High-temperature superconductivity - Chalmersdelsing/Superconductivity/Lectures... ·...
Transcript of High-temperature superconductivity - Chalmersdelsing/Superconductivity/Lectures... ·...
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High-temperature
superconductivity
Superconductivity and Low temperature physics, FMI036
Alexey Kalabukhov Quantum Device Physics Laboratory, MC2
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Electronic phase diagram
Superconductivity and Low temperature physics, FMI036 2
Superconductivity exists only in narrow doping range. Non-doped material is AF
insulator (”parent compund”). At high doping level cuprates are ”normal” metals.
Pseudogap region in low doping levels
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Superconductivity and Low temperature physics, FMI036 3
Flux quantization
Low-Tc SQUID measures variation of magnetic flux in HTS ring:
Low-TC SQUID High-TC ring
T = 4 K
Vout
Mi
ΦR
SQUID voltage: Flux quantization: 𝑉𝑜𝑢𝑡~∆Φ𝑆~𝑀𝑖∆Φ𝑅 ∆Φ𝑅 = 𝑛Φ0 = 𝑛ℎ
𝑄
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Superconductivity and Low temperature physics, FMI036 4
Flux quantization
C.E. Cough at el., Nature, 326, 855 (1987)
Measurements of flux jumps as a function of time in a HTS superconducting ring by LTS SQUID: Q = 2e
0 = h/2e Gough, C. E et al., 1987, Nature (London) 326, 855.
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Superconductivity and Low temperature physics, FMI036 5
Important superconducting parameters
•Very short coherence lengths ~ interatomic distance
•Anisotropy in (a,b) and c axis
• Type II with high Hc2
“High-Temperature Superconducting Materials Science and Engineering” ed. Donglu Shi, 1995
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Role of thermal fluctualtions
Superconductivity and Low temperature physics, FMI036 6
Ginznurg-Landau model: variation of the free energy:
Fluctuations assumed to be small if L << ξ:
This condition is not valid in some temperature region close to Tc:
GL fluctuation parameter
Change of the free energy:
Fluctuations are small if:
𝐹𝑠0 = 𝐹𝑛 + 𝛼 Ψ2 +
𝛽
2Ψ 4
𝛿Ψ∗(𝑟 )𝛿Ψ(0) 𝑟~𝜉 ≪ Ψ
𝐹𝑠𝑛 = 𝐹𝑠0 − 𝐹𝑛 =4𝜋𝛼2
2𝛽= 𝐻𝐶
2(𝑇) 𝜉3 𝑇 = 𝐻𝐶2(0) 𝜉3 0 𝑇 − 𝑇𝐶
1/2
𝑘𝐵𝑇𝐶 ≪ 𝐹𝑠𝑛
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Role of thermal fluctualtions
Superconductivity and Low temperature physics, FMI036 7
In low-Tc superconductors: Fluctuations are negligible!
In high-Tc superconductors: 𝑘𝐹𝜉 0 < 10, ∆𝑇𝑓𝑙 ~ 1 𝐾 !
Fluctuation effects in cuprates are much stronger!!
