Forging a theory of unconventional superconductors: a new paradigm for electron pairing

Transcription

1 Forging a theory of unconventional superconductors: a new paradigm for electron pairing P.J. Hirschfeld, U. Florida PH, M.M. Korshunov & I.I. Mazin, Rep. Prog. Phys. 74, (2011) UF August 2014

2 Collaborators FeSC theory from rest of world: from U. Florida Dept. of Physics: Roser Valenti Frankfurt Brian Andersen Niels Bohr Inst. Doug Scalapino UCSB Thomas Maier ORNL Vivek Mishra (Argonne) Maxim Korshunov (Krasnoyarsk) Lex Kemper (L. Berkeley) Hai-Ping Cheng Tom Berlijn (ORNL) Andrey Chubukov U. Minn. Igor Mazin, NRL Greg Boyd (Georgetown) YanWang (U. Tenn.) Saurabh Maiti Wenya Rowe NHMFL Dirac Pdoc (Saclay) Peayush Choubey Ilya Vekhter, LSU Ilya Eremin, Bochum

3 Heike Kammerling Onnes (1911) Discovery of superconductivity

4 Conventional superconductors During 46 years, from 1911 to 1957, superconductivity is recognized as one of the most important problems in theoretical physics - Search for a theory of superconductivity: series of failures (see J. Schmalian in 50 Years of BCS) Richard Feynman: No one is brilliant enough to figure it out Fail: F Fail: F Fail: F Fail: F Fail: F Bohr Landau Feynman Einstein Heisenberg

5 Conventional superconductors BCS theory (1957) Quantum mechanical behavior at the macroscopic scale Leon Cooper Nobel prize : 1972 John Bardeen Macro. Quantum State s-wave symmetry Robert Schrieffer ( u vc c ) 0 Ψ = + > BCS k k k k k V c -k c k ~ 0 e iφ

6 SC Ground State Normal State (Metal) KY Low Temp. Cooper Pairing L=0 S=0 Superconducting Ground State KY K F K X k> -k> K F K X Degenerate ~free electron gas ~ Gas of Cooper Pairs

7 How can two electrons attract each other? Dance analogy: coherent pairs J. Robert Schrieffer: By dancing they lower their energy or make themselves happier Another analogy:

8 How Cooper pairs form in conventional superconductors: the glue : electron-phonon interaction Effective residual e-e interaction including Coulomb ( Jellium model ) a b For realistic system, a b! Depend on details Screened Coulomb Electron-phonon attraction Note: electrons avoid Coulomb repulsion in time (interaction is retarded)

9 Why do some elements superconduct, others not? a,b depend on details! a b

10 Superconductivity: why is pairing good? Discovery channel answer: once we have an attraction, we get pairs. Pairs of fermions are bosons, So they can Bose condense pair superfluid S=0

11 Superconductivity: Ground state Quiz 1: is this a good picture of Cooper pairs?

12 Superconductivity: Ground state A: No! For most SC, pair size ξ >> interparticle spacing n -1/d n -1/d In this picture, ξ n -1/d

13 Superconductivity: Ground state In reality, ξ=v F / >> n -1/d Remember that all pairs are phase coherent! Simple metal: ξ ~ 10 3 A n -1/d ~ 1A St. Matthew s Passion Oxford, UK

14 Superconductivity: Excited states ξ=v F / >>n -1/d Bogoliubov quasiparticle

15 Quiz: a statement about SC Cooper Cooper pairs are not independent bosons! pendant Grace à Henri Alloul

16 Is that all there is? Brian Pippard and The Cat and the Cream speech IBM 1961

17 Is that all there is? Brian Pippard and The Cat and the Cream speech IBM 1961 I think I might remark that in low-temperature physics the disappearance of liquid helium, superconductivity, and magneto-resistance from the list of major unsolved problems has left this branch of research looking pretty sick from the point of view of any young innocent who thinks he's going to break new ground.

18 High temperature superconductivity Z. Physik, June 1986 Alex Müller and Georg Bednorz

19 High temperature superconductivity Z. Physik, June 1986 Alex Müller and Georg Bednorz

20 Great expectations 1987

21 Wires Applications 2014 Ag BiSrCaCuO to make transmission lines large magnets maglev technology

22 Cuprates: status report T p~0.1 p~0.2 doping d-wave SC: T c is too high for electron-phonon glue to work! What holds pairs together? 0 = cos cos 2 ( k k ) k x y

23 Discovery of LaO 1 x F x FeAs Kamihara et al JACS 2008 H. Hosono T c,max =26 K

24 Monolayer FeSe?? Monolayer FeSe??

25 Comparison with cuprates Strong vs. weak coupling? bands Single vs. multibands? correlation 2D vs. 3D? I. Mazin, Nature 2010 Can we learn what the essential ingredients for high-t c are from the comparison?

