n TTC Topical Workshop -RF superconductivity: Pushing Cavity - - PowerPoint PPT Presentation

β–Ά
n ttc topical workshop rf superconductivity pushing
SMART_READER_LITE
LIVE PREVIEW

n TTC Topical Workshop -RF superconductivity: Pushing Cavity - - PowerPoint PPT Presentation

Dec 03, 2022 248 likes β€’1.06k views

arXiv:1711.03077 To be published in Physical Review B n TTC Topical Workshop -RF superconductivity: Pushing Cavity Performance Limits Fermilab, IL, USA (2017) 1 The surface resistance of an SRF cavity is usually written as the summation of

slide-1
SLIDE 1

1

n TTC Topical Workshop -RF superconductivity: Pushing Cavity Performance Limits Fermilab, IL, USA (2017)

arXiv:1711.03077 To be published in Physical Review B

slide-2
SLIDE 2

2

The surface resistance of an SRF cavity is usually written as the summation of

𝑆𝑁𝐢 : Mattis-Bardeen surface resistance

slide-3
SLIDE 3

3

𝑆𝑁𝐢 : Mattis-Bardeen surface resistance π‘†π‘π‘’β„Žπ‘“π‘ π‘‘ : other than the above

Damaged layer Metallic sub-oxide Subgap states Dielectric losses

etc

π‘†π‘”π‘šπ‘£π‘¦ : trapped flux contribution

The surface resistance of an SRF cavity is usually written as the summation of

slide-4
SLIDE 4

4

𝑆𝑁𝐢 : Mattis-Bardeen surface resistance π‘†π‘π‘’β„Žπ‘“π‘ π‘‘ : others

Damaged layer Metallic sub-oxide Subgap states Dielectric losses

etc

π‘†π‘”π‘šπ‘£π‘¦ : trapped flux contribution

The surface resistance of an SRF cavity is usually written as the summation of

slide-5
SLIDE 5

5

𝑆𝑁𝐢 π‘†π‘π‘’β„Žπ‘“π‘ π‘‘

Damaged layer Metallic sub-oxide Subgap states Dielectric losses

etc

π‘†π‘”π‘šπ‘£π‘¦ Rs =RMB+Rflux+Rothers

The surface resistance of an SRF cavity is usually written as the summation of

slide-6
SLIDE 6

6

Today, Rflux can be substantially reduced by cooling down a cavity with a large temperature gradient.



  • A. Romanenko, et al., Appl. Phys. Lett. 105

105, 234103 (2014). 

  • S. Posen et al., J. Appl. Phys. 119

119, 213903 (2016) 

  • S. Huang, T. Kubo, and R. Geng, Phys. Rev. Accel. Beams 19

19, 082001 (2016)

Rs =RMB+Rflux+Rothers 𝑆𝑁𝐢 π‘†π‘π‘’β„Žπ‘“π‘ π‘‘

Damaged layer Metallic sub-oxide Subgap states Dielectric losses

etc

π‘†π‘”π‘šπ‘£π‘¦

slide-7
SLIDE 7

7

Today, Rflux can be substantially reduced by cooling down a cavity with a large temperature gradient.



  • A. Romanenko, et al., Appl. Phys. Lett. 105

105, 234103 (2014). 

  • S. Posen et al., J. Appl. Phys. 119

119, 213903 (2016) 

  • S. Huang, T. Kubo, and R. Geng, Phys. Rev. Accel. Beams 19

19, 082001 (2016)

Understanding this part is is becoming im important more and more!

Rs =RMB+Rflux+Rothers 𝑆𝑁𝐢 π‘†π‘π‘’β„Žπ‘“π‘ π‘‘

Damaged layer Metallic sub-oxide Subgap states Dielectric losses

etc

π‘†π‘”π‘šπ‘£π‘¦

slide-8
SLIDE 8

8

Today, Rflux can be substantially reduced by cooling down a cavity with a large temperature gradient.



  • A. Romanenko, et al., Appl. Phys. Lett. 105

105, 234103 (2014). 