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Paraconductivity (Aslamasov-Larkin effect)
Superconductivity and Low temperature physics, FMI036 8
𝜎𝐴𝐿2𝐷 =
𝑒2
ℏ
𝑇𝐶𝑇 − 𝑇𝐶
𝜎𝐴𝐿3𝐷~
𝑇𝐶𝑇 − 𝑇𝐶
1/2
2D: Thin superconducting film, d < ξ
3D: Bulk superconductor
W. Lang et al., PRB 51, 9180 (1995)
Masked by inhomogeneous Tc
Can be used to analyze
coupling between CuO2-planes
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Flux creep
Superconductivity and Low temperature physics, FMI036 9
Broadening of the resistive transition in HTS materials
Temperature fluctuations of flux result in “glassy” behavior –
depends on history of the state
ρ,
Ω∙c
m
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Superconductivity and Low temperature physics, FMI036 10
Thermally activated flux flow (TAFF)
LTS: HTS (YBCO): HTS (BSCCO):
Vortex liquid: flux pinning is ineffective
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Superconductivity and Low temperature physics, FMI036 11
Vortices in HTS: pancakes formation
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Josephson effect
Superconductivity and Low temperature physics, FMI036 12
GHz/mV 483or
2sin
2
2
sin 12
eVtII
tteV
eV
t
II
JoJc
oJo
c
Josephson effect:
coupling of two
superconductors
through a ”weak link”
(S-I-S, S-N-S…)
DC and AC Josephson effects:
- dc supercurrent if I<IC
- Oscillating ac current if I>IC
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Tunneling S-I-S JJs:
Superconductivity and Low temperature physics, FMI036 13
Barrier thickness: d ~ ξ ~ 10 Å in cuprates
How to make a Josephson Junction from HTS?
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Grain boundaries in HTS
Superconductivity and Low temperature physics, FMI036 14
I
V
JCGB << JC BULK
- Weak link!
H. Hilgenkamp and J. Mannhart, Rev Mod Phys 74, p 485, APRIL 2002
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high-Tc
epitaxial film
Bicrystal
substrate
H. Hilgenkamp and J. Mannhart, Rev Mod Phys 74, p 485, APRIL 2002
Grain boundaries in cuprates
Quality of the grain boundary depends
on the misorientation angle
Superconductivity and Low temperature physics, FMI036
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Artificial grain boundaries
Superconductivity and Low temperature physics, FMI036 16
5 mm GB
GB
YBCO
Bicrystal technology and epitaxial
thin film deposition:
Bicrystal Bi-epitaxial
Bi-epitaxial Step-edge
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Superconductivity and Low temperature physics, FMI036 17
30 40 0 10 20
misorientation angle (degree)
Jcgb
/ J
cg
0
0.2
0.4
0.6
0.8 [001] tilt
[100] tilt
[100] twist
T = 4.2 K
Artificial grain boundaries
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Defects in grain boundaries
Superconductivity and Low temperature physics, FMI036 18
Grain boundary junctions are not S-I-S – there is a normal component (”shunt”)
Non-superconducting region,
due to non-stoichiometry
(oxygen) – S-N-S
Insulating region + localized
states, S-I-N-I-S
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Superconductivity and Low temperature physics, FMI036 19
Intrinsic Josephson junctions
Tunneling between superconducting
CuO2-planes through insulating layers in
c-axis direction
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Ar ion milling
Carving out a single junction
Superconductivity and Low temperature physics, FMI036
A. Yurgens, M. Torstesson, L. You APL 88, 222501 2006
Intrinsic Josephson junctions: fabrication
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Symmetry of the order parameter
Superconductivity and Low temperature physics, FMI036 21
Symmetry of the Fermi surface of cuprates in CuO2-planes:
How superconducting order parameter will change in this case?
ARPES of fermi surface in
cuprates: 4-fold symmetry
Tsuei&Kirtley, Rev. Mod. Phys., Vol. 72, No. 4, October 2000
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D-wave symmetry
Superconductivity and Low temperature physics, FMI036 22
𝑉𝑘,𝑘′ = −𝑉 BCS, cubic (spherical) symmetry.
∆𝛼,𝛽(𝑘)~ 𝑐𝛼,𝑘 , 𝑐𝛽,−𝑘 Pair wave function in general case:
Spin operators
(↑↓) Annihilation
operator
𝛼 = −𝛽
𝛼 = 𝛽
S = 0 L = 0 singlet, S-wave
S = 0 L = 2 singlet, D-wave
S = 1 L = 1 triplet, P-wave
Must be symmetric for
electron
commutations!
