Experimental manifiesta/ons of the Josephson effect

Transcription

1 Experimental manifiesta/ons of the Josephson effect

2 Josephson junc,on in the magne,c field Spin- filter Josephson junc/ons, Kar/k Senapa/, Mark G. Blamire & Zoe H. Barber, Nature Materials 10, (2011) NbN GdN NbN In- plane magne/c field dependence of junc/on cri/cal current for a 5±2 nm GdN barrier, showing Fraunhofer- like oscilla/ons at 4.2 and 8.2 K. The solid line shows a fit to the 8.2 K data, where the effec/ve field seen by the junc/on has an addi/onal 10 Oe origina/ng from the barrier moment, which reverses smoothly at low field. The calculated Fraunhofer pazerns at 4.2 K (using a constant field- shi[) are shown as dozed lines, to emphasize the suppression of side- lobe cri/cal current Ic2.

3 ac Josephson effect: Voltage oscilla/ons for I>I c O. Monnoye, Congrès de métrologie, Toulon, (2003)

4 Pairing mechanism in conven,onal superconductors

5 Proof of the phonon pairing mechanism?

6 Isotope effect: Isotope Effect in the Superconduc/vity of Mercury Phys. Rev. 78, 477 Published 15 May 1950 Emanuel Maxwell; Superconduc/vity of Isotopes of Mercury Phys. Rev. 78, 487 Published 15 May 1950 C. A. Reynolds, B. Serin, W. H. Wright, and L. B. NesbiZ BCS: T c = 1.13T D exp( 2 / g F λ) T D = ω D = s / a 0 ; s = v F T D 1/ ( Deforma/on poten/al model: λg F ~ Ξ2 k F a 0 ) 3 Ms 2 E F M :independent of M m / M

7 Caveats of the isotope effect: 1. In heavy elements, rela/ve changes of masses are small: the case for power- law scaling is not very convincing. 2. In compounds, one can replace only one one element. 3. The coupling constant is independent of M only in a very simple model. 4. The exponent varies drama,cally even within low Tc superconductors and some,mes is even nega,ve ( inverse isotope effect ).

8 Isotope effect T c M α phonon model: α =1/2 CaC 6 (T c 11 K) : α B 0.5 (Ba,K)BiO 3 (T c 30 K): α O 0.4 MgB 2 (T c 40 K) : α B 0.3 A. Bill, V.Z. Kresin, and S.A. Wolf in: Many Fermion Systems, edited by V.Z. Kresin, (Plenum Press, New York, 1998) p. 25; arxiv:

9 Iron- based superconductors: inverse isotope effect T c M α Fe phonon model: α =1/2

10 Another confirma/on of e- ph pairing : λ = g F λ / 2 = Strong- coupling (Eliashberg) theory Treats electron- phonon interac/on explicitly (rather than as a model azrac/on in the BCS model) McMillan- Dynes formula T c = ω D 1.12 exp 1.04(1+ λ ) λ µ c λ λ = 2 1.6, Hg 1.4, Pb 2.1, Pb 0.65 Bi 0.35 ( ) dω ω α 2 ( ω ) g ph ( ω ) matrix element phonon density of states ; µ c First-principle calculations of α 2 ( ω ), g ph ω = "Coulomb pseudopotential" ( ) T c Sa,sfactory explana,ons of the experiment (T c, tunneling spectra) but not a single (correct) predic,on for a new superconductor Strong cri/que of the e- ph coupling model (and BCS in general): J. E. Hirsch, Phys. Scripta 80 (2009)

11 Unconven/onal superconduc/vity s- wave superconductors: Con,nuum: Δ(k)=const La^ce: Δ(k)>0 for all k Non- s- wave: nodes Δ(k n )=0 Non- s- wave symmetry of the order parameter: p- wave (l=1), d- wave (l=2), f- wave (l=3) Spin singlet even orbital momentum (s,d ) Spin triplet odd orbital momentum (p,f ) Triplet superconduc,vity: He 3 (superfluid), Sr 2 RuO 4, UPt 3, UGe 2 (?) Spin- singlet, d- wave: cuprates Iron- based superconductors: spin- singlet. Orbital symmetry: the jury is s,ll out. One possibility: s± NB: unconven,onal HTC (Sr 2 RuO 4, UPt 3, UGe 2 : T c ~1 K)

12 Unconven/onal superfluidity: He 3 J. Wheatley, RMP 47, 415 (1975)

13 Spin triplet: (l=1) p- wave orbital symmetry B- phase: L=1,S=1, superposi/on of the S z =- 1,0,1 states A- phase: L=1, S=1, S z =+1/- 1

