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Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Interactions between Superconductivity and Quantum Criticality inCeCoIn5, URhGe and UCoGe
Ludovic Howald
IMAPEC/SPSMS/INAC/DSM/CEA17 Rue des Martyrs38054 Grenoble
France
11 February 2011
Panel:H. SuderowC. MeingastC. Berthier
Thesis supervisor: J.P. Brison
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
My PhDwork
CeCoIn5
Transport: Resistivity under magnetic field.
Field induced QCP
Analysis of the upper critical field.
Effect of magnetic fluctuations on SC
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
My PhDwork
CeCoIn5
Transport: Resistivity under magnetic field.
Field induced QCP
Analysis of the upper critical field.
Effect of magnetic fluctuations on SC
Ferromagnetic superconductors URhGe & UCoGe
First Thermal conductivity measurements
Bulk superconducting transitionOther low T contributions than e−, magnetic fluctuations?Two band superconductivity?Large and anisotropic thermoelectric power
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Experimental setups
Low temperature (8mK) high field (8.5T) resistivity on CeCoIn5
First low T thermal conductivity measurement on URhGe and UCoGe
Design of 2 new setups with:
rotating stage
sample holder in Ag to allow high fieldmeasurements
low temperature transformer
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Heavy Fermions
S. Nakatsuji et al.: Phys. Rev. Lett., 89, 106402 (2002) G. Knebel et al.: J. Phys. Soc. Jpn., 77, 114704 (2008)
Large effective mass,
Proximity to magnetic phase transition.
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Quantum Critical Points (QCP)
second order phase transition at T = 0
Characterized by critical exponents, effective dimension d+ z, z ∈ [1, 3]
Non Fermi Liquid (Fermi liquid region vanishes at QCP)Experimentally:
ρ(T) = AT2 + ρ0 (T < TFL), ρ(T) ∝ T(T >> TFL)TFL → 0 at QCPA diverges at QCP
G. Knebel et al.: J. Phys. Soc. Jpn., 77, 114704 (2008) G. Knebel et al.: Phys. Rev. B, 65, 024425 (2001)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Superconductivity
TSC = Ω exp(
−1.04(1+λ)λ−µ⋆(1+0.62λ)
)
λ = N(EF)V
V(~r, t) =Charges interactions
ee′g2eχe(~r, t)+
Spins interactions
~s · ~s′g2sχs(~r, t)
At a magnetic QCP soft modes re-enforced λ
What is the pairing mechanism? → Experimental probe of λ?
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Upper critical field Hc2
Hc2 → λ
TSC under field is limited by two mechanisms:
Kinetic energy, (given by 12m
(p− e~A)2): HOrbital ∝(
TSCvF
)2
Zeeman splitting: HPauli∼= ∆
gµB
J. P. Brison: Habilitation a Diriger des Recherches (1997)
Parameters:
effective mass: vF ∝ 1/m⋆
gyromagnetic ratio: g
characteristic energy scale: Ω
coupling constant: λ
TSC
m⋆ = mb(1 + λ)HPauli
∼= ∆
gµB⇒ HPauli/TSC ր if λ ր
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Phase diagram of CeRhIn5
In CeRhIn5 one critical pressure Pc = 2.5 GPa.
Hc2 can be fitted with:
λ maximum at Pc,Ω constant,g smoothly evolves with pand vF only depend on λ.
G. Knebel et al.: J. Phys. Soc. Jpn., 77, 114704 (2008)
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Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Phase diagram of CeRhIn5 & CeCoIn5
G. Knebel et al.: J. Phys. Soc. Jpn., 77, 114704 (2008)
CeCoIn5 p = 0 ⇔CeRhIn5 p ∼= 2GPa
G. Knebel et al.: Phys. Status Solidi B, 247, 557 (2010)
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Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Phase diagram of CeRhIn5 & CeCoIn5
G. Knebel et al.: J. Phys. Soc. Jpn., 77, 114704 (2008)
CeCoIn5 p = 0 ⇔CeRhIn5 p ∼= 2GPa
No sign of QCP under p
G. Knebel et al.: Phys. Status Solidi B, 247, 557 (2010)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Phase diagram of CeRhIn5 & CeCoIn5
G. Knebel et al.: J. Phys. Soc. Jpn., 77, 114704 (2008)
No AFM phase detected but close toAFM (FFLO/Q-phase, Cd doping, ...)