Pairing potential:
Tsuei&Kirtley, Rev. Mod. Phys., Vol. 72, No. 4, October 2000
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D-wave symmetry
Superconductivity and Low temperature physics, FMI036 23
∆𝑠(𝑘)~ ∆𝑠0 + ∆𝑠1 cos 𝑘𝑥 + cos 𝑘𝑦
∆𝑔(𝑘)~ ∆𝑔0 sin 2𝑘𝑥 sin 𝑘𝑦 − sin 2𝑘𝑦 sin 𝑘𝑥
∆𝑥2−𝑦2(𝑘)~ ∆𝑥2−𝑦20cos 𝑘𝑥 − cos 𝑘𝑦
∆𝑥𝑦(𝑘)~ ∆𝑥𝑦0sin 𝑘𝑥 sin 𝑘𝑦
In the limit to 2D case (x-y CuO2 planes, no dispersion
in z-direction):
s wave
dx2-y2 wave
g wave
dxy wave
Which configuraion is realized in HTS?
Tsuei&Kirtley, Rev. Mod. Phys., Vol. 72, No. 4, October 2000
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Superconductivity and Low temperature physics, FMI036 24
Symmetry of the order parameter
Symmetry of the order parameter in k-space:
D-wave symmetry: nodes and lobes, ns = 0 in nodes!
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Superconductivity and Low temperature physics, FMI036 25
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Phase sensitive experiments
Superconductivity and Low temperature physics, FMI036 26
Ψ𝑘 𝑟 , 𝑡 = Ψ𝑘 𝑒𝑖𝜑
𝑘~∆𝑥2−𝑦20cos 𝑘𝑥 − cos 𝑘𝑦 𝑒𝑖𝜑𝑘, 𝑘 = 𝐿, 𝑅
Supercurrent across grain boundary:
𝐼𝑆~ Ψ∗𝛻Ψ−Ψ𝛻Ψ∗ ~𝐼0 cos 2𝜃𝐿 cos 2𝜃𝑅 sin𝜑
Sigrist-Rice formula (clean limit)
Tsuei&Kirtley, Rev. Mod. Phys., Vol. 72, No. 4, October 2000
𝜃𝐿 = 0, 𝜃𝑅 = 45° 𝐼𝑆 = 0 Equivalent to phase shift by π! -> Pi-junctions
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Phase sensitive experiments
Superconductivity and Low temperature physics, FMI036 27
Tsuei&Kirtley, Rev. Mod. Phys., Vol. 72, No. 4, October 2000
Pi-junction in a superconducting ring: flux quantization (neglecting self-inductance):
ℏ𝛻𝜑 = 2𝑒𝐴
ℏ 𝛻𝜑𝑑𝑙 = 2𝑒 𝐴 𝑑𝑙
ℏ 𝜋 + 2𝜋𝑛 = 2𝑒Φ
Φ = ℏ
2𝑒2𝜋 𝑛 +
1
2= Φ0 𝑛 +
1
2
𝜋
Half-integer flux quantum effect
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Superconductivity and Low temperature physics, FMI036 28
Pairing symmetry: tri-crystal experiment
Pure dx2-y2 order parameter in tetragonal Tl2Ba2CuO6+d
C.C. Tsuei et al., Nature 387,481(1997).
