Superconductivity from repulsion in LiFeAs: novel s-wave symmetry and time-reversal symmetry breaking

Transcription

1 Supercoductivity from repulsio i LiFeAs: ovel s-wave symmetry ad time-reversal symmetry breakig Ilya Eremi Theoretische Physik III, Ruhr-Uiversität Bochum Work doe i collaboratio with: Felix Ruhr-Uiversität Bochum A.V. Uiversity of Wiscosi, Madiso J. MPI Physik komplexer Systeme, Dresde S. Boriseko, V. Zabolotyy, B. IFW Dresde

2 Supercoductivity reaches the iro age Iro pictides first high-temperature supercoductors sice the cuprates! stoe age copper age iro age

3 Iro-based supercoductors Layered materials: trasitio metal (Fe) plus pictoge (itroge group, such as As) Ba Fe As BaFe 2 As 2

4 Iro-based supercoductors Layered materials: trasitio metal (Fe) plus pictoge (itroge group, such as As) T c =28K (55K for Sm) Kamihara et al JACS (2008) Re et al Chi. Phys. Lett. (2008) T c =38K Rotter et al. PRL (2008) Ni et al Phys. Rev. B 2008 (sigle xtals) T c =18K Wag et al Sol. St. Comm T c =8K Hsu et al PNAS 2008 No arseic!

5 Iro-based supercoductors: what are the commo electroic features?

6 Electroic-structure calculatios LaFePO Lebegue 2007 (T c =6K) LaFeAsO Sigh & Du 2008 (T c =26K) Bad structures for 2 materials early idetical! Hole pocket ear, electro pocket ear M 2D!

7 Electroic-structure: multiorbad structure Fe 2 3d 6 4 holes per site multibad structure. chemical potetial lies i the gap LaFeAsO Crystallie electric field of the tetrahedra is weak All 5 Fe d-orbitals are ear the Fermi level

8 Hole pockets ear (0,0) Electro pockets ear () Compariso with other materials La-1111 Ba-122 FeTe courtesy of I. Mazi

9 ARPES NdFeAs(O 1-x F x ) (x=0.1) A. Kamiski et al. Ba06K04Fe2As2 H. Dig et al. dhva LaFePO A. Coldea et al, LiFeAs A. Kordyuk et al Hole pockets ear (0,0) Electro pockets ear ()

10 Multiorbital structure Mutiorbital ad multibad physics: several d-orbitals close to E F L. Boeri, O.V. Dolgov, ad A.A. Golubov, PRL 101, (2008)

11 Iro-Pictides: typical phase diagram disorder, pressure magetic, structural, ad supercoductig order

12 Iro pictides: structural ad magetic trasitios I) Structural Trasitio II) Magetic Trasitio 122/1111/111 FeTe DFT correctly Trasitios reproduces are simultaeous (or eve predicts) for FeTe ad correct almost magetic for ad structural paret 122 s, groud but states, structural but trasitio requires magetism first i 1111 s as a prior coditio ad doped for 122 s distortio

13 Is the physics behid supercoductivity uiversal or model depedet?

14 Uiversality due to electro-phoo iteractio? NO Electro-phoo iteractio is probably too weak L. Boeri, O.V. Dolgov, ad A.A. Golubov, PRL 101, (2008) =0.44 for Al icludig magetism L. Boeri et al., PRB 82, (2010) Too small to accout for Tc ~ 50K Is there ay uiversality i these systems?

15 Uiversality due to proximity to atiferromagetism? Pairig due to spi fluctuatios? Cuprates Pictides ( ) 0 (cos k x - cos k y) 0 ( ) 0 (cos k x cos k y) k k' V eff ( k k') 2E( k') k' Mazi et al. Although i some materials this may give a reasoable explaatio this is ot the true origi of uiversality

16 Uiversality due to iitial electroic structure impact o the iteractios 2-body Hamiltoia with itrasite iteractios oly! u 1 u 4 u 3 L. Befatto, P. Hirschfeld, S. Graser, A. Chubukov, K. Kuroki, H. Aoki, R. Thomale, C. Hoerkamp, Ch. Platt, W. Hake,

17 electro FS u 4 u 3 hole FS s +- supercoductivity, BCS theory u 4 toy model: oe hole ad oe electro FSs s - Pairig iteractios: ( ) u - u, SC 3 4 Pair hoppig Itra-bad repulsio u 4 iteractio eed ( s - SC ) 0 If the itra-pocket repulsio (u 4 ) is stroger tha the pair hoppig (u 3 ), the pairig iteractio is repulsive I geeral, itra-pocket iteractio should be the largest ( u 4 is Coulomb repulsio at a small mometum trasfer ) Itra-orbital iteractios are bigger tha the iterorbital oes A.V. Chubukov, D. Efremov, ad I. Eremi, PRB (2008)

18 frg ad/or oe-loop RG is extremely importat A.V. Chubukov, I. Eremi, F. Wag, D.-H. Lee, C. Platt, R. Thomale, C. Hoerkamp, W. Hake, u ee ad u he are bare iteractios at eergies of a badwidth For SC we eed iteractios at eergies smaller tha the Fermi eergy 0 EF ~ 0.1 ev W ~3-4 ev E Coupligs flow due to reormalizatios i particle-particle ad particle-hole chaels

