[PDF] Interactions between Superconductivity and Quantum

Geometrical frustration, phase transitions and dynamical order

magnetic transition at T c = 0 88(1) K frustration index f ’ 14 neutron diffraction : → ordered spin ice → magnetic moments with both ferro and antiferromagnetic components Mirebeau et al , Phys Rev Lett 94 (2005) Dalmas de R´eotier et al , Phys Rev Lett 96 (2006) Yann Chapuis (CEA/Grenoble - Inac/SPSMS) September 2009 12 / 36

Mots de transition et expressions denchaînement

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Interactions between Superconductivity and Quantum

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 + ρ 0 (T< T FL), ρ(T) ∝ T(T>> T FL) T FL → 0 at QCP Adiverges at QCP G Knebel etal : J Phys Soc Jpn , 77, 114704 (2008) G Knebel etal : Phys

CONTRIBUTION TO CERTAIN PHYSICAL AND NUMERICAL ASPECTS OF THE

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Phase 1 : entre 0’ et 10’ : montée en puissance progressive de l’attention Phase 2 : entre 10’ et 20’ : temps de concentration, maximum d’attention Phase 3 : entre 20’ et 30’ : décroissance progressive de l’attention au delà de 30’ : l’indifférence s’installe

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Introduction CeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion Interactions between Superconductivity and Quantum Criticality in

CeCoIn

5, URhGe and UCoGe

Ludovic Howald

IMAPEC/SPSMS/INAC/DSM/CEA

17 Rue des Martyrs

38054 Grenoble

France

11 February 2011

Panel:

H. Suderow

C. Meingast

C. Berthier

Thesis supervisor: J.P. Brison

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

My PhD work

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 IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

My PhD work

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 transition

Other 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 IntroductionCeCoIn5Ferromagnetic 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 field measurements low temperature transformer

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Heavy Fermions

S. Nakatsujiet al.: Phys. Rev. Lett., 89, 106402 (2002) G. Knebelet 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 IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Quantum Critical Points (QCP)

second order phase transition atT=0 Characterized by critical exponents, effective dimensiond+z,z[13] Non Fermi Liquid (Fermi liquid region vanishes at QCP)

Experimentally:

(T) =AT2+0(TTFL),(T)T(TTFL)

TFL0 at QCP

Adiverges at QCP

G. Knebelet al.: J. Phys. Soc. Jpn., 77, 114704 (2008) G. Knebelet al.: Phys. Rev. B, 65, 024425 (2001)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Superconductivity

TSC= Ωexp?104(1+)(1+062)?

=N(EF)V

V(rt) =Charges interactions

eeg2ee(rt)+

Spins interactions

s·sg2ss(rt)

At a magnetic QCP soft modes re-enforced

What is the pairing mechanism?Experimental probe of?

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Upper critical fieldHc2

Hc2 T

SCunder field is limited by two mechanisms:

Kinetic energy, (given by12m(peA)2):HOrbital?TSCvF? 2

Zeeman splitting:HPauli=ΔgB

J. P. Brison: Habilitation `a Diriger des Recherches (1997)Parameters: effective mass:vF1m gyromagnetic ratio:g characteristic energy scale:Ω coupling constant: TSC m=mb(1+)

HPauli=ΔgBHPauliTSCif

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Phase diagram of CeRhIn5

In CeRhIn5one critical pressurePc=25 GPa.

Hc2can be fitted with:

maximum atPc,

Ωconstant,

g smoothly evolves withp andvFonly depend on. G. Knebelet al.: J. Phys. Soc. Jpn., 77, 114704 (2008)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Phase diagram of CeRhIn5& CeCoIn5

G. Knebelet al.: J. Phys. Soc. Jpn., 77, 114704 (2008)

CeCoIn5p=0

CeRhIn

5p=2GPa

G. Knebelet al.: Phys. Status Solidi B, 247, 557 (2010)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Phase diagram of CeRhIn5& CeCoIn5

G. Knebelet al.: J. Phys. Soc. Jpn., 77, 114704 (2008)

CeCoIn5p=0

CeRhIn

5p=2GPa

No sign of QCP underp

G. Knebelet al.: Phys. Status Solidi B, 247, 557 (2010)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Phase diagram of CeRhIn5& CeCoIn5

G. Knebelet al.: J. Phys. Soc. Jpn., 77, 114704 (2008)

No AFM phase detected but close to

AFM (FFLO/Q-phase, Cd doping, ...)

Proximity to a field induced QCP

Hc G. Knebelet al.: Phys. Status Solidi B, 247, 557 (2010) C. F. Micleaet al.: Phys. Rev. Lett., 96, 117001 (2006)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Previous experiments; Field induced QCP

J. Paglioneet al.: Phys. Rev. Lett., 91, 246405 (2003) A. Bianchiet al.: Phys. Rev. Lett., 91, 257001 (2003)

QCP obtained from limit of the Fermi-liquid domain. ((T) =AT2+0)

H(QCP)=Hc2?

magneto-resistance problems at low temperatures (c 1), specific heat data only available down to80mK. At 100mK 70% signal from hyperfine contribution.

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

This experiment

3 samples

ACeCoIn5ja-axis

BCeCoIn5jc-axis

CCe099La001CoIn5jc-axis

2 fields orientations:

Hc-axis

H 45c-axis

jc-axis more sensitive to NFL [9] c 1 sample B, C and for 3 samples when H 45 c-axis

Low noise high resolution

(T) =AT2+0(TTFL)

TFLdetermined from2

A

M. A. Tanataret al.: Science, 316, 1320 (2007)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Phase diagrams Hc-axis

J. Paglioneet al.: Phys. Rev. Lett., 91, 246405 (2003) Previous results reproduced with unfavourable geometry (jc-axis),

No true coincidence betweenHc2(0)andHQCP.