  • S. Posen et al., J. Appl. Phys. 119

119, 213903 (2016) 

  • S. Huang, T. Kubo, and R. Geng, Phys. Rev. Accel. Beams 19

19, 082001 (2016)

Would contain in information

  • n the meaning of surface

processing recipes.

Rs =RMB+Rflux+Rothers 𝑆𝑁𝐢 π‘†π‘π‘’β„Žπ‘“π‘ π‘‘

Damaged layer Metallic sub-oxide Subgap states Dielectric losses

etc

π‘†π‘”π‘šπ‘£π‘¦

slide-9
SLIDE 9

9

Rs =RMB+Rflux+Rothers

Based on the BCS theory we calc lculate Rs Rs sim imultaneously taking in into account both the contrib ibutio ions.

𝑆𝑁𝐢 π‘†π‘π‘’β„Žπ‘“π‘ π‘‘

Damaged layer Metallic sub-oxide Subgap states Dielectric losses

etc

π‘†π‘”π‘šπ‘£π‘¦

slide-10
SLIDE 10

10

Structures, parameters, and theoretical tool

slide-11
SLIDE 11

11

superconductors with im imperfect surface

slide-12
SLIDE 12

12

superconductors with im imperfect surface 𝑒 πœπ‘œ

Conductance

πœπ‘‘ 𝑆𝐢

Interface resistance

slide-13
SLIDE 13

13

superconductors with im imperfect surface 𝑒 πœπ‘œ

Conductance

πœπ‘‘ 𝑆𝐢

Interface resistance

These structures model realistic surfaces of superconducting materials which can contain

  • xide layers, absorbed impurities or

nonstoichiometric composition.

slide-14
SLIDE 14

14

Theoretical tool

We use the quasiclassical theory in the diffusive limit.  Self-consistency condition  Usadel equation  Boundary conditions

  • K. D. Usadel, Phys. Rev. Lett. 25, 507 (1970).
  • M. Yu. Kuprianov and V. F. Lukichev, Sov. Phys. JETP 67, 1163 (1988).

It is convenient to define the following dimensionless parameters:

slide-15
SLIDE 15

15

Theoretical tool

We use the quasiclassical theory in the diffusive limit.  Self-consistency condition  Usadel equation  Boundary conditions

  • K. D. Usadel, Phys. Rev. Lett. 25, 507 (1970).
  • M. Yu. Kuprianov and V. F. Lukichev, Sov. Phys. JETP 67, 1163 (1988).

It is convenient to define the following dimensionless parameters:

𝛽 = π‘‚π‘œ 𝑂𝑑 𝑒 πœŠπ‘‘ = 0.05

(when d = 1nm, πœŠπ‘‘ = 20nm, and π‘‚π‘œ = 𝑂𝑑)

slide-16
SLIDE 16

16

Theoretical tool

We use the quasiclassical theory in the diffusive limit.  Self-consistency condition  Usadel equation  Boundary conditions

  • K. D. Usadel, Phys. Rev. Lett. 25, 507 (1970).
  • M. Yu. Kuprianov and V. F. Lukichev, Sov. Phys. JETP 67, 1163 (1988).

It is convenient to define the following dimensionless parameters:

𝛽 = π‘‚π‘œ 𝑂𝑑 𝑒 πœŠπ‘‘ = 0.05

(when d = 1nm, πœŠπ‘‘ = 20nm, and π‘‚π‘œ = 𝑂𝑑)

𝛾 = 4𝑓2 ℏ π‘†πΆπ‘‚π‘œΞ”π‘’ = 16𝑒 𝜊0 𝑆𝐢 π‘†πΏπœ‡πΊ

2 ~

𝑆𝐢 10βˆ’14Ξ©m2

(when d = 1nm, 𝜊0 = 40nm)

For example, RB of YBCO/Ag obtained in [J. W. Ekin et al., Appl. Phys. Lett. 62, 369 (1993)] is RB~ 10-13-10-12Ξ©m2, which yields Ξ²~10-100.

slide-17
SLIDE 17

17

Theoretical tool

We use the quasiclassical theory in the diffusive limit.