Proximity to a field induced QCPH ‖~c 0.0 0.5 1.0 1.5 2.0 2.5
0
1
2
3
4
5
6
P = 0 GPa P = 0.45 GPa P = 1.34 GPa
H (T
esla
)
T (K)
CeCoIn5
H//c
G. Knebel et al.: Phys. Status Solidi B, 247, 557 (2010)C. F. Miclea et al.: Phys. Rev. Lett., 96, 117001 (2006)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Previous experiments; Field induced QCP
J. Paglione et al.: Phys. Rev. Lett., 91, 246405 (2003) A. Bianchi et al.: Phys. Rev. Lett., 91, 257001 (2003)
QCP obtained from limit of the Fermi-liquid domain. (ρ(T) = AT2 + ρ0)
H(QCP)=Hc2?
magneto-resistance problems at low temperatures (ωcτ > 1),
specific heat data only available down to∼ 80mK. At 100mK 70% signal fromhyperfine contribution.
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
This experiment
3 samples
A CeCoIn5~j ‖ a-axis
B CeCoIn5~j ‖ c-axis
C Ce0.99La0.01CoIn5~j ‖ c-axis
2 fields orientations:
H‖ c-axisH 45 c-axis
~j ‖ c-axis more sensitive to NFL[9]
ωcτ < 1 sample B, C and for 3samples when H 45 c-axis
Low noise high resolution
ρ(T) = AT2 + ρ0 (T < TFL)
TFL determined from χ2
A
M. A. Tanatar et al.: Science, 316, 1320 (2007)
0,0 0,1 0,2 0,3 0,4 0,52,0
2,5
3,0
3,5
4,0
4,5
5,0
5,5
B (x=0) C (x=0.01)
T (K)
(T) (
cm) j
//[10
0]
(T
) (cm
) j//[
001]
0,6
0,8
1,0
1,2
1,4
j//[100] A (x=0)
j//[001]
H=7T//[001]CexLa1-xCoIn5
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Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Phase diagrams H‖ c-axis
0 2 4 6 8 10 12 140
500
1000
1500
2000
2500
Paglione et al. Our data sample A
CeCoIn5 j//a
H (T)
Fermi-Liquid
T (m
K)
Sup
erco
nduc
tivity
J. Paglione et al.: Phys. Rev. Lett., 91, 246405 (2003)
3 4 5 6 7 8 90.0
0.1
0.2
0.3
0.4
0.5
0.61% La
cross
over
T (K
)
SC
Quantum
Critical
FL
a)
H (T)
Previous results reproduced with unfavourable geometry (~j ‖~c-axis),
No true coincidence between Hc2(0) and HQCP.
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Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
All curves
0,0 0,1 0,2 0,3 0,4
0,050
0,055
0,060
0,065
0,015
0,020
0,025
0,030
0,035
0,0 0,1 0,2 0,3 0,4
0,015
0,020
0,025
0,03
0,04
0,05
0,06
0,07
0,0 0,1 0,2 0,3 0,4
0,06
0,07
0,045
0,050
H//[011]
H//[001]
7 T8 T8.5T
Sample A
8T7T6T
(T)/
(300
K,H=0
)
8 T7.5T7 T6.7T6.5T
Sample C
Sample B
8.5T7 T6 T5.7T
5.5T5.3T
T (K)
8.5T8 T7.5T7 T
5.7T6.7T7 T5.3T8.5T
5 sets of data can be used tofit
A ∝ |H − HQCP|−α
TFL ∝ |H − HQCP|z/2
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Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Dynamical exponent
3 4 5 6 7 8 90
10
20
30
40
50
60
HQCP
A (
cmK-2
)j//[0
01]
H (T)
(H-4.81)-1.08
Hc2
SC
b)0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7T
(K)
SC
cross
over
Quantum
Critical
FL
a) CeCoIn5
A ∝ |H −HQCP|−α. Fits found
α = 1.09± 0.37
TFL ∝ |H −HQCP|z/2
Hertz-Millis theory for AFM z = 2
for coincidence of divergence of Acoefficient and TFL = 0 we needz = 1.16± 0.14
Single energy scale:
ρ(T) = a(T/T0)2 + ρ0 → A = a/T2
0
A ∝ |H − HQCP|−α
→ T0 ∝ |H − HQCP|α/2
TFL ∝ |H − HQCP|z/2
TFL ∝ T0 → α = z
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
QCP points scenarios
Divergence of m⋆ along hot spot directions
Mostly developed theory(Hertz-Millis-Moriya) Predicts z = 2,
ρ(T) ∝ T3/2(3d),...