LTS SQUID-microscope
Detecting spantaneous half flux quantum in tri-crystal junctions:
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Models of HTS
• Challenges:
– High-TC: does not fit BCS
– Non-metallic ground state, quazi-2D
– Anti-ferromagnetic ordering
– Dependence of TC on doping
– D-wave symmetry
– Strong e-e correlation effects (insulating at
low doping)
– Pseudogap
Superconductivity and Low temperature physics, FMI036 29
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Problem of high-Tc
Superconductivity and Low temperature physics, FMI036 30
𝜔𝐷 = 𝑐𝑆 6𝜋2𝑛 1/3 𝑇𝐷 =
ℏ𝜔𝐷𝑘𝐵
𝑇𝐶 = 1.14𝑇𝐷𝑒𝑥𝑝 −1
𝑁𝐹(0)𝑉
𝜆 ≡ 𝑁𝐹(0)𝑉
Al : TD = 428 K, λ ~ 0.18, TC = 1.6 K (experiment: 1.6 K)
YBCO : TD = 100 K, λ ~ 0.5, TC = 13 K (experiment: 92.5 K)
Critical temperature in
BCS model
Coupling constant, typically λ < 0.2
Debye temperature:
corresponds to a highest frequency mode of lattice vibrations (ωD)
Simple estimations:
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Superconductivity and Low temperature physics, FMI036 31
The isotope effect
• Oxygen Isotope Effect: Replacement of O16 -> O18
• Very small change of TC in optimally doped regime
K.A. Muller, J.Phys.Cond.Matter, 19, 251002 (2007)
𝜔𝐷~1
𝑀=> 𝑇𝐶~
1
𝑀
𝛼 ≡ −𝑀 ∆𝑀
𝑇𝐶 ∆𝑇𝐶 ~0.5
Electron-phonon coupling is not
main paring mechanism in
cuprates?
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Pseudogap
Superconductivity and Low temperature physics, FMI036 32
• Gap-like features in all underdoped cuprates above Tc
• Manifests in various experiments
• Preformation of cooper pairs OR non-superconducting phases?
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Models of HTS
• Non-Fermi liquid models:
– Resonance valence band (RVB, t-J model): AFM
ground state, e-e pairing through magnetic
interactions (spin-density waves, SDW)
• Fermi-liquid models:
– Hartri-Fock calculations from Fermi liquid,
approximation of interacting electrons (BCS-like)
Superconductivity and Low temperature physics, FMI036 33
None of the models correctly predicts high-Tc in cuprates!
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t-J model
• Doped Mott insulator
• No Fermi liquid – quasiparticle approach does not work
• Ground state: AFM insulator
• Underdoping: 1D state (”stripes”) hole delocalization
• Optimal doping: 2D state (Josephson tunneling between stripes),
superconducting coherence
• Overdoping: 3D state, loss of coherence
• Pairing is due to magnetic interactions
• Referred to RVB-model (Anderson 1987)
Superconductivity and Low temperature physics, FMI036 34
“Concepts in High Temperature Superconductivity”, E. W. Carlson, V. J. Emery, S. A. Kivelson, D.
Orgad, http://arxiv.org/abs/cond-mat/0206217v1
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Experimental observation of stripes
Superconductivity and Low temperature physics, FMI036 35
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Superconductivity and Low temperature physics, FMI036 36
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Fermi-liquid models
Superconductivity and Low temperature physics, FMI036 37
- Hartree-Fock computations, Fermi-liquid hamiltonian. No initial
assumptions about the electronic state of the HTS
- Existence of Fermi surface from recent SdH experiments
- Pseudogap: transformation of Fermi surface into pockets (spin-
waves state)
- Conventional fermionic quasiparticles exist,but pairing due to
antiferomagnetic spin fluctuations
- Completely rules out Mott insulators (observed experimentally!)
R. B. Laughlin, PHYSICAL REVIEW B 89, 035134 (2014)
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Fermi-liquid models
Superconductivity and Low temperature physics, FMI036 38
R. B. Laughlin, PHYSICAL REVIEW B 89, 035134 (2014)
This model seems to predict correctly Tc in cuprates:
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Heavy-fermion superconductors
Superconductivity and Low temperature physics, FMI036 39
Large values of the electronic specific heat ->
“Heavy electrons”
CeCu2Si2 discovered by Steglich in 1979
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Superconductivity and Low temperature physics, FMI036 40
Heavy-fermion superconductors
Phase diagram similar to cuprates
Co-existence of superconducting and magnetic phases
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Organic superconductors
Superconductivity and Low temperature physics, FMI036 41
1963: First prediction by W.A. Little (Stanford Univ.), metal chains in organic
molecules
1980: Discovery of TMTSF, TC ~ 0.9 K at 12 kBar
1988: Other various organic superconductors, TC ~ 11.2 K at ambient pressure
TM2X, quasi-1D: ET2X, quasi-2D:
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Organic superconductors
Superconductivity and Low temperature physics, FMI036 42
From: Paul Chaikin, NYU (http://www.physics.nyu.edu/~pc86/)
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Organic superconductors
Superconductivity and Low temperature physics, FMI036 43
Highly anisotropic: 105
Phase boundary between superconductivity and anti-ferromagnetic order
Possible p-wave superconductors
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2006: Oxypnictides
Superconductivity and Low temperature physics, FMI036 44
Hiroki Takahashi, Tokyo:
(Fe,As) LaO:
TC ~ 43 K
Yoichi Kamihara, Tokyo:
(Fe,P) LaO:
TC ~ 4 K
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45
Compound (powder & single
crystals)
Tc Reference
LaOFeP ~5 K Y. Kamihara et al., J. Am. Chem.
