and engineering optimal surface nano structuring of SRF cavities T Kubo KEKODU and A Gurevich ODU 1 Supported by NSF under Grant NoPHY1416051 Supported by JSPS KAKENHI Grant No17H04839 and No17KK0100 ID: 790071
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Slide1
Field-dependent surface resistance
and engineering optimal surface nano-structuring of SRF cavities
T. Kubo
(KEK,ODU) and A. Gurevich (ODU)
1
Supported by NSF under Grant No.PHY-1416051
Supported by JSPS KAKENHI Grant No.17H04839, and No.17KK0100
Slide2What is the origin of many different Q-E curves?
A. Grassellino, et al.,Supercond. Sci. Technol. 30,
094004 (2017)
G. Ciovati, J. Appl. Phys. 96, 1591 (2004);P. Dhakal, et al., Phys. Rev. ST
Accel. Beams 16, 042001 (2013)
A. Grassellino et al.,
Supercond.
Sci
.
Technol
.
26
(2013) 102001
The longstanding mystery in SRF
C.
Benvenuti
et al.,
Physica
C 351, 421 (2001)
T. Kubo
etal., IPAC14, Dresden, Germany (2014), p. 2519, WEPRI022
2
Slide3Unfortunately, the
Mattis-Bardeen’s formula for the weak-field Rs tells you nothing about the shape of Q-E curve. ?
A. Grassellino, et al.,Supercond.
Sci. Technol. 30, 094004 (2017)3
Slide4Unfortunately, the Mattis
-Bardeen’s formula for the weak-field Rs tells you nothing about the shape of Q-E curve. It is valid only at the weak-field limit: the left end of Q-E curve.
4
Slide5Unfortunately, the Mattis
-Bardeen’s formula for the weak-field Rs tells you nothing about the shape of Q-E curve. It is valid only at the weak-field limit: the left end of Q-E curve. Moreover, effects of material features other than mfp are not taken into account: thus may not be valid even at the weak-field limit.
?
?
5
Slide6Unfortunately, the Mattis
-Bardeen’s formula for the weak-field Rs tells you nothing about the shape of Q-E curve. It is valid only at the weak-field limit: the left end of Q-E curve. Moreover, effects of material features other than mfp are not taken into account: thus may not be valid even at the weak-field limit.
?
?
Need to develop
a theory of
field dependent
R
s
including realistic material features.
6
Slide77
Review: Progresses in theory A. Gurevich, Phys. Rev. Lett. 113, 087001 (2014)A. Gurevich and T. Kubo, Phys. Rev. B 96
, 184515 (2017)
Slide8Review: Progresses in theory (part 1)A.
Gurevich, Phys. Rev. Lett. 113, 087001 (2014)8
Slide9Review: Progresses in theory (part 1)
DOS
The surface resistance is given by
Here
is roughly (when
and
)
A.
Gurevich
, Phys. Rev. Lett.
113
, 087001 (2014)
9
Slide10Idealized
BCS DOS
Weak-field limit
Review: Progresses in theory (part 1)
DOS
The surface resistance is given by
A.
Gurevich
, Phys. Rev. Lett.
113
, 087001 (2014)
10
Here
is roughly (when
and
)
Slide11Idealized
BCS DOS
Weak-field limit
Mattis
Bardeen’s formula
comes from this DOS
Review: Progresses in theory (part 1)
DOS
The surface resistance is given by
A.
Gurevich
, Phys. Rev. Lett.
113
, 087001 (2014)
11
Here
is roughly (when
and
)
Slide12Idealized
BCS DOS
Weak-field limit
Mattis
Bardeen’s formula
comes from this DOS
Review: Progresses in theory (part 1)
DOS
The surface resistance is given by
Broadening of the gap peaks in N(ε) by current was calculated 50 years ago:
K. Maki,
Prog
.
Theor
. Phys.
29
, 333 (1963).
K. Maki, in Superconductivity, part 2, ed. R.D. Parks, 1967.
Anthore
et al., PRL
90
, 127001 (2003)
DOS under a dc current
However,
we know the DOS is modified under the pair-breaking current.
Experimentally confirmed:
A.
Gurevich
, Phys. Rev. Lett.
113
, 087001 (2014)
12
Here
is roughly (when
and
)
Slide13Idealized
BCS DOS
Weak-field limit
Mattis
Bardeen’s formula
comes from this DOS
Review: Progresses in theory (part 1)
DOS
The surface resistance is given by
Under a strong
rf
current
DOS peaks oscillate (animation)
However,
we know the DOS is modified under the pair-breaking current.