Other models: Disorder (Rosch et al.), KondoNecklace model (Reyes et al.), ...
Complete reconstruction of the Fermi surfaceat QCP: divergence of m⋆ in all directions.
Few theoretical predictions.
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
CeCoIn5 Phase diagram suggested by Zaum et al.
S. Zaum et al.: arXiv:1010.3175v1 (2010)F. Ronning et al.: Phys. Rev. B, 73, 064519 (2006)
Conclusion
Proximity between QCP and Hc2 at p = 0is a coincidence
divergence of A under p (Ronning et al.)
Hall effect anomaly (Singh et al.)
S. Singh et al.: Phys. Rev. Lett., 98, 057001 (2007)
How to explain Hc2?
G. Knebel et al.: Phys. StatusSolidi B, 247, 557 (2010)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Decoupling between maximum of TSC and maximum of λ:Magnetic Pair breaking mechanisms
In CeCoIn5 at p = 0,∆C/C ∼= 4.5,BCS value 1.43,
Kos et al. and Bang et al. explain thisjump with magnetic pair breakingeffect. [13] T⋆ ∼ 6K → TSC = 2.3K(coupling between SC andmagnetization needed),
Monthoux et al. show for SC withstrong coupling & AFM pairing
⇒ pair breaking associated to the QCP⇒ the maximum of TSC is not at the
QCP
S. Kos et al.: Phys. Rev. B, 68, 052507 (2003)Y. Bang and A. V. Balatsky: Phys. Rev. B, 69, 212504 (2004)P. Monthoux and G. Lonzarich: Phys. Rev. B, 63, 054529 (2001)
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Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Data of Hc2
First measurements fromMiclea et al.to pmax and recent measurement ofKnebel et al. up to more than 2 · pmax
0,0 0,5 1,0 1,5 2,0 2,50
2
4
6
8
10
12
14
P = 0 GPa P = 0.45 GPa P = 1.34 GPa
H//[100]
H (T
esla
)
T (K)
H//[001]
C. F. Miclea et al.: Phys. Rev. Lett., 96, 117001 (2006)
0,0 0,5 1,0 1,5 2,0 2,50
1
2
3
4
5
6 P = 0 GPa P = 0.35 GPa P = 1.3 GPa P = 1.5 GPa P = 2.6 GPa P = 4 GPa
H (T
esla
)
T (K)
H//[001]
0,0 0,5 1,0 1,5 2,0 2,50
2
4
6
8
10
12
14 P = 0 GPa
P = 1 GPa P = 1.5 GPa P = 2.6 GPa
H (T
esla
)
T (K)
H//[100]
G. Knebel et al.: J. Phys.: Condens. Matter, 16, 8905 (2004)
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Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Parameters of the model
TSC(p,H) fitted with an Eliashberg model
We include magnetic pair breaking in the calculation:
TSC(H = 0)/Ω = F(λ, µ⋆, TM)And defined T⋆ = ΩF(λ, µ⋆, TM = 0)
+ Orbital and paramagnetic limit for field dependence.
