!"#$%& IIT Kanpur. !"#$%&. Kanpur, How spins become pairs: Composite and magnetic pairing in the 115 Heavy Fermion Superconductors

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1 How spins become pairs: Composite and magnetic pairing in the 115 Heavy Fermion Superconductors!"#$%& IIT Kanpur Feb Interaction, Instability and Transport!"#$%&. Kanpur, 1857.

2 How spins become pairs: Composite and magnetic pairing in the 115 Heavy Fermion Superconductors!"#$%& IIT Kanpur Feb Interaction, Instability and Transport M. Dzero R. Flint P. Coleman Local Moment Center for Materials Theory 4.5K Heavy Fermion S.C NpAl2Pd5

3 How spins become pairs: Composite and magnetic pairing in the 115 Heavy Fermion Superconductors!"#$%& IIT Kanpur Feb Interaction, Instability and Transport M. Dzero R. Flint P. Coleman Local Moment Center for Materials Theory Local Moment 4.5K Heavy Fermion S.C NpAl2Pd5

4 How spins become pairs: Composite and magnetic pairing in the 115 Heavy Fermion Superconductors!"#$%& IIT Kanpur Feb Interaction, Instability and Transport M. Dzero R. Flint P. Coleman Local Moment Center for Materials Theory composite pair 4.5K Heavy Fermion S.C NpAl2Pd5

5 Acknowledgments: Nature Physics 4, 643 (2008). arxiv: Rebecca Flint Maxim Dzero (U. Maryland).

6 Acknowledgments: Nature Physics 4, 643 (2008). arxiv: Rebecca Flint Maxim Dzero (U. Maryland). Scott Thomas (Rutgers) Pascoal Pagliuso & group (Unicamp) Joe Thompson (LANL) Filip Ronning (LANL) E. D. Bauer (LANL) Zachary Fisk (UCIrvine) Cigdem Capan (UCIrvine) Alexei Tsvelik (BNL) Natan Andrei (Rutgers) Hae Young Kee (Toronto) PRB 60, 3609, (1998).

7 Acknowledgments: Nature Physics 4, 643 (2008). arxiv: Rebecca Flint Maxim Dzero (U. Maryland). Scott Thomas (Rutgers) Pascoal Pagliuso & group (Unicamp) Joe Thompson (LANL) Filip Ronning (LANL) E. D. Bauer (LANL) Zachary Fisk (UCIrvine) Cigdem Capan (UCIrvine) Alexei Tsvelik (BNL) Natan Andrei (Rutgers) Hae Young Kee (Toronto) PRB 60, 3609, (1998).

8 Outline

9 Outline! The materials: Why the 115s are so special?

10 Outline! The materials: Why the 115s are so special?! The concept: How do spins pair?! Composite pairing and the Two Channel Kondo model

11 Outline! The materials: Why the 115s are so special?! The concept: How do spins pair?! Composite pairing and the Two Channel Kondo model! The tool: Symplectic-N

12 Outline! The materials: Why the 115s are so special?! The concept: How do spins pair?! Composite pairing and the Two Channel Kondo model! The tool: Symplectic-N! The results: Composite pairing phase diagram

13 Outline! The materials: Why the 115s are so special?! The concept: How do spins pair?! Composite pairing and the Two Channel Kondo model! The tool: Symplectic-N! The results: Composite pairing phase diagram! Hybridization: of magnetic and composite pairing T C

14 Outline! The materials: Why the 115s are so special?! The concept: How do spins pair?! Composite pairing and the Two Channel Kondo model! The tool: Symplectic-N! The results: Composite pairing phase diagram! Hybridization: of magnetic and composite pairing T C

15 Conventional Heavy Fermion Superconductivity Example: UPt 3 T* ~ 100K, T C =.56K Pauli Susceptibility Curie

16 Conventional Heavy Fermion Superconductivity Example: UPt 3 Stage one: QP formation T* ~ 100K, T C =.56K Pauli paramagnetism fully Pauli Susceptibility developed by 30K~50 T C Curie