19 Oe-loop parquet RG Itra-bad repulsio u 4 Pair hoppig iteractio Iter-bad desity-desity ad exchage iteractio (H. Shultz, Dzyaloshiskii & Yakoveko, Rice, Hoerkamp ) SDW u 3 is pushed up by u 1, which gives rise to SDW If the tedecy towards SDW is strog, u 3 becomes larger tha u 4, leadig to a attractio i s +- supercoductig chael u 0 L

20 Tests for pairig symmetry (s +- ) 0 - h e

21 ARPES: Symmetry of the supercoductig gap - early isotropic gap i ARPES Ba 0.6 K 0.4 Fe 2 As 2 H. Dig et al., EPL (2008) NdFeAsO 1-x F x T. Kodo et al., PRL 101 (2008)

22 Nodal gap: the behavior of BaFe 2 (As 1-x P x ) 2, Tc =30K Y. Matsuda et al BaFe(AsP) (BaK)FeAs Cosistet with lie odes

23 Extesio for the realistic model covert the model ito bad basis, fit the iteractios by the lowest agular harmoics, ad extracted parameters u eh,u ee, etc. solve ad aalyze the gap equatios for moderate ad large hole ad electro dopigs for a bare iteractio ad for iteractio dressed by the higher order bubble ad ladder diagrams (spi fluctuatios )

24 Multiorbital physics is missig Origi of the gap aisotropy 1. importace of orbital character o Fermi sheets 2. scatterig betwee 1 ad 2 sheets 3. itrabad Coulomb repulsio See also: Chubukov et al 2009, Thomale et al 2009, 2011 (bad picture), Kemper et al 2010, P. Hirschfeld et al.(orbital picture) Fermi surface with orbital character Gap

25 Pairig vertex i multibad (multiorbital) systems S-wave pairig k - k p - p (k, p), m (k),m m (p) ( k x, k y),m( k y, k x ), m Near k=0, k) A B cos 4 C cos 8... ( alog hole FS Near p (p) (A ~ (D B ~ cos 2 E cos 4 C ~ cos 6...) cos 8...) alog electro FS

26 Leadig harmoics i the supercoductig s-wave gap ( k) A B cos 4 C cos 8... A A ~ B ~ C ~ (p) (D ~ cos 4 cos 8... cos 2 E ~ cos 6...) A ~ D ~ cos 2 Near hole FSs Near electro FSs effective iteractios depedet o the agles alog electro FSs h, h (k, p) u h,h, e,h (k,p) u e, h (1 2 cos 2 ), h (q) h, e,1,2 (q) e cos 2 Depedig o the ratio the gap is just aisitropic or odal

27 Leadig harmoics i the supercoductig s-wave gap combiatio of magetic fluctuatios ad agle-depedece of the iteractio betwee hole ad electro pockets attractio i s-wave chael for all electro ad hole dopigs. S +- gap with or without odes iteractio is ecessary agle-depedet, the gaps o electro FSs have cos 2 compoets ad may have accidetal odes electro FSs

28 Sesitivity to the relatively small chages Nevertheless the physics is still uiversal a) isotropic s +/- b) odes c) deep miima s +- solutio exists for ANY u 2 he/u hh u ee

29 Aother example: LiFeAs

30 LiFeAs: weak-characterized electroic structure Boriseko et al. Putzke et al ( k) A B cos 4 C cos 8... A Exp STM: Alla et al Near hole FSs

31 LiFeAs: low-q fluctuatios competig with icommesurate AF fluctuatios Low-q fluctuatios (almost FM): Brydo et al PRB 83 (2011) Icommesurate AF fluctuatios: J. Kolle, I. Eremi, et al PRB 86 (2012)

32 How the supercoductig istability arises i this case Subset 1: two hole pockets maily of xz ad yz character h1, h2 Subset 2: large hole pocket ad two electro pockets with strog admixture of xy orbital h3, e 1, e2 e e cos 2 The couplig betwee two subsets is relatively weak without takig ito accout spi fluctuatios Possibility for the time-reversal symmetry breakig s+is

33 Subset 2, k z =0 Subset 2: large hole pocket ad two electro pockets If oly the γ pocket ad two β pockets are preset, the gap chages sig betwee them

34 Weakly coupled subsets, degeeracy of various s-wave states

35 Weakly coupled subsets, degeeracy of various s-wave states

36 Weakly coupled subsets, degeeracy of various s-wave states

37 Weakly coupled subsets, degeeracy of various s-wave Theory states Experimet A-state matches the experimetal results

38 Possible time-reversal symmetry breakig

39 Supercoductivity i iro-based systems - Iter-bad iteractio (ehaced by spi fluctuatios) glue for the pairig for all dopigs, gap structure ad symmetry may chage -if both h ad e pockets are preset drivig force is electro-hole iteractio. [SC gap has s+- form, d-wave is a competitor, s-wave gap with accidetal odes o electro FS] LiFeAs orbital character may chage the character of the s-wave state - Novel effects due to multiorbital structure