Ω const.µ⋆ const. ∼= 0.1λ vary with pTM vary with p, TM = 0 at p = 4GPavF vary with p as: vF = vF0(1+ λ(p = 0))/(1+ λ(p))g vary with p and field orientation
λ(p) given by vF(p) ∝ TSC/dHc2dT
|T=TSC
Ω, TM(0) and λ0 are related through the condition T⋆(p = 0) = 6K.(∆C/C)
TM(p) given by TSC(p)
L. N. Bulaevskii et al.: Phys. Rev. B, 38, 11290 (1988)
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Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Fits of Hc2
0,0 0,5 1,0 1,5 2,0 2,50
2
4
6
8
10
12
14
P = 0 GPa P = 0.45 GPa P = 1.34 GPa
H//[100]
H (T
esla
)
T (K)
H//[001]
fixed parameters
vF0, Ω, µ⋆
Pressure dependent parameters
λ, TM, ga, gc
C. F. Miclea et al.: Phys. Rev. Lett., 96, 117001 (2006)
0,0 0,5 1,0 1,5 2,0 2,50
1
2
3
4
5
6 P = 0 GPa P = 0.35 GPa P = 1.3 GPa P = 1.5 GPa P = 2.6 GPa P = 4 GPa
H (T
esla
)
T (K)
H//[001]
0,0 0,5 1,0 1,5 2,0 2,50
2
4
6
8
10
12
14 P = 0 GPa
P = 1 GPa P = 1.5 GPa P = 2.6 GPa
H (T
esla
)
T (K)
H//[100]
G. Knebel et al.: J. Phys.: Condens. Matter, 16, 8905 (2004)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Resulting parameters
0
1
2
3
4
TM
a
0
2
4
g
ga
P (GPa)
gc
0 1 2 3 40
5
10
gc
0
2
4
6
T (K
) b
Tc
T*
0
10
20
30
40
T(K
)
Maximum of ga, gc, T⋆, λ and TM
around 0.4GPa in agreement withQCP at this pressure,
M. Yashima et al.: J. Phys. Soc. Jpn., 73, 2073 (2004)M. Nicklas et al.: J. Phys.: Condens. Matter, 13, L905 (2001)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Resulting parameters
0
1
2
3
4
TM
a
0
2
4
g
ga
P (GPa)
gc
0 1 2 3 40
5
10
gc
0
2
4
6
T (K
) b
Tc
T*
0
10
20
30
40
T(K
)
Maximum of ga, gc, T⋆, λ and TM
around 0.4GPa in agreement withQCP at this pressure,
Relatively large value of gc ∼= 8 (couldbe reduced to 6 with a lower value ofλ0)
Difference between λz → m⋆ &λ∆ → TSC,Contribution of localized momentmay leads to large g.
T. Tayama et al.: Journal of the Physical Society of Japan,74, 1115 (2005)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Proposed phase diagram
02
46
0 1 2 3 4
0
1
2
3
57
H(T)
P(GPa)
T(K)
10 · TFL
T⋆
Conclusion
Features of CeCoIn5
(∆C/C, pressuredependence of: TSC,∆0/TSC, paramagneticlimit, ...) in this scenario.
Phase diagram of CeCoIn5
is a paradigm of an(almost 2D) stronglycoupledanti-ferromagneticallymediated superconductor.
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Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Ferromagnetic superconductors
Upper critical field of Ferromagnetic superconductors?
D. Aoki et al.: J. Phys. Soc. Jpn., 78, 113709 (2009)
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Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Introduction
0 2 4 6 80
20
40
60
80
100
120
140
160
PM
SC
FM
(cm
)
T (K)
H=0T T2 fits
UCoGe j//c
Co-existence SC+Ferro →Triplet superconductivity,
Unusual Hc2: Re-entrance,positive curvature, strongangular dependence.
W. A. Fertig et al.: Phys. Rev. Lett., 38, 987(1977)D. Aoki et al.: J. Phys. Soc. Jpn., 78, 113709(2009)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Measured Thermal Conductivity
0.1 1 10500
1000
1500
2000
2500
TSC 0T 0.2T 1T
/T(Wcm
-1K
-2)
T (K)
TCurie
UCoGe H//c j//c
Large residual term,
sharp superconducting phase transition,
Sample Quality?
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Superconducting Phase diagram H‖~c-axis
0.0 0.2 0.4 0.6 0.80.0
0.2
0.4
0.6
(T) (T)
H (T
)
T (K)
UCoGe H//c j//c
Unusual shape of Hc2
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Superconducting Phase diagram H‖~c-axis
0.0 0.2 0.4 0.6 0.80.0
0.2
0.4
0.6
(T) (T)
H (T
)
T (K)
UCoGe H//c j//c
0 1 2 30
2
4
A(cm
K-2)
H (T)
UCoGe J//cH//c
Unusual shape of Hc2 requires either:
increase of λdecrease of orbital limitation
Possible explanations:
Increasem⋆ meta-magnetic transition→ increase λ (Miyake et al.),Field⊥moment superconductingpair→ increase λ (Mineev)
A. Miyake et al.: J. Phys. Soc. Jpn., 77, 094709 (2008)V. P. Mineev: arXiv:1011.3753v1 (2010)
F. Hardy et al.: to be publiehed in: J. Phys. Soc. Jpn. (2011)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Superconducting Phase diagram H‖ ~b-axis
0
2
4
6
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
(T) (T) (T) H 5° b-axis (T) H 5° b-axis
T (K)
H (T
)
UCoGe H//b j//c
0.1 1
500
1000
1500
0T 1T 2T 4T 6T 8.5T
/T(Wcm
-1K
-2)
T (K)
UCoGe H//b j//c
We confirm by bulk measurements:
strong angular dependence
re-entrance and positive curvature forHc2
importance of rotation mechanism
D. Aoki et al.: J. Phys. Soc. Jpn., 78, 113709 (2009)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Model of Lifshitz phase transition
Developed from an idea of(and with) Vincent Michaland V. Mineev
Lifshitz phase transition =topological anomaly on FS
cyclotronic vF → 0 for someH orientations
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Fits with a divergence of the effective mass
0.0 0.2 0.4 0.6 0.80
5
10
15
20
H(T)
T(K)D. Aoki et al.: J. Phys. Soc. Jpn., 78, 113709 (2009)
0 10 200
1
2
m*(
arbi
trary
uni
ts)
H(T)
m*
m⋆ = m0 · log(1+ α| Hcrit.H−Hcrit.