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

All curves

5 sets of data can be used to

fit

A H?HQCP

TFL H?HQCPz2

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Dynamical exponent

A HHQCP. Fits found

=109037

TFL HHQCPz2

Hertz-Millis theory for AFMz=2

for coincidence of divergence ofA coefficient andTFL=0 we need z=116014

Single energy scale:

(T) =a(TT0)2+0A=aT2 0

A H?HQCP

T0 H?HQCP2

T

FL H?HQCPz2

TFLT0=z

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

QCP points scenarios

Divergence ofmalong hot spot directions

Mostly developed theory

(Hertz-Millis-Moriya) Predictsz=2, (T)T32(3d),...

Other models: Disorder (Rosch et al.), Kondo

Necklace model (Reyes et al.), ...

Complete reconstruction of the Fermi surface

at QCP: divergence ofmin all directions.

Few theoretical predictions.

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

CeCoIn5Phase diagram suggested by Zaum et al.

S. Zaumet al.: arXiv:1010.3175v1 (2010)

F. Ronninget al.: Phys. Rev. B, 73, 064519 (2006)

Conclusion

Proximity between QCP andHc2atp=0

is a coincidence divergence ofAunderp(Ronning et al.)

Hall effect anomaly (Singh et al.)

S. Singhet al.: Phys. Rev. Lett., 98, 057001 (2007)

How to explainHc2?

G. Knebelet al.: Phys. Status

Solidi B, 247, 557 (2010)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Decoupling between maximum ofTSCand maximum of:

Magnetic Pair breaking mechanisms

In CeCoIn5atp=0,ΔCC=45,

BCS value 1.43,

Kos et al. and Bang et al. explain this

jump with magnetic pair breaking effect. [13]T6KTSC=23K (coupling between SC and magnetization needed),

Monthoux et al. show for SC with

strong coupling & AFM pairing pair breaking associated to the QCP the maximum ofTSCis not at the QCP

S. Koset 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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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Data of Hc2

First measurements from Miclea et al.

topmaxand recent measurement of

Knebel et al. up to more than 2·pmax

C. F. Micleaet al.: Phys. Rev. Lett., 96, 117001 (2006) G. Knebelet al.: J. Phys.: Condens. Matter, 16, 8905 (2004)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Parameters of the model

TSC(pH)fitted with an Eliashberg model

We include magnetic pair breaking in the calculation:

TSC(H=0)Ω =F( TM)

And definedT= ΩF( TM=0)

+Orbital and paramagnetic limit for field dependence.

Ωconst.

const.≂=01 vary withp

TMvary withp,TM=0 atp=4GPa

vFvary withpas:vF=vF0(1+(p=0))(1+(p)) gvary withpand field orientation (p)given byvF(p)TSCdHc2dTT=TSC Ω,TM(0)and0are related through the conditionT(p=0) =6K.(ΔCC)

TM(p)given byTSC(p)

L. N. Bulaevskiiet al.: Phys. Rev. B, 38, 11290 (1988)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Fits of Hc2

fixed parameters vF0,Ω,

Pressure dependent parameters

,TM,ga,gc C. F. Micleaet al.: Phys. Rev. Lett., 96, 117001 (2006) G. Knebelet al.: J. Phys.: Condens. Matter, 16, 8905 (2004)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Resulting parameters

Maximum ofga,gc,T,andTMaround 0.4GPa in agreement withQCP at this pressure, M. Yashimaet al.: J. Phys. Soc. Jpn., 73, 2073 (2004) M. Nicklaset al.: J. Phys.: Condens. Matter, 13, L905 (2001)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Resulting parameters

Maximum ofga,gc,T,andTMaround 0.4GPa in agreement withQCP at this pressure,

Relatively large value ofgc=8 (could

be reduced to 6 with a lower value of 0)

Difference betweenzm&

ΔTSC,

Contribution of localized moment

may leads to largeg. T. Tayamaet 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 IntroductionCeCoIn5Ferromagnetic superconductors URhGe & UCoGe Conclusion

Proposed phase diagram

02 4 6 01234
0 1 2 3 5 7

H(T)P(GPa)T(K)

10·TFLT

Conclusion

Features of CeCoIn5

(ΔCC, pressure dependence of:TSC,

0TSC, paramagnetic

limit, ...) in this scenario.

Phase diagram of CeCoIn

5 is a paradigm of an (almost 2D) strongly coupled anti-ferromagnetically mediated superconductor.

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe Introduction CeCoIn5Ferromagnetic superconductors URhGe & UCoGeConclusion

Ferromagnetic superconductors

Upper critical field of Ferromagnetic superconductors? D. Aokiet al.: J. Phys. Soc. Jpn., 78, 113709 (2009)

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Interactions between Superconductivity and Quantum Criticality in CeCoIn5, URhGe and UCoGe Introduction CeCoIn5Ferromagnetic superconductors URhGe & UCoGeConclusion

Introduction

Co-existence SC+Ferro

Triplet superconductivity,

UnusualHc2: Re-entrance,

positive curvature, strong angular dependence.

W. A. Fertiget al.: Phys. Rev. Lett., 38, 987

(1977)

D. Aokiet al.: J. Phys. Soc. Jpn., 78, 113709

(2009)quotesdbs_dbs11.pdfusesText_17