A.
Gurevich
, Phys. Rev. Lett.
113
, 087001 (2014)
13
Here
is roughly (when
and
)
Slide14Idealized
BCS DOS
Weak-field limit
Mattis
Bardeen’s formula
comes from this DOS
Review: Progresses in theory (part 1)
DOS
The surface resistance is given by
Under a strong
rf
current
DOS peaks oscillate (animation)
However,
we know the DOS is modified under the pair-breaking current.
A.
Gurevich
, Phys. Rev. Lett.
113
, 087001 (2014)
This logarithmic factor
in MB’s formula comes from the sharp peak of the idealized BCS DOS
14
Here
is roughly (when
and
)
Slide15Idealized
BCS DOS
Weak-field limit
Mattis
Bardeen’s formula
comes from this DOS
Review: Progresses in theory (part 1)
DOS
The surface resistance is given by
Under a strong
rf
current
DOS peaks oscillate (animation)
However,
we know the DOS is modified under the pair-breaking current.
A.
Gurevich
, Phys. Rev. Lett.
113
, 087001 (2014)
decreases
15
Here
is roughly (when
and
)
Slide16Review: Progresses in theory (part 1)
Under a strong rf current
DOS peaks oscillate (animation)
A. Gurevich, Phys. Rev. Lett. 113, 087001 (2014)
decreases
Broadening of DOS peaks
causes the Q rise
Gap shrinks
This is
the ideal QE curve
derived from
the
BCS theory.
16
Slide17Incorporated effects of pair-breaking mechanisms originating from realistic material features into Rs at the weak-field limit.
Review: Progresses in theory (part 2)A. Gurevich and T. Kubo, Phys. Rev. B 96, 184515 (2017)17
Slide18Incorporated effects of pair-breaking mechanisms originating from realistic material features into Rs at the weak-field limit.
Review: Progresses in theory (part 2)Subgap states originating from a finite quasiparticle lifetime.Surface layer of gradually reduced BCS pairing constant. Proximity coupled thin Normal layer on the surface
Small density of magnetic impurities
18A. Gurevich and T. Kubo, Phys. Rev. B 96, 184515 (2017)
Slide19Incorporated effects of pair-breaking mechanisms originating from realistic material features into Rs at the weak-field limit.
Review: Progresses in theory (part 2)Subgap states originating from a finite quasiparticle lifetime.Surface layer of gradually reduced BCS pairing constant. Proximity coupled thin Normal layer on the surface
Small density of magnetic impurities
19A. Gurevich and T. Kubo, Phys. Rev. B
96, 184515 (2017)
Slide20Incorporated effects of pair-breaking mechanisms originating from realistic material features into Rs at the weak-field limit.
Review: Progresses in theory (part 2)Subgap states originating from a finite quasiparticle lifetime.Surface layer of gradually reduced BCS pairing constant. Proximity coupled thin Normal layer on the surface
Small density of magnetic impurities
SN
Thinner than
20
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
Slide21Incorporated effects of pair-breaking mechanisms originating from realistic material features into Rs at the weak-field limit.
Review: Progresses in theory (part 2)Subgap states originating from a finite quasiparticle lifetime.Surface layer of gradually reduced BCS pairing constant. Proximity coupled thin Normal layer on the surface
Small density of magnetic impurities
SN
Thinner than
Magnetic impurities
21
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
Slide22Incorporated effects of pair-breaking mechanisms originating from realistic material features into Rs at the weak-field limit.
Review: Progresses in theory (part 2)Subgap states originating from a finite quasiparticle lifetime.Surface layer of gradually reduced BCS pairing constant. Proximity coupled thin Normal layer on the surface
Small density of magnetic impurities
SN
Thinner than
Magnetic impurities
These structures model realistic surfaces of superconducting materials which can contain
oxide layers, absorbed impurities or nonstoichiometric composition
.
22
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
Slide2323
Review: Progresses in theory (part 2) Proximity-coupled thin N layer
DOS
of Normal conductor
Normal
conductor
BCS
superconductor
DOS
of
BCS superconductor
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
Slide2424
DOS of Normal conductor
Normal
conductor
BCS
superconductor
DOS
of
BCS superconductor
?
?
Review: Progresses in theory (part 2)
Proximity-coupled thin N layer
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
The proximity
effect
changes
DOS
Slide2525
Review: Progresses in theory (part 2) Proximity-coupled thin N layer
A.
Gurevich and T. Kubo, Phys. Rev. B 96, 184515 (2017)d
We can calculate DOS by using the well-established method:Quasiclassical Green’s function formalism of the BCS theory.
The proximity
effect
changes
DOS
Slide2626
The proximity effect
changes DOS
Review: Progresses in theory (part 2) Proximity-coupled thin N layer
~thickness
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
d
We can calculate DOS by using the well-established method
:
Quasiclassical
Green’s function formalism of the BCS theory.
Parameters are sensitive to material processing!
is an N layer thickness.
(e.g., thickness of suboxide on the
Nb
surface)
Slide2727
The proximity effect
changes DOS
Review: Progresses in theory (part 2) Proximity-coupled thin N layer
~thickness
~barrier
between N&S
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
d
We can calculate DOS by using the well-established method
:
Quasiclassical
Green’s function formalism of the BCS theory.
Parameters are sensitive to material processing!
is an interface resistance
Sensitive to heat treatment
(e.g., between
Nb
suboxide and
Nb
)
is an N layer thickness.
(e.g., thickness of suboxide on the
Nb
surface)
Ref: The lowest contact resistance of YBCO/Ag is
J. W.
Ekin
et al., Appl. Phys. Lett.
62
, 369 (1993)
Slide2828
The proximity effect
changes DOS
Review: Progresses in theory (part 2) Proximity-coupled thin N layer
~thickness
~barrier
between N&S
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
d
We can calculate DOS by using the well-established method
:
Quasiclassical
Green’s function formalism of the BCS theory.
Parameters are sensitive to material processing!
is an interface resistance
Sensitive to heat treatment
(e.g., between
Nb
suboxide and
Nb
)
is an N layer thickness.
(e.g., thickness of suboxide on the
Nb
surface)
Ref: The lowest contact resistance of YBCO/Ag is
J. W.
Ekin
et al., Appl. Phys. Lett.
62
, 369 (1993)
Conductance
N region
S region
Slide2929
The proximity
effect
changes
DOS
Review: Progresses in theory (part 2)
Proximity-coupled thin N layer
N-side
DOS
~thickness
~barrier
between N&S
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
d
Slide3030
The proximity
effect
changes
DOS
Review: Progresses in theory (part 2)
Proximity-coupled thin N layer
N-side
DOS
As
increases,
the
minigap
decreases
~thickness
~barrier
between N&S
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
d
Slide3131
The proximity
effect
changes
DOS
Review: Progresses in theory (part 2)
Proximity-coupled thin N layer
N-side
DOS
As
increases,
the
minigap
decreases
~thickness
~barrier
between N&S
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
d
Slide3232
The proximity
effect
changes
DOS
Review: Progresses in theory (part 2)
Proximity-coupled thin N layer
N-side
DOS
As
increases,
the
minigap
decreases
~thickness
~barrier
between N&S
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
d
Slide3333
N-side
DOS
S-side DOS
The proximity
effect
changes
DOS
Review: Progresses in theory (part 2)
Proximity-coupled thin N layer
~thickness
~barrier
between N&S
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
d
Slide3434
S-side DOS
Γ=0.05
N-side
DOS
Γ=0.05
The proximity
effect
changes
DOS
Taking a finite quasi particle lifetime into account (
), the cusps are smeared out.
Review: Progresses in theory (part 2)
Proximity-coupled thin N layer
~thickness
~barrier
between N&S
These
subgap
states contribute to
residual resistance
at T -> 0
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
Slide3535
Rs depends on the N-layer parameters.
Review: Progresses in theory (part 2)
Proximity-coupled thin N layer
(~ barrier between N&S) can be changed by
heat treatments
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
Slide3636
Rs depends on the N-layer parameters.Rs
can be optimized
by tuning them.
Review: Progresses in theory (part 2)
Proximity-coupled thin N layer
(~ barrier between N&S) can be changed by
heat treatments
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
Slide3737
Rs depends on the N-layer parameters.Rs
can be optimized
by tuning them.Rs can be smaller than the ideal surface without N layer
Review: Progresses in theory (part 2)
Proximity-coupled thin N layer
(~ barrier between N&S) can be changed by
heat treatments
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
Slide3838
Rs depends on the N-layer parameters.Rs
can be optimized
by tuning them.Rs can be smaller than the ideal surface without N layer
Review: Progresses in theory (part 2)
Proximity-coupled thin N layer
(~ barrier between N&S) can be changed by
heat treatments
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
Taking
Nb
for example,
Nb-suboxide thickness on the surface
the interface resistance between
Nb
suboxide and
Nb
These can be easily affected by material processing recipes.
→
Link to the dependence of Rs on recipes?
Slide39: mean spacing of magnetic impurities
39
Review: Progresses in theory (part 2)
Magnetic impurities can also broaden DOS peaks
Magnetic impurities
An appropriate density of magnetic impurities
significantly reduce
Rs!
corresponds to the mean spacing of magnetic impurities
4
μm
A.
Gurevich
and T. Kubo,
Phys. Rev. B
96
, 184515 (2017)
Slide4040
Magnetic
impurities
Thin N layer
Ideal SC
Summary of the review part
Pair-breaking current
Pair-breaking mechanism originating from realistic material features
Slide4141
Magnetic
impurities
Thin N layer
Ideal SC
Summary of the review part
Current
broadens DOS
and
affects R
s
→
field dependence
Proximity effect
broadens DOS
and
affects Rs.
The N layer properties are sensitive to material processing.
Magnetic impurities
broaden DOS
and
affect R
s
Pair-breaking current
Pair-breaking mechanism originating from realistic material features
11 min
Slide4242
What is the origin of many different Q-E curves?
Slide4343
Now we are ready to attack this mysteryWhat is the origin of many different Q-E curves?
Slide44we have studied a theory of
field dependent surface resistance of a dirty superconductor in a strong RF field, taking into account realistic materials features, such as magnetic and nonmagnetic impurities, subgap states originating from finite quasiparticle lifetimes, and a proximity-coupled normal layer at the surface. Recent progress
Based on our previous studies
A. Gurevich, Phys. Rev. Lett. 113, 087001 (2014)A. Gurevich and T. Kubo, Phys. Rev. B 96, 184515 (2017)
44
Slide4545
Strong rf current
Magnetic
impurities
Thin N layer
Ideal SC
proximity coupled N layer at the surface
Proximity effect
Strong rf current
Incorporate
a finite
quasiparticle lifetime
Magnetic
impurities
Strong rf current
Strong rf current
A.
Gurevich
, Phys. Rev. Lett.
113
, 087001 (2014)
A.
Gurevich
and T. Kubo, Phys. Rev. B
96
, 184515 (2017)
Slide4646
Slide47Dirty SC with nonmagnetic impurities;
Can incorporate a finite quasiparticle lifetime and can include magnetic impurities
Strong rf current
Γ=0.02
Γ
p
=0
H
0
=0.3H
c
Γ = 0
Γ
p
= 0.02
H
0
=0.3H
c
Effect of a finite quasiparticle lifetime
Effect of magnetic impurities
DOS under a strong rf field
DOS
DOS
E/
△
E/
△
Contain animations. See in
Slide Show Mode
.
47
Slide48Strong rf current
Field dependent Surface resistance R
s
(H
0
)
48
(1) Effect of a finite quasiparticle lifetime (Γ parameter)
Slide49Field dependent Surface resistance R
s(H0)
49
(1) Effect of a finite quasiparticle lifetime (Γ parameter)
The Ideal BCS SC exhibits
the N-dope-like R
s
dip
Slide50Field dependent Surface resistance R
s(H0)
50
(1) Effect of a finite quasiparticle lifetime (Γ parameter)
The nearly Ideal BCS SC exhibits the N-dope-like
R
s
dip.
The first
R
s
rise disappears
Slide51Field dependent Surface resistance R
s(H0)
51
(1) Effect of a finite quasiparticle lifetime (Γ parameter)
The R
s
dip almost disappears, but the low-field R
s
is better than ideal BCS SC due to the DOS broadening effect.
Slide52Field dependent Surface resistance R
s(H0)
52
(1) Effect of a finite quasiparticle lifetime (Γ parameter)
The
R
s
dip disappears,
but the low-field
R
s
is better than ideal BCS SC due to the DOS broadening effect.
Slide53Field dependent Surface resistance R
s(H0)
53
(1) Effect of a finite quasiparticle lifetime (Γ parameter)
The
R
s
dip disappears.
R
s
becomes larger.
Slide54Field dependent Surface resistance R
s(H0)
54
(1) Effect of a finite quasiparticle lifetime (Γ parameter)
The
N-dope-like
extended R
s
reduction (Q rise) appears when
the
parameter is small enough!
Slide55Strong rf current
Field dependent Surface resistance Rs(H0
)
(2) Effect of magnetic impurities (
Γ
p
parameter)
Magnetic impurities
55
Magnetic impurities affect
R
s
(H
0
) in the similar manner as a finite quasi particle lifetime.
The R
s
dip becomes shallower as
Γ
p
increases.
The low field
R
s
for (
) is much smaller than the ideal BCS superconductor
(
)
.