Normal and anomalous Quasiclassical Matsubara Green functions

 Self-consistency condition  Usadel equation  Boundary conditions

  • K. D. Usadel, Phys. Rev. Lett. 25, 507 (1970).
  • M. Yu. Kuprianov and V. F. Lukichev, Sov. Phys. JETP 67, 1163 (1988).
  • T. Matsubara, Prog. Theor. Phys. 14, 351 (1955).

It is convenient to define the following dimensionless parameters:

Penetration depth

slide-18
SLIDE 18

18

Theoretical tool

We use the quasiclassical theory in the diffusive limit.

Normal and anomalous Quasiclassical Matsubara Green functions

 Self-consistency condition  Usadel equation  Boundary conditions

Retarded normal and anomalous Quasiclassical Green functions

Density of states and surface resistance

  • K. D. Usadel, Phys. Rev. Lett. 25, 507 (1970).
  • M. Yu. Kuprianov and V. F. Lukichev, Sov. Phys. JETP 67, 1163 (1988).
  • T. Matsubara, Prog. Theor. Phys. 14, 351 (1955).

It is convenient to define the following dimensionless parameters:

Penetration depth

slide-19
SLIDE 19

19

Density of States

slide-20
SLIDE 20

20

DOS of Normal conductor

Density of states

slide-21
SLIDE 21

21

DOS of Normal conductor DOS of BCS superconductor

Density of states

DOS of BCS superconductor

slide-22
SLIDE 22

22

DOS of Normal conductor DOS of BCS superconductor

BCS superconductor Normal conductor

slide-23
SLIDE 23

23

BCS superconductor Normal conductor

DOS of Normal conductor DOS of BCS superconductor

N-side DOS S-side DOS

slide-24
SLIDE 24

24

? ?

DOS of Normal conductor DOS of BCS superconductor

N-side DOS S-side DOS

The proximity effect changes DOS BCS superconductor Normal conductor

slide-25
SLIDE 25

25

N-side DOS

𝛽 = 0.05

slide-26
SLIDE 26

26

N-side DOS

𝛽 = 0.05

minigap

slide-27
SLIDE 27

27

N-side DOS S-side DOS

𝛽 = 0.05 𝛽 = 0.05

minigap

slide-28
SLIDE 28

28

N-side DOS S-side DOS

𝛽 = 0.05 Ξ“=0.05 𝛽 = 0.05 Ξ“=0.05

Taking into account a finite quasi particle life time (𝜁 β†’ 𝜁 + 𝑗Γ) smears out the cusps.

slide-29
SLIDE 29

29

DOS for the right figure (SC with a surface layer of gradually reduced BCS pairing constant) can also be calculated.

slide-30
SLIDE 30

30

Temperature dependence of penetration Depth

slide-31
SLIDE 31

31

Without subgap states

Exponential T dependence at any temperature

slide-32
SLIDE 32

32

Effect of subgap states Without subgap states π‘ˆ β‰ͺ π‘ˆ

𝑑

Exponential T dependence at any temperature quadratic T dependence at a low temperature

slide-33
SLIDE 33

33

Surface Resistance

(1)Ideal surface without subgap states (2)Ideal surface with subgap states (3)normal thin layer on the surface

slide-34
SLIDE 34

34

Surface Resistance

(1)Ideal surface without subgap states (2)Ideal surface with subgap states (3)normal thin layer on the surface

slide-35
SLIDE 35

35

gap Quasiparticles

T→0

DOS

slide-36
SLIDE 36

36

As T decreases, a number of quasiparticles exponentially decrease.

gap Quasiparticles

𝑆𝑑 ∝ π‘“βˆ’ βˆ†

π‘™π‘ˆ β†’ 0

T→0

T β†˜

gap

slide-37
SLIDE 37

37

As T decreases, a number of quasiparticles exponentially decrease.