14 How do we know that this is a triplet? Singlet state: spin suscep/bility=0 at T=0 B- phase: χ=(1/3)χ N A- phase: : χ=χ N UPt 3 Gannon et al. PRL 86, (2012) Mackenzie & Maeno, RMP 75, 657 Wheatley, 1975

15 Cuprates: spin singlet (NMR) s or d. How do we know that this is a d- wave? Normal quasipar,cles reside near nodal lines even at T=0: Thermodynamics of a nodal superconductor is very much different from s- wave. s-wave: Λ 1/ n s ( T ) n n s exp( 2Δ / T ) Λ = Λ 0 d-wave: n n s T Λ=Λ 0 ( ) + cexp( 2Δ / T ) ( ) + ct Hardy et al. PRL 70, 3999 (1993)

16 Which d- wave? Possible symmetries of the order parameter on a square lattice s: Δ k s : d x 2 y 2 d xy : ( ) = const ( ) = Δ cosk x a + cosk y a Δ k : Δ k ( ) = Δ cosk x a cosk y a ( ) = Δsin k x asin k y a Δ k

17 Smoking- gun: corner junc/on experiment

18 Urbana experiment: Wollman et al. PRL 71, 2134 (1993) φ a φ b = 2π Φ Φ 0 + δ ab s-wave: δ ab = 0 d-wave: δ ab = π Edge junc/on: both junc/ons on the same side NB: R is 90 shi[ed compared to I

19 ARPES CaZerjee et al. Nature Phys. 6, 99 (2009) Observa/on of a d- wave nodal liquid in highly underdoped Bi 2 Sr 2 CaCu 2 O 8+δ

20 AZrac/on from repulsion: Kohn- Luvnger mechanism To second order in a short- range repulsive interac/on, the effec6ve interac/on in the Cooper channel is ATTRACTIVE at least for odd L and for L>>1. W. Kohn, and J. M. Luvnger, New Mechanism for Superconduc6vity, Physical Review LeZers, Vol. 15, No. 12, pp (1965) Recent review: S. Mai/ (UF) and A. V. Chubukov, arxiv: U>0 Original KL result: pairing amplitude in L-channel: Γ L c = Uδ L,0 + ( ) L c U 2 L L, L 1 4

21 Origin of the effect: the same as in Friedel oscilla/ons

22 Myth and truth about the KL mechanism Myth: the mechanism produces only ridiculously low T c Origin of the myth: KL obtained the result valid only for L>>1 and applied it to L=2. U ( r) = 4πa ( r) m δ 3 a = scattering length. For He 3 : k F a 2 Truth: Values of T c are reasonable For L~1. Lay and Layzer, PRL 20, 187 (1968) L = 1:T c / E F 10 3 Superfluid He 3 (Lee, Oscheroff, Richardson 1972) : T c / E F 10 3!

23 Nodes are a consequence of repulsive interac/on Suppose that the pairing interaction is anisotropic. BCS equation ( ) = ( V k,k' ) Δ( k' ) Δ k k' If V k,k' > 0, Δ k 2E k' ( ) 1 2n k' ( ) must change sign for the eq-n to have a solution. Another consequence of repulsion: enhanced magne/sm Fermi liquid interaction function F αγ,βδ ( θ ) = F s ( θ )δ αγ δ βδ + F a θ p,α p,γ p,α ( ) σ αγ i σ βδ p θ k k,δ F αγ,βδ F αγ,βδ ( θ ) = k,β k,δ ( θ ) = δ αγ δ βδ U 0 ( ) 1 2 U 2 p sin θ F 2 k,β 1 2 U 2 p sin θ F 2 σ αγ iσ βδ p,γ

24 Singlet vs triplet Singlet: the orbital part of the wave func/on is even Triplet: the orbital part of the wavefunc/on is odd Repulsive interac/on favors larger distances between par/cles: triplet pairing is preferred Strong ferromagne/c fluctua/ons favor triplet pairing (He 3, Sr 2 RuO 4 )

25 URhGe (a) and UGe 2 (b) Superconduc/vity: A different class? Gilbert G. Lonzarich Nature Physics 3, (2007)

26 What about an6ferromagne/sm? cuprates Fe- based superconductors (pnic,des)

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28 Cuprates: pairing via an/ferromagne/c fluctua/ons Doped an/ferromagne/c insulator Staggered spin suscep/bility q π = ( π,π ) ( ) = < S r i S r+a χ q r ( ) > e iqir ~ Effec/ve interac/on q q π 1 ( ) 2 + ξ 2 H int = k,q,α,β c α,k+qσ αβ c β,k i S q + k,q,α,β c α,k+qσ αβ q S q i S q χ q ( ) ( ) c β,k i c γ,p qσ γδ c p,δ χ q The interac,on is repulsive and strongest along the diagonals: the d x 2 - y 2 state wins!