26 Iron-based superconductors Recent reviews: Paglione & Greene Nat Phys 2010; Johnston Adv. Phys T c =28K T c =38K T c =18K T c =8K (55K for Sm) Kamihara et al JACS (2008) Ren et al Chin. Phys. Lett. (2008) Rotter et al. arxiv: PRL (2008) Ni et al Phys. Rev. B 2008 (single xtals) Wang et al Sol. St. Comm Hsu et al PNAS 2008 No arsenic!

27 Electronic structure calculations LaFePO Lebegue 2007 (T c =6K) LaFAs0 Cao et al2008 (T c =26K) Band structures for 2 materials nearly identical! Hole pocket near Γ, electron pocket near M Kotliar et al, Cao et al: correlations can be important 2D!

28 Multiorbital physics DOS near Fermi due almost entirely to 5 Fe d-states Complications: calculations will be harder Novelty: surprising new aspects of multiorbital/ multiband physics Total LaO Fe 3d As 4p LaOFeAs Total DOS Band structure LaO Fermi surface

29 Magnetic order in most (not all) parent compounds de la Cruz et al Nature 453, 899 (2008) Stripe like order

30 Doping the parent compound Various chemical substituents or pressure lead to SC dome Alireza et al. (2008) Fang et al. (2009)

31 Two phase transitions I) Structural Transition II) Magnetic Transition 122/1111 FeTe DFT correctly reproduces (or even predicts) correct magnetic and structural Transitions ground are states, simultaneous but requires for magnetism FeTe and parent as a prior 122 s, but condition structural for distortion transition is first in 1111 s and doped 122 s Courtesy of M. Johannes & I. Mazin

32 SC gap symmetry and structure (k) = energy gap or order parameter or pair wave function A 1g B 1g

33 e-ph interaction is too weak Phonon spectrum, density of states Singh & Du PRL 2008 Mazin et al, PRL 2008, see also Mu et al CPL (2008), Boeri et al. PRL 2008

34 superconductivity from e-e interactions Pairing by exchange of spin, charge/orbital, nematic fluctuations? Hint: magnetism is usually nearby: 1111-pnictides T c =26-55K LaFePO T c =6K KFe 2 As 2 T c =3.6K nonmagnetic no magnetism low T c Luetkens et al 08 Pratt et al 09

35 Prehistory: Kohn-Luttinger 1965 Walter Kohn Quinn Luttinger Also: Landau and Pitaevskii KL (1962): an electron gas with no phonons and only repulsive Coulomb interactions can be a superconductor! A new paradigm: electrons avoid repulsive part of Coulomb interaction in space rather than time!

36 Prehistory: Kohn-Luttinger 1965 Friedel: screened Coulomb interaction V ( r) = cos 2k r / r F 3 At finite distances, screened Coulomb interaction becomes attractive: finite-l pairing

37 Prehistory: Kohn-Luttinger 1965 U effective pairing interaction bare interaction (repulsive) screening terms (attractive in some L-channels) Example: short range U>0 for rotationally invariant system ( 3 He ) T c E F exp( 2.5L 4 ) Best calculation in 1965: Brueckner Soda Anderson Morel PR 1960 : predicted L=2 for 3 He T c ~ K But had they taken L=1 they would have gotten T c ~ 1 mk!

38 2 paradigms for superconductivity according to how pairs choose to avoid Coulomb interaction conventional : isotropic s-wave pair wave fctn, interaction retarded in time Overall effective interaction attractive unconventional : anisotropic or sign-changing pair wave fctn, Overall effective interaction repulsive

39 Spin fluctuation theories of pairing Effective singlet interaction from spin fluctuations (Berk-Schrieffer 1966) V s Screened Coulomb U χ 0 χ 0 χ 0

40 Spin fluctuation theories of pairing Effective interaction from spin fluctuations (Berk-Schrieffer 1966) paradigm: d-wave in cuprates from antiferromagnetic spin fluctuations From DJ Scalapino, Phys Rep 1995 d-wave takes advantage of peak in spin susceptibility at q=(π,π)! p+ ( ππ, ) = p

41 remember at least some interactions attractive in order to form Cooper bound state k-space: V s (k-k ) V 0 +V 2 φ d (k) φ d (k )+ r-space

42 Similar argument from Mazin et al PRL 2008 for FeSC: electron-hole pocket pair scattering dominates χ(q) also: α β Kuroki et al 2008 Seo et al Chubukov et al nesting peaks interaction V s at π,0 in 1-Fe zone. - interaction is constant over sheet since they are small. - therefore isotropic sign-changing s +/- state solves gap eqn