gap Quasiparticles

T=0

𝑆𝑑 ∝ π‘“βˆ’ βˆ†

π‘™π‘ˆ β†’ 0

(𝑆𝑗 = 0)

T→0

T β†˜ T β†˜

gap gap

slide-38
SLIDE 38

38

Mattis-Bardeen

Typical behavior of Nb cavities

𝑆𝑁𝐢~𝑓

βˆ’ βˆ† π‘™πΆπ‘ˆ

slide-39
SLIDE 39

39

Surface Resistance

(1)Ideal surface without subgap states (2)Ideal surface with subgap states (3)normal thin layer on the surface

slide-40
SLIDE 40

40

Subgap states Quasiparticles

DOS

slide-41
SLIDE 41

41

Subgap states Quasiparticles Subgap states Quasiparticles

T β†˜

slide-42
SLIDE 42

42

Even at T→0, quasiparticles can be excited by the microwave field when finite subgap states exist.

Subgap states Quasiparticles

T→0

Subgap states Quasiparticles

T β†˜ T β†˜

Subgap states

slide-43
SLIDE 43

43

Even at T→0, quasiparticles can be excited by the microwave field when finite subgap states exist.

Subgap states Quasiparticles

T→0

Subgap states Quasiparticles

T β†˜ T β†˜

Subgap states

slide-44
SLIDE 44

44

examples

Ξ“ Ξ” = 0.06

slide-45
SLIDE 45

45

examples

Ξ“ Ξ” = 0.06 Ξ“ Ξ” = 0.03

slide-46
SLIDE 46

46

examples

Ξ“ Ξ” = 0.06 Ξ“ Ξ” = 0.03 Ξ“ Ξ” = 0.01

slide-47
SLIDE 47

47

examples

Ξ“ Ξ” = 0.06 Ξ“ Ξ” = 0.03 Ξ“ Ξ” = 0.01

slide-48
SLIDE 48

48

Ξ“ Ξ” =

slide-49
SLIDE 49

49

Ξ“ Ξ” =

As Ξ“ increases, the residual resistance 𝑆𝑗 increases.

slide-50
SLIDE 50

50

Ξ“ Ξ” =

At this region, 𝑆𝑑 decreases as Ξ“ increases.

Ξ“ Ξ” = 0.06 Ξ“ Ξ” = 0.03 Ξ“ Ξ” = 0.01

slide-51
SLIDE 51

51

𝑆𝑑~ ΰΆ± π‘’πœ— 𝑂 πœ— 𝑂(πœ— + β„πœ•)π‘“βˆ’πœ—/π‘™π‘ˆ

Why does Rs decrease as Ξ“ increases?

𝑆𝑑 ∝ ln π‘™π‘ˆ β„πœ•

Since we have

  • A. Gurevich, Phys. Rev. Lett. 113, 087001 (2014)
  • A. Gurevich, Supercond. Sci. Technol. 30, 034004 (2017)
slide-52
SLIDE 52

52

𝑆𝑑~ ΰΆ± π‘’πœ— 𝑂 πœ— 𝑂(πœ— + β„πœ•)π‘“βˆ’πœ—/π‘™π‘ˆ

Why does Rs decrease as Ξ“ increases?

𝑆𝑑 ∝ ln π‘™π‘ˆ β„πœ•

Since we have

Ξ“ Ξ” = 0.01

𝑆𝑑 ∝ ln π‘™π‘ˆ Ξ“

>

  • A. Gurevich, Phys. Rev. Lett. 113, 087001 (2014)
  • A. Gurevich, Supercond. Sci. Technol. 30, 034004 (2017)
slide-53
SLIDE 53

53

Ξ“ Ξ” = 0.06 Ξ“ Ξ” = 0.01

𝑆𝑑~ ΰΆ± π‘’πœ— 𝑂 πœ— 𝑂(πœ— + β„πœ•)π‘“βˆ’πœ—/π‘™π‘ˆ

Why does Rs decrease as Ξ“ increases?

