.4Fe2As2, Tc = 38 K, Hc = 0.9T, Hs =756 mT, λ = 200 nm
Hm = 588 mT, dm = 310 nm.
more than doubles the superheating field of clean Nb

24. Conclusions
• Multilayers can be optimized in such a way that they can screen the magnetic field
exceeding the superheating fields of both the layer material and substrate
• Can push the accelerating gradients over 100 MV/m
• S-I-S multilayers provide best protection of cavities against local penetration of vortices
• Significant reduction of vortex dissipation and suppression of thermomagnetic
avalanches as compared to thick films or uncoated cavities
• Lots of materials to play with (Nb3Sn, NbN, pnictides)
• Key material challenges are: weak-linked grain boundaries, second phase precipitation
and the broadening of the gap peaks in the density of states by impurities and
inhomogeneities
• New opportunities to use a 89-90 nm thick dirty Nb overlayer on a thin (few nm)
dielectric layer deposited onto the Nb cavity