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 𝑆 𝑁𝐶 : Mattis-Bardeen surface resistance 2
The surface resistance of an SRF cavity is usually written as the summation of 𝑆 𝑁𝐶 : Mattis-Bardeen surface resistance 𝑆 𝑝𝑢ℎ𝑓𝑠𝑡 : other than the above Damaged layer Metallic sub-oxide Subgap states Dielectric losses etc 𝑆 𝑔𝑚𝑣𝑦 : trapped flux contribution 3
The surface resistance of an SRF cavity is usually written as the summation of 𝑆 𝑁𝐶 : Mattis-Bardeen surface resistance 𝑆 𝑝𝑢ℎ𝑓𝑠𝑡 : others Damaged layer Metallic sub-oxide Subgap states Dielectric losses etc 𝑆 𝑔𝑚𝑣𝑦 : trapped flux contribution 4
The surface resistance of an SRF cavity is usually written as the summation of 𝑆 𝑁𝐶 𝑆 𝑝𝑢ℎ𝑓𝑠𝑡 Damaged layer Metallic sub-oxide R s =R MB +R flux +R others Subgap states Dielectric losses etc 𝑆 𝑔𝑚𝑣𝑦 5
Today, R flux 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 𝑁𝐶 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) 𝑆 𝑝𝑢ℎ𝑓𝑠𝑡 Damaged layer Metallic sub-oxide R s =R MB +R flux +R others Subgap states Dielectric losses etc 𝑆 𝑔𝑚𝑣𝑦 6
Today, R flux 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 𝑁𝐶 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) 𝑆 𝑝𝑢ℎ𝑓𝑠𝑡 Damaged layer Metallic sub-oxide R s =R MB +R flux +R others Subgap states Dielectric losses Understanding this part etc is becoming im is important 𝑆 𝑔𝑚𝑣𝑦 more and more! 7
Today, R flux 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 𝑁𝐶 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) 𝑆 𝑝𝑢ℎ𝑓𝑠𝑡 Damaged layer Metallic sub-oxide R s =R MB +R flux +R others Subgap states Dielectric losses Would contain in information etc on the meaning of surface 𝑆 𝑔𝑚𝑣𝑦 processing recipes. 8
Based on the BCS theory we calc lculate Rs Rs 𝑆 𝑁𝐶 sim imultaneously taking into account both the in contrib ibutio ions. 𝑆 𝑝𝑢ℎ𝑓𝑠𝑡 Damaged layer Metallic sub-oxide R s =R MB +R flux +R others Subgap states Dielectric losses etc 𝑆 𝑔𝑚𝑣𝑦 9
Structures, parameters, and theoretical tool 10
superconductors with im imperfect surface 11
superconductors with im imperfect surface 𝑒 Conductance 𝜏 𝑜 𝜏 𝑡 Interface resistance 𝑆 𝐶 12
superconductors with im imperfect surface 𝑒 Conductance 𝜏 𝑜 𝜏 𝑡 Interface resistance 𝑆 𝐶 These structures model realistic surfaces of superconducting materials which can contain oxide layers, absorbed impurities or nonstoichiometric composition . 13
Theoretical tool We use the quasiclassical theory in the diffusive limit. Usadel equation Self-consistency condition 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: 14
Theoretical tool We use the quasiclassical theory in the diffusive limit. Usadel equation Self-consistency condition 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 = 𝑂 𝑜 𝑒 = 0.05 (when d = 1 nm, 𝜊 𝑡 = 20 nm, and 𝑂 𝑜 = 𝑂 𝑡 ) 𝑂 𝑡 𝜊 𝑡 15
Theoretical tool We use the quasiclassical theory in the diffusive limit. Usadel equation Self-consistency condition 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 = 𝑂 𝑜 𝑒 = 0.05 (when d = 1 nm, 𝜊 𝑡 = 20 nm, and 𝑂 𝑜 = 𝑂 𝑡 ) 𝑂 𝑡 𝜊 𝑡 𝛾 = 4𝑓 2 ℏ 𝑆 𝐶 𝑂 𝑜 Δ𝑒 = 16𝑒 𝑆 𝐶 𝑆 𝐶 (when d = 1 nm, 2 ~ 𝜊 0 = 40 nm) 10 −14 Ωm 2 𝜊 0 𝑆 𝐿 𝜇 𝐺 For example, R B of YBCO/Ag obtained in [J. W. Ekin et al., Appl. Phys. Lett. 62 , 369 (1993)] is R B ~ 10 -13 -10 -12 Ωm2, which yields β~10 -100. 16