Soc.128, 10012 (2006)
LaNiOP ~3 K T. Watanabe et al., Inorg. Chem. 46,
7719 (2007)
La[O1-xF-x]FeAs
La[O1-xCa2+x]FeAs
26 K (x=0.05-0.12)
0 K
Y. Kamihara et al., J. Am. Chem.
Soc.130, 3296 (2008)
La[O1-xFx]NiAs 3.8 K (x=0.1)
2.75 K (x=0)
Z. Li et al., arXiv:0803.2572
(La1−xSrx)ONiAs 3.7 K (x=0.1-0.2)
2.75 K (x=0)
L. Fang et al., arXiv:0803.3978
(La1−xSrx)OFeAs 25 K (x=0.13) H.-H. Wen et al., EPL 82, 17009 (2008)
Ce[O1−xFx]FeAs 41 K (x=0.2) G.F. Chen et al., arXiv:0803.3790
Pr[O1-xFx]FeAs
Nd[O1-xFx]FeAs
52 K (x=0.11) Z.-A. Ren et al., arXiv:0803.4283; Z.-A.
Ren et al., arXiv:0803.4234
Gd[O1−xFx]FeAs 36 K (x=0.17) P. Cheng et al., arXiv:0804.0835
Sm[O1− xFx]FeAs 55 K (x=0.1-0.2) Z.-A. Ren et al., arXiv:0804.2053;
R.H. Liu et al., arXiv:0804.2105
(Eu,Tm)[O1− xFx]FeAs no stable ZrCuSiAs structure G. F. Chen et al., arXiv:0803.4384
From: I. Eremin, Entanglement in Spin and Orbital Systems, Cracow 18-22 June 2008
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Superconducting properties
Superconductivity and Low temperature physics, FMI036 46
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Phase diagram:
Superconductivity and Low temperature physics, FMI036 47
J. Zhao et al., arXiv:0806.2528
• Parent compound: AFM normal metal • Layered structure • No pseudogap! • Electron and hole doped • Doping also possible by replacing Fe by Co • S-type symmetry of the order parameter
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2001: MgB2
Superconductivity and Low temperature physics, FMI036 48
”High” critical temperature: TC ~ 39 K
Discovered by J. Akimitsu, Aoyama Nature, Vol. 410 No. 6824 (2001) pp.63-64.
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Discovery of MgB2
• Discovered by J. Akimitsu, (2001)
• Metallic graphite-like structure
• ”High” critical temperature TC ~ 39 K
• Very difficult to make thin films
Superconductivity and Low temperature physics, FMI036 49
Nature 410, 63-64 (2001)
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Superconductivity and Low temperature physics, FMI036 50
Cristina Buzea et al 2001
Supercond. Sci. Technol. 14
R115-R146
Superconducting properties of MgB2
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• Coupling in B planes is stronger
• Double-gap model: Δπ ~ 2.0 meV, Δσ ~ 6.5 meV
• Explains TC and specific heat capacity
Superconductivity and Low temperature physics, FMI036 51
Two gaps in MgB2
P. Szabo et al., PRL 87 135002 (2001)