|)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Fits with a divergence of the effective mass
0.0 0.2 0.4 0.6 0.80
5
10
15
20
H(T)
T(K)D. Aoki et al.: J. Phys. Soc. Jpn., 78, 113709 (2009)
0 10 200
1
2
m*
m*(
arbi
trary
uni
ts)
H(T)
m*
m⋆ = m0 · log(1+ α| Hcrit.H−Hcrit.
|)
α size of the “S” (α = 0.2)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Other experimental support for a Lifshitz scenario
Strong increase of thermolectricpower (TEP) at HR unrelated to FMphase (measurements done with L.Malone at LNCMI)
Strong anisotropy on TEP~j ‖~c-axis ∼= −30,~j ‖ ~a-axis ∼= −3(measurements done with L. Maloneat LNCMI)
0 5 10 15 20-7
-6
-5
-4
-3
-2
-1
0
1
2,9K 0,48K
S/T
(V
K-2)
H(T)
UCoGe H//bj//a
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Other experimental support for a Lifshitz scenario
Strong increase of thermolectricpower (TEP) at HR unrelated to FMphase (measurements done with L.Malone at LNCMI)
Strong anisotropy on TEP~j ‖~c-axis ∼= −30,~j ‖ ~a-axis ∼= −3(measurements done with L. Maloneat LNCMI)
2D character of the compoundobserved from slope dHc2/dT
Small specific heat γ ∼= 50 and smallFermi velocity (dHc2/dT large) →small number of quasi-particles withlarge effective masses. → Small FSpockets of heavy carriers
D. Aoki et al.: J. Phys. Soc. Jpn., 78, 113709 (2009)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Fits of upper critical field
0
5
10
15
0 0.2 0.4 0.6 0.8 T (K)
H (Tesla)bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bc
bcbc rrrr rrrrrr
rrrrrrrrrr
rrrr
r
r
rrrrrrrrr
r
r
r
r
r
H ‖ ~a H ‖ ~b
u
u
u
u
u
u
u
u
u
u
u
u
uu
u
Shape of Hc2 can be reproduced for:
H‖ ~b-axis Hcrit. = 12TH‖~a-axis Hcrit. = 30Tχb
∼= 2χa (Huy et al.)
Does not explain Hc2 for H ‖~c-axis
Pair breaking like in CeCoIn5?
However suppression of orbitallimitation must happen in case ofLifshitz phase transition and gives anexplanation for the shape of Hc2.
N. T. Huy et al.: Phys. Rev. Lett., 100, 077002 (2008)
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Conclusion and Prospectives
CeCoIn5
no true QCP at Hc2(0)
Field dependence of TFL suggestsz = 1 QCP type?
Inclusion of pair breaking due tomagnetic fluctuations explain the SCpressure phase diagram.
L. Howald et al.: Journal of the Physical Society of Japan,80, 024710 (2011)
Prospectives
confirm position QCP at 0.4GPa withmore measurements of Hc2,
dHvA measurements to get moreinformation on the type of QCP,
Study of the pressure field phasediagram of other compounds withlarge strong coupling constant:NpPd5Al2?
Ferromagnetic superconductors
First thermal conductivity and firstbulk measurements of SC!
Confirmation of the unusualcurvature of Hc2 by bulkmeasurements.
We propose a new scenario to explainthe “re-entrance” of SC.
Prospectives
Lots to do... Test different qualitiessamples / other geometry, ...
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe
Introduction CeCoIn5 Ferromagnetic superconductors URhGe & UCoGe Conclusion
Thank you for your attention
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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe