Spin-orbit coupling and superconductivity in materials without inversion symmetry. CePt 3 Si

Transcription

1 Spin-obit coupling and supeconductivity in mateials without invesion symmety Sendai, June 29, 2006 Manfed Sigist, ETH Züich Paity as a key symmety fo supeconductivity ole of antisymmetic spin-obit coupling CePt 3 Si Physical popeties discussion of expeimental esults

2 Collaboatos: Theoy ETH Zuich: Uni Wisconsin: Osaka Uni: Expeiment TU Wien: Uni Illinois: Kyoto Uni: IBM Watson Lab: P.A. Figei, N. Hayashi, K. Wakabayashi, I. Milat, Y. Yanase D.F. Agtebeg, R.P. Kau A. Koga E. Baue and his team H-Q. Yuan, T. Shibauchi, Y. Matsuda, L. Kuzin-Elbaum Funding:

3 Supeconductivity Electical esistance (1911) Field expulsion (1933) Meissne-Ochsenfeld effect 2 esistivity B B=0 B T c tempeatue T>T c T<T c Supeconductivity as a themodynamic phase B London theoy (1935) " # $ 2 j = % B " # B = 4$ c j density of supeconducting electons " 2 B = # $2 B " #2 = 4$e2 n s mc 2 London penetation depth λ x

4 Supeconductivity Electical esistance (1911) Field expulsion (1933) Meissne-Ochsenfeld effect 3 esistivity B B=0 B T c tempeatue T>T c T<T c Supeconductivity as a themodynamic phase Ode paamete: " F ", A ( ) = " ( )e i# & [ ] =, d 3 a(t) " 2 + b " 4 + K ' ( Ginzbug-Landau theoy (1950) ( ) condensate with a boken U(1)-gauge symmety D " # $ % A minimal coupling ( ) 2 ) * + D = " + i 2e hc A

5 Mikoscopic viewpoint of supeconductivity Ode paamete " ( ) = " ( )e i# ( ) complex condensate wave function 4 Coheent state of electon pais (Coope pais) not a state of fixed paticle numbe Badeen-Coope-Schieffe k " (1957) " k # Femi sea P tot = 0 fixed phase violation of U(1)-gauge symmety condensate wavefunction ''U(1) - Higgs field''

6 Paiing inteaction 12 Coope pai fomation (bound state of 2 electons) needs attactive inteaction k k k -k k -k -k -k electon phonon inteaction: attactive inteaction scatteing between electon states with degeneate enegy

7 Altenative mechanism fo Coope paiing 25 Paiing fom puely epulsive inteactions: Kohn & Luttinge (1965) sceened Coulomb potential in metal has long-anged oscillatoy tail (shap Femi edge) Fiedel oscillations: attactive pat paiing in high-angula momentum channel l >0 vey low! Paiing by magnetic fluctuations: Bek & Schieffe (1966) CeIn 3 easily spin polaizable medium longe anged inteaction T Quantum Citical Point T c easonable fo highe angula momentum paiing AF SC

8 Novel Supeconductos

9 Unexpected beakthoughs K HgBa 2 Ca 2 Cu 3 O 9 T(K) liquid N 2 High-T c supeconductos 1986 K.A. Mülle liquid H 2 La 2-x Ba x CuO 4 MgB 2 J.G. Bednoz H. Kamelingh-Onnes 1911 liquid He heavy Femion SC, oganic SC, S 2 RuO 4 Stat of SC yea

10 The novel supeconductos Heavy Femion supeconductos: 15 CeCu 2 Si 2 Steglich et al. (1979) U 1-x Th x Be 13 Ott et al. (1983) 1 nomal CeIn 3 Mathu et al. (1998) T(K) 0 A B A+B T-violating x(%) A UPt 3 Stewat et al. (1984) magnetic field C B A T(K) nomal Quantum Citical point AF PM CeRhIn 5 Thompson et al. (2001) T (K) T N T Max T c CeRhIn P (GPa)

11 The novel supeconductos High-tempeatue supeconductos Layeed peovskite coope-oxides Mülle & Bednoz (1986) Oganic supeconductos Jeome, Bechtgad et al (1980) (TMTSF) 2 M (M=PF 6, SbF 6, ReO 4, ) T c ~ 1K 16 La 2-x S x CuO 4 T c =45K YBa 2 Cu 3 O 6+δ T c =92K (BEDT-TTF) 2 M.. T c ~ 10K HgBa 2 Ca 2 Cu 3 O 9 T c =133.5K T T N T* AF T c SC x

12 The novel supeconductos Feomagnetic supeconductos: UGe 2 Saxena et a. (2000) S 2 RuO 4 17 RuO 2 plane some similaities with high-t c supeconductos, ZZn 2 Pfleidee et al. (2001) Supeconductivity within the feomagnetic phase but T c = 1.5 K spin-tiplet supeconducto

13 The novel supeconductos 19 Plutonium compounds Skutteudite 0.0 4πχ C/T (mj/mol 2 K ) T (K) T (K) PuCoGa 5 Tc = 18 K POs 4 Sb 12 T c = 1.8 K Thompson et al. (Los Alamos) Baue et al. PRB 65, R (2002) Multiple phases

14 Coope paiing and Symmety

15 Altenative ways to Coope paiing Coulomb and electon-phonon inteaction vey shot-anged (λ TF ) contact inteaction 22 Bound Coope pai wavefunction: f() l = 0 How to avoid Coulomb epulsion? highe-angula momentum paiing with elative angula momentum l =0 impotant fo contact inteaction l > 0 l > 0 contact inteaction not effective Symmety of pais of identical electons: wave function totally antisymmetic unde paticle exchange k s " k s' k # " k s! s' " ss' ( k ) = # c ˆ k sˆ even paity: odd paity: c $ % = &( k ) ' (s,s') k s' obital spin l =0,2,4,, S=0 singlet even odd l = 1,3,5,, S=1 tiplet odd even

16 Requiements fo the fomation of Coope pais Andeson s Theoems (1959,1984) Coope pai fomation with P=0 elies on symmeties which guaantee degeneate patne electons Spin singlet paiing: time evesal symmety k " T k " = # k $ time evesal " k,s' hamful: magnetic impuities feomagnetism paamagnetic limiting k,s 23 Spin tiplet paiing: time evesal & invesion symmety k " I k " = # k " T k " = # k $ IT k " = k $ invesion hamful: cystal stuctue without invesion cente

17 The essential symmeties Non-centosymmetic supeconductos CePt 3 Si

18 CePt 3 Si Heavy Femion supeconducto: T c = 0.75 K E. Baue et al. PRL 92, (2004) " # 350 mj molk 2 H c2 (T = 0) "5T paamagnetic limiting H p " # 0 2µ B " k B T C µ B "1T H C2 (0) ~ 3T No paamagnetic limiting spin tiplet paiing? T. Yasuda et al., JPSJ 73, 1657 (2004)

19 Symmety of supeconducting phase CePt 3 Si Cystal space goup P4mm tetagonal geneating point goup C 4v (mio plane z -z missing) No invesion cente: spin tiplet paiing? Andeson s second theoem

20 Basic Model of a system without invesion cente

21 Lack of invesion symmety Electon band Spin-obit coupling Symmety conditions time evesal symmety: and invesion symmety: and time evesal and/o invesion symmety absent

22 Lack of invesion symmety Desselhaus 1955; Rashba 1960 CePt 3 Si E ˆ z v B x-y-plane not a mio plane Special elativity: Zeeman coupling: time evesal symmety conseved

23 Band splitting k-dependent spin splitting (Zeeman) Enegy spectum: k y k x Splitted Femi suface of CePt 3 Si A.Kozhevnikov, V. Anisimov simila K. Samokhin et al

24 Supeconductivity Hamiltonian: ˆ H = ' [" #] c ˆ + c ˆ s,s' k,s k,s,s' # 0 + $ % k k & k,s' ' V k, k c ˆ + + c ˆ ' k,s ( c ˆ k,s' ( c ˆ k ',s' k ',s k, k ',s,s' Mean field: spin singlet, even paity spin tiplet, odd paity 1 configuation 3 configuations

25 Spin-obit coupling and supeconductivity spin-obit coupling as a petubation k y spin singlet paiing: mino effect k x spin tiplet paiing: allmost all paiing states seveely suppessed weakly affected paiing states: CePt 3 Si:

26 The Supeconducting Phase and the Magnetic Field

27 Uppe citical field How to destoy Coope pais by a magnetic field? Obital depaiing: Spin depaiing: Loentz foce on moving chaged paticles Zeeman coupling spin polaization