𝑆𝑑 ∝ ln π‘™π‘ˆ β„πœ• 𝑆𝑑 ∝ ln π‘™π‘ˆ Ξ“

>

Since we have

>

DOS broadening can reduce Rs

  • A. Gurevich, Phys. Rev. Lett. 113, 087001 (2014)
  • A. Gurevich, Supercond. Sci. Technol. 30, 034004 (2017)

Ξ“ Ξ” = 0

slide-54
SLIDE 54

54

Ξ“ Ξ” =

At this region, 𝑆𝑑 decreases as Ξ“ increases. This comes from DOS broadening.[A. Gurevich, Phys. Rev.

  • Lett. 113, 087001 (2014)]

Ξ“ Ξ” = 0.06 Ξ“ Ξ” = 0.03 Ξ“ Ξ” = 0.01

slide-55
SLIDE 55

55

Surface Resistance

(1)Ideal surface without subgap states (2)Ideal surface with subgap states (3)normal thin layer on the surface

As seen in the above, DOS is broaden due to proximity effect. Thus we can expect Rs can be reduced by the same mechanism as before: Rs reduction by the broadening of DOS peak.

slide-56
SLIDE 56

56

Subgap states

N S

slide-57
SLIDE 57

57

Subgap states

N S

T β†˜

N S

T→0

Even at T→0, quasiparticles can be excited by the microwave field when finite subgap states exist.

slide-58
SLIDE 58

58

Subgap states

N S

T β†˜

N S

T→0

Even at T→0, quasiparticles can be excited by the microwave field when finite subgap states exist.

slide-59
SLIDE 59

59

Rs as functions of T-1

𝛾 =

slide-60
SLIDE 60

60

𝛾 = Similar as the ideal surface with subgap states

Rs as functions of T-1

slide-61
SLIDE 61

61

𝛾 = Similar as the ideal surface with subgap states

The slope is changed to that corresponding to the minigap

Rs as functions of T-1

slide-62
SLIDE 62

62

𝛾 = Similar as the ideal surface with subgap states

The slope is changed to that corresponding to the minigap N and S are decoupled. The residual resistance is given by normal N.

Rs as functions of T-1

slide-63
SLIDE 63

63

𝛾 =

Rs as functions of T-1

Extrapolating the results

  • btained in a limited

temperature window may lead to a wrong conclusion. e.g. At Ξ”/kT < 10, the curves for Ξ²=4 and 30 are nearly the same: the traditional fitting based on Rs=RMB+Ri would suggest Ri at Ξ²=30, while their actual T dependence are much different at a lower T.

slide-64
SLIDE 64

64

𝛾 =

Rs as functions of T-1

𝛾 =

slide-65
SLIDE 65

65

Ξ“ = Ξ“ =

Rs as functions of Ξ² for different T

Ξ“ = Ξ“ =

slide-66
SLIDE 66

66

Ξ“ = Ξ“ =

Rs as functions of Ξ² for different T

Ξ“ = Ξ“ =

The minimum in Rs(Ξ²) mainly results from interplay of two effects. The first effect which causes Rs to increase with Ξ² is rather transparent: as the barrier parameter Ξ² increases the proximity-induced superconductivity in N layer weakens, so the RF dissipation and Rs increase.

slide-67
SLIDE 67

67

Ξ“ = Ξ“ =

Rs as functions of Ξ² for different T

Ξ“ = Ξ“ =

The minimum in Rs(Ξ²) mainly results from interplay of two effects. The first effect which causes Rs to increase with Ξ² is rather transparent: as the barrier parameter Ξ² increases the proximity-induced superconductivity in N layer weakens, so the RF dissipation and Rs increase. The second effect which causes the initial decrease of Rs with Ξ² results from the change in DOS around N layer. A moderate broadening of the gap peaks in N(Ξ΅) eliminates the BCS logarithmic divergence at Ο‰β†’0 and reduces Rs .