Theoretical tool We use the quasiclassical theory in the diffusive limit. Usadel equation Self-consistency condition 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: Normal and anomalous Quasiclassical Matsubara Green functions T. Matsubara, Prog. Theor. Phys. 14 , 351 (1955). Penetration depth 17
Theoretical tool We use the quasiclassical theory in the diffusive limit. Usadel equation Self-consistency condition 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: Normal and anomalous Quasiclassical Matsubara Green functions T. Matsubara, Prog. Theor. Phys. 14 , 351 (1955). Penetration depth Retarded normal and anomalous Quasiclassical Green functions Density of states and surface resistance 18
Density of States 19
Density of states DOS of Normal conductor 20
Density of states DOS of Normal conductor DOS of BCS superconductor DOS of BCS superconductor 21
DOS of DOS of BCS superconductor Normal conductor BCS Normal superconductor conductor 22
DOS of DOS of BCS superconductor Normal conductor BCS Normal superconductor conductor N-side DOS S-side DOS 23
DOS of DOS of BCS superconductor Normal conductor BCS Normal superconductor conductor N-side DOS S-side DOS The proximity effect ? ? changes DOS 24
N-side DOS 𝛽 = 0.05 25
N-side DOS 𝛽 = 0.05 minigap 26
N-side DOS S-side 𝛽 = 0.05 DOS 𝛽 = 0.05 minigap 27
Taking into account a finite quasi particle life time ( 𝜁 → 𝜁 + 𝑗Γ ) smears out the cusps. N-side DOS S-side DOS 𝛽 = 0.05 Γ=0.05 𝛽 = 0.05 Γ=0.05 28
DOS for the right figure (SC with a surface layer of gradually reduced BCS pairing constant) can also be calculated. 29
Temperature dependence of penetration Depth 30
Without subgap states Exponential T dependence at any temperature 31
Without subgap states Exponential T dependence at any temperature Effect of subgap states 𝑈 ≪ 𝑈 𝑑 quadratic T dependence at a low temperature 32
Surface Resistance (1)Ideal surface without subgap states (2)Ideal surface with subgap states (3)normal thin layer on the surface 33
Surface Resistance (1)Ideal surface without subgap states (2)Ideal surface with subgap states (3)normal thin layer on the surface 34
DOS Quasiparticles gap T → 0 35
T ↘ Quasiparticles gap gap As T decreases, a number of quasiparticles exponentially decrease. 𝑆 𝑡 ∝ 𝑓 − ∆ 𝑙𝑈 → 0 T → 0 36
T=0 T ↘ T ↘ Quasiparticles gap gap gap As T decreases, a number of quasiparticles exponentially decrease. 𝑆 𝑡 ∝ 𝑓 − ∆ 𝑙𝑈 → 0 (𝑆 𝑗 = 0) T → 0 37
Typical behavior of Nb cavities Mattis-Bardeen − ∆ 𝑙 𝐶 𝑈 𝑆 𝑁𝐶 ~𝑓 38
Surface Resistance (1)Ideal surface without subgap states (2)Ideal surface with subgap states (3)normal thin layer on the surface 39
DOS Quasiparticles Subgap states 40
T ↘ Quasiparticles Quasiparticles Subgap Subgap states states 41
T ↘ T ↘ T → 0 Quasiparticles Quasiparticles Subgap Subgap Subgap states states states Even at T → 0, quasiparticles can be excited by the microwave field when finite subgap states exist. 42
T ↘ T ↘ T → 0 Quasiparticles Quasiparticles Subgap Subgap Subgap states states states Even at T → 0, quasiparticles can be excited by the microwave field when finite subgap states exist. 43
examples Γ Δ = 0.06 44
examples Γ Δ = 0.06 Γ Δ = 0.03 45
examples Γ Δ = 0.06 Γ Δ = 0.03 Γ Δ = 0.01 46
examples Γ Δ = 0.06 Γ Δ = 0.03 Γ Δ = 0.01 47
Γ Δ = 48
As Γ increases, the residual resistance 𝑆 𝑗 increases. Γ Δ = 49
Γ At this region, 𝑆 𝑡 Δ = 0.06 decreases as Γ increases. Γ Γ Δ = Δ = 0.03 Γ Δ = 0.01 50
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