28 Spin anisotopy spin singlet paiing Yosida behavio of spin susceptibility χ pai beaking by spin polaization χ p T c T spin tiplet paiing χ no pai beaking fo equal spin paiing χ p χ = const. fo d ( k )" H =0 T c T

29 Modified spin susceptibility "Spin singlet": Yosida behavio H z ˆ H " z ˆ "Spin tiplet": independent of α χ/χ Ν 1 H z ˆ 0.5 H " z ˆ T/T ct singlet and tiplet become simila

30 Paamagnetic limiting destuction of supeconductivity due to Zeeman splitting of electon spins Compaison of supeconducting condensation enegy paamagnetic enegy quasipaticle gap Pauli susceptibility paamagnetic limiting field

31 Paamagnetic limiting destuction of supeconductivity due to Zeeman splitting of spin Susceptibility: H c-axis H ab-axis weak limiting intemediate limiting 1 H z ˆ 0.5 H " z ˆ Expeiment: T/T c T. Yasuda et al. JPSJ 73, 1657 (2004) expected in-plane H p uppe citical fields almost identical fo both field diections

32 Helical Phase

33 Helical phase in a magnetic field effect of magnetic field on the Femi sufaces magnetic field H

34 Helical phase in a magnetic field effect of magnetic field magnetic field Femi suface shifts by

35 Helical phase in a magnetic field effect of magnetic field k+q magnetic field q with -k+q Coope pais with momentum q Ginzbug-Landau expansion fo single-component ode paamete: new tem possible Mineev & Samokhin (1994) Helical state:

36 Helical phase and uppe citical field Additional stuctue in the ode paamete possible in non-centosym. systems Yasuda et al. Kau, Agtebeg & MS Enhanced H c2 : obital depaiing paamagnetic helical

37 Indications of the paiing symmety

38 Quasipaticle gap stuctue NMR-1/T 1 London penetation depth Hebel-Slichte peak powelaw T 3 fo T 0 Baue et al. powelaw T fo T 0 Bonalde et al.

39 Quasipaticle gap stuctue NMR-1/T 1 conventional London penetation depth unconventional Hebel-Slichte peak powelaw T 3 fo T 0 Baue et al. powelaw T fo T 0 Bonalde et al.

40 Quasipaticle gap stuctue Paity mixing "even + odd-paity" invesion symmety even-paity state no invesion symmety gaps on two split Femi sufaces

41 Quasipaticle gap stuctue Paity mixing s- + p-wave 2 Femi sufaces: + and full gap line nodes Anisotopic gaps: diffeent on the two Femi sufaces no spin degeneacy (''spinless Femions") accidential line nodes possible!

42 London penetation depth and supefluid density T-linea behavio fo T 0 mixed paity state with nodes Bonalde et al 2004 linea Hayashi et al 2004 effect of accidental nodes!?

43 Complication fo CePt 3 Si heavy Femion compound: localized 4f-moments of Ce supeconductivity: T c = 0.75 K antifeomagnetism: T N = 2.2K possible phase diagam T T N AF N. Metoki et al. (2004) SC T c p

44 Othe ecently discoveed non-centosymmetic supeconductos

45 UI Feomagnetic quantum phase tansition Space goup: P2 1 monoclinic Coexistence of Supeconductivity and Feomagnetism!? Akazawa et al. (2004) supeconductivity T c =0.15 K CeRhSi 3 Antifeomagnetic quantum phase tansition Space goup: I4mm tetagonal T N ~ 2 K T c ~ 1 K Kimua et al. (2005)

46 Li 2 Pd 3 B, Li 2 Pt 3 B Space goup: P cubic London penetation depth Li 2 Pd 3 B T c = 8 K full gap Togano et al. (2004) alloy intepolation: Li 2 (Pd x Pt 1-x ) 3 B vaying spin-obit coupling Li 2 Pt 3 B T c = 2.5 K nodes Yuan et al. (2005) KOs 2 O 6 destoted pyochlo lattice H c2 T c =9.6 K Space goup: F43m tetahedal Schuck et al. (2006) Shibauchi et al. (2006) Yonezawa et al. (2004)

47 Conclusions Symmety of Coope pais: invesion symmety no invesion symmety even-paity odd-paity spin-singlet spin-tiplet mixed-paity mixed-spin no invesion symmety stong Femi suface effect: k y k x antisymmetic spin-obit coupling paamagnetic effect gap stuctue helical phase in high magnetic fields..