17 Conventional Heavy Fermion Superconductivity Example: UPt 3 Stage one: QP formation T* ~ 100K, T C =.56K Pauli paramagnetism fully Pauli Susceptibility developed by 30K~50 T C Curie

18 Conventional Heavy Fermion Superconductivity Example: UPt 3 Stage one: QP formation T* ~ 100K, T C =.56K Pauli paramagnetism fully Pauli Susceptibility developed by 30K~50 T C Curie Spin Fluctuations

19 Conventional Heavy Fermion Superconductivity Example: UPt 3 Stage one: QP formation Pauli T* ~ 100K, T C =.56K Susceptibility Curie Pauli paramagnetism fully developed by 30K~50 T C Stage two Unconventional superconductivity mediated by spin fluctuations

20 Conventional Heavy Fermion Superconductivity Example: UPt 3 T* ~ 100K, T C =.56K Stage one: QP formation Pauli paramagnetism fully developed by 30K~50 T C Stage two Unconventional superconductivity mediated by spin fluctuations Nodal SC Kohori 1988

21 Conventional Heavy Fermion Superconductivity Example: UPt 3 T* ~ 100K, T C =.56K Stage one: QP formation Pauli paramagnetism fully developed by 30K~50 T C Stage two Unconventional superconductivity mediated by spin fluctuations Led to proposal that AFM spin fluctuations drive d-wave pairing Nodal SC Beal-Monod, Bourbonnais and Emery Scalapino, Loh and Hirsch Miyake, Schmitt-Rink, and Varma 1986 Kohori 1988

22 115 materials: a new family of superconductors In

23 115 materials: a new family of superconductors Oxides T c? YBa 2 Cu 3 O 7 92K In Ba K

24 115 materials: a new family of superconductors Oxides 115 Intermetallics T c T c? YBa 2 Cu 3 O 7 92K Mathur et al, Nature 394, 39 (1998) In Ba K 0.2K CeIn 3 96

25 115 materials: a new family of superconductors Ce Co Oxides 115 Intermetallics T c T c? YBa 2 Cu 3 O 7 92K 2K CeCoIn 5 01 In Ba K 0.2K CeIn 3 96

26 115 materials: a new family of superconductors Ce Co Oxides 115 Intermetallics Tuson Park, (2007). CeRhIn 5 T c T c? YBa 2 Cu 3 O 7 92K 2K CeCoIn 5 01 In Ba K 0.2K CeIn 3 96

27 115 materials: a new family of superconductors Oxides 115 Intermetallics T c T c? 18.5K PuCoGa 5 02 YBa 2 Cu 3 O 7 92K 2K CeCoIn 5 01 In Ba K 0.2K CeIn 3 96

28 115 materials: a new family of superconductors Oxides 115 Intermetallics T c T c? 18.5K PuCoGa 5 02 NpAl 2 Pd 5 4.5K 07 YBa 2 Cu 3 O 7 92K 2K CeCoIn K Heavy Fermion S.C NpAl2Pd5 In D. Aoki et al., JPSJ 76 (2007) Ba K 0.2K CeIn 3 96

29 The 115s: local moments at T C NpPd 5 Al 2 T C = 4.5K Curie No Pauli paramagnetism ~1/3 R ln(2) Large condensation entropy Aoki et al 2007

30 The 115s: local moments at T C NpPd 5 Al 2 T C = 4.5K CeCoIn 5 T C = 2.3K Ce Co In ~1/3 R ln(2) ~1/3 R ln(2) Aoki et al 2007 Petrovic et al 2001

31 The 115s: local moments at T C Ce In NpPd 5 Al 2 T C = 4.5K CeCoIn 5 T C = 2.3K Co Follow spins below T C ~1/3 R ln(2) 1/3 R ln(2) 1/3 R ln(2) Knight Shift Aoki et al 2007 Petrovic et al 2001 Aoki et al 2007 Curro et al 2001

32 Curro et al 2001 The 115s: local moments at T C Above T C ~1/3 R ln(2) Curie Free local moments down to T C Aoki et al 2007 Below T C Knight Shift Spin singlet, nodal SC Spins pair and quench simultaneously Curro et al 2001 Sarrao and Thompson 2007 How are spins incorporated into the pair?

33 Kondo effect and Heavy Fermions Review: cond-mat/ Nozieres 74

34 Kondo effect and Heavy Fermions Review: cond-mat/ H = Jσ (0) S J. Kondo 64 Nozieres 74

35 Kondo effect and Heavy Fermions Review: cond-mat/ H = Jσ (0) S T K F e F J J. Kondo 64 Nozieres 74

36 Kondo effect and Heavy Fermions Review: cond-mat/ χ T K 1 T K H = Jσ (0) S χ 1/T T K F e F J T K J. Kondo 64 T Nozieres 74

37 Kondo effect and Heavy Fermions Review: cond-mat/ χ T K 1 T K H = Jσ (0) S χ 1/T T K F e F J T K J. Kondo 64 T Nozieres 74

38 Kondo effect and Heavy Fermions Review: cond-mat/

39 Kondo effect and Heavy Fermions Review: cond-mat/ PuCoGa 5 H = Jσ (0) S

40 Kondo effect and Heavy Fermions Review: cond-mat/ PuCoGa 5 H = Jσ (0) S Directly Curie PM to SC

41 Kondo effect and Heavy Fermions Review: cond-mat/ PuCoGa 5 H = Jσ (0) S S.C. Directly Curie PM to SC

42 Kondo effect and Heavy Fermions Review: cond-mat/ PuCoGa 5 H = Jσ (0) S S.C. How do spins quench and form pairs?

43 Outline! The materials: Why the 115s are so special?! The concept: How do spins pair?! Composite pairing and the Two Channel Kondo model model! The tool: Symplectic-N! The results: Composite pairing phase diagram! Hybridization: of magnetic and composite pairing T C

44 Cotunneling and composite fermions

45 Cotunneling and composite fermions van der Wiel et al, Science (2000)

46 Cotunneling and composite fermions van der Wiel et al, Science (2000) + T>>TK: Coulomb Blockade

47 Cotunneling and composite fermions van der Wiel et al, Science (2000) T<<TK

48 Cotunneling and composite fermions van der Wiel et al, Science (2000) T<<TK

49 Cotunneling and composite fermions van der Wiel et al, Science (2000) Cotunneling (Glazman +Pustilnik) (quantum dots) f = c S T<<TK

50 Cotunneling and composite fermions Cotunneling Cotunneling (Glazman +Pustilnik) (quantum dots) Heavy electron = (electron x spinflip) f = c S

51 Cotunneling and copairing: Copairing Cotunneling (Glazman +Pustilnik) (quantum dots) Heavy Cooper pair = (pair x spinflip) f = c S

52 Cotunneling and copairing: Copairing Cotunneling (Glazman +Pustilnik) (quantum dots) Heavy Cooper pair = (pair x spinflip) f = c S Ψ = c 1 c 2 S +

53 Cotunneling and copairing: Copairing Cotunneling (Glazman +Pustilnik) (quantum dots) Heavy Cooper pair = (pair x spinflip) f = c S Ψ = c 1 c 2 S + Abrahams, Balatsky, Scalapino, Schrieffer 1995

54 Two-channel model for composite pairing.

55 The Two Channel Kondo Model Wannier functions at site j:

56 The Two Channel Kondo Model Wannier functions at site j:! Both {

57 The Two Channel Kondo Model Wannier functions at site j:! Both {

58 The Two Channel Kondo Model Wannier functions at site j:! Both {

59 H = k k c kσ c kσ + 1 N cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

60 Impurity: quantum critical point for J 1 = J 2 Nozieres and Blandin 1980 T/TK FL1 FL2 J2/J1 H = k k c kσ c kσ + 1 N cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

61 Impurity: quantum critical point for J 1 = J 2 Nozieres and Blandin 1980 Singular composite pair fluctuations Emery and Kivelson 1992 T/TK FL1 FL2 J2/J1 H = k k c kσ c kσ + 1 N cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

62 Impurity: quantum critical point for J 1 = J 2 Nozieres and Blandin 1980 Singular composite pair fluctuations Emery and Kivelson 1992 T/TK Avoided in the lattice by composite pairing. FL1 FL2 J2/J1 H = k k c kσ c kσ + 1 N cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

63 Impurity: quantum critical point for J 1 = J 2 Nozieres and Blandin 1980 Singular composite pair fluctuations Emery and Kivelson 1992 T/TK Avoided in the lattice by composite pairing. FL1 - - FL2 J2/J1 H = k k c kσ c kσ + 1 N cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

64 Outline! The materials: Why the 115s are so special?! The concept: How do spins pair?! Composite pairing and the Two Channel Kondo model! The tool: Symplectic-N! The results: Composite pairing phase diagram! Hybridization: of magnetic and composite pairing T C

65 H = k cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k c kσ c kσ + 1 N k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

66 S[ψ] So how can we solve this τ,x model? ψ(x, τ) Wild quantum fluctuations! H = k cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k c kσ c kσ + 1 N k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

67 Method: symplectic large N Flint & Coleman ʼ08 PRB 79, (2009) S[ψ] So how can we solve this τ,x model? ψ(x, τ) H = k cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k c kσ c kσ + 1 N k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

68 Method: symplectic large N Flint & Coleman ʼ08 PRB 79, (2009) S[ψ] τ,x Large N limit ψ(x, τ) H = k cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k c kσ c kσ + 1 N k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

69 Method: symplectic large N Flint & Coleman ʼ08 PRB 79, (2009) S[ψ] τ,x Large N limit ψ(x, τ) H = k cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k c kσ c kσ + 1 N k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

70 S[ψ] τ,x Large N limit 1 N eff ψ(x, τ) H = k cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k c kσ c kσ + 1 N k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

71 S[ψ] τ,x Large N limit 1 N eff ψ(x, τ) H = k cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k c kσ c kσ + 1 N k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

72 S[ψ] τ,x Large N limit 1 N eff classical path ψ(x, τ) H = k cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k c kσ c kσ + 1 N k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk S ba (j) c k e ik x j

73 S[ψ] τ,x Large N limit 1 N eff classical path ψ(x, τ) H = k cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k c kσ c kσ + 1 N k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk? S ba (j) c k e ik x j

74 Symplectic N (large N + time reversal symmetry) R. Flint and PC 08 S[ψ] τ,x Large N limit 1 N eff classical path ψ(x, τ) H = k cf Cox, Pang, Jarell (96) PC, Kee, Andrei, Tsvelik (98) k c kσ c kσ + 1 N k,k J 1 ψ 1a (j)ψ 1b(j) + J 2 ψ 2a (j)ψ 2b(j) Single FS, two channels. ψ Γ (j) = 1 V k γ Γk? S ba (j) c k e ik x j

75 The one channel model in Symplectic N H I = J K N = J K N ψ a ψ b S ba f b f a ã bf af b (ψ f)(f ψ) + (ψ σ 2 f )(fσ 2 ψ).

76 The one channel model in Symplectic N H I = J K N = J K N ψ a ψ b S ba f b f a ã bf af b (ψ f)(f ψ) + (ψ σ 2 f )(fσ 2 ψ) Hybridization.

77 The one channel model in Symplectic N H I = J K N = J K N ψ a ψ b S ba f b f a ã bf af b (ψ f)(f ψ) + (ψ σ 2 f )(fσ 2 ψ). Hybridization Pairing

78 The one channel model in Symplectic N H I = J K N = J K N ψ a ψ b S ba f b f a ã bf af b (ψ f)(f ψ) + (ψ σ 2 f )(fσ 2 ψ). Hybridization Pairing H I [V f + ( fσ 2 )]ψ + H.c + N V V + J K.

79 The one channel model in Symplectic N H I = J K N = J K N ψ a ψ b S ba f b f a ã bf af b (ψ f)(f ψ) + (ψ σ 2 f )(fσ 2 ψ). Hybridization Pairing Aside: Continuous particle-hole symmetry Reflects the neutrality of the spin Pairing can be gauged away N= 2: Affleck, Zou, Hsu and Anderson 1988 H I [V f + ( fσ 2 )]ψ + H.c + N V V + J K.

80 The one channel model in Symplectic N H I = J K N = J K N ψ a ψ b S ba f b f a ã bf af b (ψ f)(f ψ) + (ψ σ 2 f )(fσ 2 ψ). Hybridization Pairing Aside: Continuous particle-hole symmetry Reflects the neutrality of the spin Pairing can be gauged away N= 2: Affleck, Zou, Hsu and Anderson 1988 H I [V f + ( fσ 2 )]ψ + H.c. = f V = f Ṽ + N V V + J K.

81 The one channel model in Symplectic N H I = J K N = J K N ψ a ψ b S ba f b f a ã bf af b (ψ f)(f ψ) + (ψ σ 2 f )(fσ 2 ψ). Hybridization Pairing Aside: Continuous particle-hole symmetry N= 2: Affleck, Zou, Hsu and Anderson 1988 Reflects the neutrality of the spin Pairing can be gauged away -recovering results of SU(N) large N.

82 The 2-channel model:

83 The 2-channel model: H I + [V 1 f +( 1 fσ 2 )]ψ 1 +H.c [V 2 f +( 2 fσ 2 )]ψ 2 +H.c + N + N V1 V J 1 V2 V J 2

84 The 2-channel model: H I + [V 1 f +( 1 fσ 2 )]ψ 1 +H.c [V 2 f +( 2 fσ 2 )]ψ 2 +H.c + N + N V1 V J 1 V2 V J 2 Gauge fixing does not remove the pairing [V 1 f ψ 1 +( 2 fσ 2 )ψ 2 ]+H.c + N V1 V J 1 J 2

85 The 2-channel model: H I + [V 1 f +( 1 fσ 2 )]ψ 1 +H.c [V 2 f +( 2 fσ 2 )]ψ 2 +H.c + N + N V1 V J 1 V2 V J 2 Gauge fixing does not remove the pairing [V 1 f ψ 1 +( 2 fσ 2 )ψ 2 ]+H.c + N V1 V J 1 J 2 The gauge-invariant cross term formation of composite pairs V 1 2 V 2 1 describe the overscreened S ψ 1 σ 2 σ ψ 2 V 1 2 V 2 1 PC, Kee, Andrei & Tsvelik. (97)

86 The 2-channel model: H I + [V 1 f +( 1 fσ 2 )]ψ 1 +H.c [V 2 f +( 2 fσ 2 )]ψ 2 +H.c + N + N V1 V J 1 V2 V J 2 Gauge fixing does not remove the pairing [V 1 f ψ 1 +( 2 fσ 2 )ψ 2 ]+H.c + N V1 V J 1 J 2 The gauge-invariant cross term formation of composite pairs V 1 2 V 2 1 describe the overscreened S ψ 1 σ 2 σ ψ 2 V 1 2 V 2 1 k k PC, Kee, Andrei & Tsvelik. (97) V 1 γ 1 (k) 2 γ 2 ( k) eff (k) V 1 2 γ 1 (k)γ 2 (k) k k 2 γ 2 (k) V 1 γ 1 ( k) resonant Andreev scattering.

87 Outline! The materials: Why the 115s are so special?! The concept: How do spins pair?! Composite pairing and the Two Channel Kondo model! The tool: Symplectic-N! The results: Composite pairing phase diagram! Hybridization: of magnetic and composite pairing T C

88 The Phase Diagram 1 V 1 " 0 # 2 " 0 V 1! 2 " !

89 The Phase Diagram 1 Heavy Fermi Liquid One Heavy Fermi Liquid Two V 1 " 0 # 2 " 0 - V 1! 2 " !

90 Outline! The materials: Why the 115s are so special?! The concept: How do spins pair?! Composite pairing and the Two Channel Kondo model! The tool: Symplectic-N! The results: Composite pairing phase diagram! Hybridization: of magnetic and composite pairing T C