slide-68
SLIDE 68

68

Ξ“ = Ξ“ =

Rs as functions of Ξ² for different T

Ξ“ = Ξ“ =

For Ξ“(<<Ξ”), optimum Ξ² is Ξ²=0.2 – 1.

slide-69
SLIDE 69

69

Ξ“ = Ξ“ =

Rs as functions of Ξ² for different T

Ξ“ = Ξ“ =

For Ξ“(<<Ξ”), optimum Ξ² is Ξ²=0.2 – 1. Taking d=1nm, Ξ²<1 corresponds to RB< 1.8*10-14Ξ©m2

This is two orders of magnitude smaller than the lowest contact resistance of YBCO/Ag [J. W. Ekin et al., Appl. Phys. Lett. 62, 369 (1993)]

slide-70
SLIDE 70

70

Surface Resistance

Bulk magnetic impurities

We will ill see bro roadening of f DOS peak du due to magnetic im impurit itie ies ca can al also re reduce Rs.

slide-71
SLIDE 71

We use the quasiclassical theory in the diffusive limit (Usadel eq.).

Magnetic impurities

Ξ“π‘ž = ℏ𝑀𝐺 2β„“π‘ž

β„“π‘ž : mean spacing of magnetic impurities

slide-72
SLIDE 72

We use the quasiclassical theory in the diffusive limit (Usadel eq.).

Magnetic impurities

Ξ“π‘ž = ℏ𝑀𝐺 2β„“π‘ž

β„“π‘ž : mean spacing of magnetic impurities Ξ“

π‘ž

Ξ” = 0.001

slide-73
SLIDE 73

We use the quasiclassical theory in the diffusive limit (Usadel eq.).

Magnetic impurities

Ξ“π‘ž = ℏ𝑀𝐺 2β„“π‘ž

β„“π‘ž : mean spacing of magnetic impurities Ξ“

π‘ž

Ξ” = 0.001 Ξ“

π‘ž

Ξ” = 0.02

slide-74
SLIDE 74

74

The surfa face re resis istance can be re reduced by an appropriate density of magnetic impurities!

π‘™π‘ˆ βˆ† =

Ξ“π‘ž Ξ” ~0.01 corresponds to the mean spacing of

magnetic impurities ℓ𝒒~ π„πŸ

𝟏.𝟏𝟐 ~ 4μm

slide-75
SLIDE 75

75

Summary

slide-76
SLIDE 76

76

 The main broadening effect can occur in a layer much thinner than πœ‡: DOS in the bulk can be much sharper than the surface.  Tunneling surface probes such as STM do not give all information about DOS in x ≲ πœ‡.  Fitting the tunneling data of DOS with Dynes formula and extracting Ξ“ to describe the low-T surface impedance Z can be misleading. A combination of tunneling measurement and Z in a sufficiently broad T range may offer a possibility to separate the surface and bulk contributions.

Summary

slide-77
SLIDE 77

77

 A thin pairbreaking layer or a weakly-coupled normal layer at the surface can radically (by orders of magnitude) increase Ri as compared to an ideal surface with only bulk broadening mechanisms.  However, Rs(T) can be reduced by optimizing DOS at the surface by tuning the properties of a proximity-coupled N layer at the surface. [β<1 corresponds to RB< 1.8*10-14Ωm2 for Nb with d=1nm normal layer]

Summary (cont.)

slide-78
SLIDE 78

78

 Introducing a tiny density of magnetic impurities (ℓ𝒒~ΞΌm for Nb) leads to moderator broaden DOS and reduces Rs.

Summary (cont.)

slide-79
SLIDE 79

79

Backup Units of temperature and surface resistance for Nb case

𝑆1 = 𝜈0

2πœ‡3πœ•Ξ”

2β„πœπ‘‘ ~10βˆ’4Ξ© 𝑆1 = 𝜈0

2πœ•2πœ‡2πœŠπ‘‘

2πœπ‘‘ ~10βˆ’7Ξ© π‘™πΆπ‘ˆ βˆ† β‰ˆ π‘ˆ 17.5K

(Slide 48) (Slide 59)