43 Comparing cuprates and FeSC I. Mazin, Nature 2010 Different symmetry superconducting order may be driven by morphology of Fermi surface --- need not imply a different pairing mechanism See Chubukov & Basov Manifesto for higher Tc, Nat. Phys 11 Scalapino, A Common Thread RMP 12

44 Spin fluctutation pairing theories in Fe-pnictides H=H 0 +H int H 0 =5-band tight-binding model most general 2-body Hamiltonian with intrasite interactions only! Effective interaction between electrons in orbitals

45 Realistic theories: realistic gaps display strong anisotropy/ nodes anisotropic extended-s -wave close: d x 2 -y 2 Graser, PJH et al 09,10 similar: (k) Kuroki et al 08, 09 Ikeda et al 09, 10 (x=0.125 e-doped) U=1.54 J=0.3 Two pairing channels nearly degenerate a) Can different FeAs materials have different symmetries? b) More likely: s-wave symmetry, differing gap structures for different materials

46 What is the origin of the gap anisotropy [Maier, PJH et al PRB 09]? 1. orbital character on Fermi sheets 2. scattering between β 1 and β 2 sheets 3. intraband Coulomb repulsion See also: Chubukov et al 2009, Thomale et al 2009 (band picture), Zhang et al 2009 Thomale et al 2010, Kemper et al 2010 d yz d xy d xz Fermi surface w/ orbital character Gap

47 ω ω ω sensitivity to small changes in electronic structure Kemper et al 2010 a) changes to small Fermi pockets big changes in gap b) any nodes are accidental rather than symmetry-enforced in ext.-s states a) isotropic s +/- b) nodes c) deep minima (φ) α φ β N(ω) N(ω) N(ω) (φ) φ (φ) φ

48 SC state: experimental lack of universality e.g., penetration depth experiments Hicks et al 2008 LaFePO T c =6K Prozorov, 2011 Co-doped Ba122 T c =25K Hashimoto et al 2009 K-doped Ba122 T c =40K f λ dω N( ω) ω dirty clean N( ω) N0 + a nodal SC gapped SC N( ω) ω 2 ω so so λ λ T T e 2 /T dirty clean

49 Big picture: evolution of gap with doping PJH, Korshunov and Mazin Rep. Prog. Phys Full gap anis. nodes? nodes KFe 2 As 2 : No electron pockets: d-wave? Thomale et al S-wave: Okazaki et al (ARPES) KFe 2 Se 2 : No hole pockets: d-wave? Wang et al Graser, PJH et al S-wave? Mazin, Fang et al

50 1 recent project: LiFeAs stoichiometric T c =18K superconductor with - nonpolar surfaces - nonmagnetic, no FS nesting Fermi surface: Borisenko et al PRL 2010

51 Importance of correlations? k z =0 Yin et al 2011 Nat Mat, Ferber et al PRB 2012 LDA+DMFT: hole pockets shrink, electron pockets unaffected see also Lee et al, PRL 2012

52 ARPES results for SC gap function (Dresden group) β electron pocket γ hole pocket See also K. Umezawa et al 2012 Borisenko et al Symmetry 2012

53 Experimental data (Disney version) ~4meV 0 Borisenko et al 2012 Umezawa et al 2012

54 Results of 3D spin fluctuation calculations I Leading pairing eigenstate 10-orbital DFT-based or ARPES-fit bands Wang et al PRB 2013

55 Comparison theory/expt Y. Wang, A. Kreisel, V. B. Zabolotnyy, S. V. Borisenko, B. Büchner, T. A. Maier, PJH, D. J. Scalapino, PRB 2013 Conclusion: s+/- pairing from spin fluctuations despite lack of Fermi surface nesting

56 Conclusions: 2 paradigms for superconductivity conventional : isotropic s-wave pair wave fctn, interaction retarded in time Overall effective interaction attractive Elements, A15s, MgB2, borocarbides, A-doped C60,. unconventional : anisotropic or sign-changing pair wave fctn, Overall effective interaction repulsive Cuprates, Fe-based, heavy fermions, organics,. Hirschfeld group: searching for T c trends within these materials classes

57 Conclusions/questions Symmetry of SC order in systems with repulsive interactions often dictated by morphology of Fermi surface. FeSC appear to be A 1g ( s-wave ), probably with overall sign change-- nodes in some systems, not in others. Tendency towards nodal behavior away from optimal doping. d-wave possible for extreme electron, hole doping. Are there several families of SC linked by common pairing mechanism common thread? Higher T c? Materials-specfic calculations needed.