91 But how to unify magnetically mediated pairing and composite pairing in the Ce 115s?

92 But how to unify magnetically mediated pairing and composite pairing in the Ce 115s? Magnetically mediated pairing

93 But how to unify magnetically mediated pairing and composite pairing in the Ce 115s? Magnetically mediated pairing

94 But how to unify magnetically mediated pairing and composite pairing in the Ce 115s? Magnetically mediated pairing

95 But how to unify magnetically mediated pairing and composite pairing in the Ce 115s? Magnetically mediated pairing Composite pairing

96 The Two channel Kondo-Heisenberg Model Two channel Kondo Model Heisenberg Model

97 The Two channel Kondo-Heisenberg Model

98 The Two channel Kondo-Heisenberg Model

99 The Two channel Kondo-Heisenberg Model - Spin liquid state

100 The Two channel Kondo-Heisenberg Model = - - Spin liquid state d-wave Anderson 1973 Baskaran, Zou and Anderson 1987

101 The Two channel Kondo-Heisenberg Model Spin liquid state d-wave Anderson 1973 Baskaran, Zou and Anderson 1987

102 The Two channel Kondo-Heisenberg Model - V V 1 -

103 The Two channel Kondo-Heisenberg Model Valence bonds become charged, mobile Cooper pairs + - V V 1 -

104 The Two channel Kondo-Heisenberg Model Valence bonds become charged, mobile Cooper pairs Inheriting d-wave nature from the antiferromagnetism - V V 1 - +

105 The Two channel Kondo-Heisenberg Model Valence bonds become charged, mobile Cooper pairs Inheriting d-wave nature from the antiferromagnetism - V V Two band version of RVB pairing - - Anderson 1987 Andrei and Coleman 1989 Miyake, Schmitt-Rink, Varma 1986

106 The Two channel Kondo-Heisenberg Model Spin Liquid # H V 1 # H Heavy Fermi Liquid V 1 Superconductor - - Andrei and Coleman 1989

107 The Phase Diagram Magnetic pairing V 1 # H " 0

108 The Phase Diagram Composite pairing V 1 # 2 " 0

109 The Phase Diagram Decoupled magnetic and composite pairing V 1 # H +V 1 # 2 " 0

110 The Phase Diagram Hybrid pairing V 1 # 2 # H " 0

111 The Phase Diagram Composite and d-wave pairing mutually reinforce. Hybrid pairing V 1 # 2 # H " 0

112 Landau Theory

113 Comparision to the Ce 115s Sarrao and Thompson 2007

114 Comparision to the Ce 115s Chemical pressure traces a path through phase space Sarrao and Thompson 2007

115 Comparision to the Ce 115s Chemical pressure traces a path through phase space CeCoIn 5 CeIrIn 5 CeRhIn 5 Sarrao and Thompson 2007

116 Comparision to the Ce 115s Chemical pressure traces a path through phase space? Sarrao and Thompson 2007

117 Comparision to the Ce 115s Chemical pressure traces a path through phase space Sarrao and Thompson 2007

118 Experimental implications! Valence shift (#n f ) associated with Kondo physics Gunnarsson and Schonhammer 1983

119 Experimental implications! Valence shift (#n f ) associated with Kondo physics! Sharp valence shift of opposite sign expected at T C! Observable in core level spectroscopy n f 1 X-ray 0 T C T K T Gunnarsson and Schonhammer 1983

120 Experimental implications! Valence shift (#n f ) associated with Kondo physics! Sharp valence shift of opposite sign expected at T C! Observable in core level spectroscopy 1 X-ray n f! Orbital Knight shift in NQR? 0 T T C T K

121 Conclusions! Spins quench as they pair in the 115s - -! Must be incorporated directly into the condensate! Two channel physics leads to composite pairs! First controlled mean field theory of heavy fermion superconductivity - Symplectic-N! Composite and magnetic pairing cooperate to enhance T C

122 Discussion: Thank You!