+6min
Slide5656
Slide57Proximity effect
57
~thickness
~barrier
between N&S
is an interface resistance
Sensitive to heat treatment
(e.g., between
Nb
suboxide and
Nb
)
is an N layer thickness.
(e.g., thickness of suboxide on the
Nb
surface)
Slide58Proximity effect
Proximity coupled
N layer
S side
,
DOS under a strong rf field
DOS
E/
△
58
Contain animations. See in
Slide Show Mode
.
~thickness
~barrier
between N&S
is an interface resistance
Sensitive to heat treatment
(e.g., between
Nb
suboxide and
Nb
)
is an N layer thickness.
(e.g., thickness of suboxide on the
Nb
surface)
Slide59Proximity effect
59
~thickness
~barrier
between N&S
is an interface resistance
Sensitive to heat treatment
(e.g., between
Nb
suboxide and
Nb
)
is an N layer thickness.
(e.g., thickness of suboxide on the
Nb
surface)
Field dependent Surface resistance R
s
(H
0
)
for different N-layer thickness
No normal layer
→
Slide60Proximity effect
60
~thickness
~barrier
between N&S
is an interface resistance
Sensitive to heat treatment
(e.g., between
Nb
suboxide and
Nb
)
is an N layer thickness.
(e.g., thickness of suboxide on the
Nb
surface)
Field dependent Surface resistance R
s
(H
0
)
for different N-layer thickness
No normal layer
→
As the N-layer thickness increases,
the dip becomes shallower and finally disappears:
Continuously changes
from “N-doping-like”
to
“EP-like” shape.
Slide61Proximity effect
61
~thickness
~barrier
between N&S
is an interface resistance
Sensitive to heat treatment
(e.g., between
Nb
suboxide and
Nb
)
is an N layer thickness.
(e.g., thickness of suboxide on the
Nb
surface)
Field dependent Surface resistance R
s
(H
0
)
α=0.05
β=1
for different N-layer conductivity
diffusivity
Slide62Proximity effect
62
~thickness
~barrier
between N&S
is an interface resistance
Sensitive to heat treatment
(e.g., between
Nb
suboxide and
Nb
)
is an N layer thickness.
(e.g., thickness of suboxide on the
Nb
surface)
Field dependent Surface resistance R
s
(H
0
)
α=0.05
β=1
for different N-layer conductivity
diffusivity
R
s
continuously changes
from “N-doping-like” to “baking-like” shape.
Slide63Proximity effect
63
~thickness
~barrier
between N&S
is an interface resistance
Sensitive to heat treatment
(e.g., between
Nb
suboxide and
Nb
)
is an N layer thickness.
(e.g., thickness of suboxide on the
Nb
surface)
Field dependent Surface resistance R
s
(H
0
)
for different temperatures
α=0.05
β=1 and 7
Blue: 1.4K for
Nb
Red: 2K for
Nb
7
Different types of temperature dependence appear.
Slide64Proximity effect
64
~thickness
~barrier
between N&S
is an interface resistance
Sensitive to heat treatment
(e.g., between
Nb
suboxide and
Nb
)
is an N layer thickness.
(e.g., thickness of suboxide on the
Nb
surface)
Field dependent Surface resistance R
s
(H
0
)
for different temperatures
α=0.05
β=1 and 7
Blue: 1.4K for
Nb
Red: 2K for
Nb
7
Different types of temperature dependence appear.
T. Kubo
etal
., IPAC14, Dresden, Germany (2014), p. 2519, WEPRI022
For the
case,
the peak shifts to higher fields and
the reduction is pronounced as T decreases:
behavior of baked cavities
[Experimental data]
QE curves for a baked cavity
Slide65Replacing N with S’ and taking
, we have an S’IS multilayer. I do not have enough time to introduce the results today. I will present elsewhere.
Recent progress (2)
Strong rf current
S
S’
65
Example of
Slide6666
SummaryWe have developed a theory of field dependent surface resistance of a dirty superconductor in a strong RF field, taking into account realistic materials features, such as magnetic and nonmagnetic impurities, subgap
states originating from finite quasiparticle lifetimes, and a proximity-coupled normal layer at the surface.
Ideal or nearly ideal superconductors (tiny , and no N layer) exhibit N-doping-like R
s(H0
).
Introducing realistic material features such as a finite
or a thin N layer on the surface, superconductors exhibit many varieties of field dependent R
s
(H
0
), including
EP-like R
s
(H
0
)
and baking-like R
s(H0
). The surface resistance
can be minimized by engineering optimum impurity concentration or properties of the surface normal layer.
Slide67Grazie mille!67