Symmetry and Gap Structure of Fe-based Superconductors. P. Hirschfeld, U. Florida

Transcription

1 Symmetry ad Gap Structure of Fe-based Supercoductors P. Hirschfeld, U. Florida U. Miesota April 2011

2 Collaborators from rest of world: from U. Florida Dept. of Physics: Vivek Mishra Maxim Korshuov Doug Scalapio UCSB Thomas Maier ORNL Siggi Graser Augsburg Adrey Chubukov Madiso Saurabh Maiti Madiso

3 Iro-based supercoductors Recet reviews: Paglioe & Greee Nat Phys 2010; Johsto Adv. Phys T c =28K (55K for Sm) Kamihara et al JACS (2008) Re et al Chi. Phys. Lett. (2008) T c =38K Rotter et al. arxiv: : 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!

4 Electroic structure calculatios LOFP Lebegue 2007 (T c =6K) LOFA Sigh & Du 2008 (T c =26K) Bad structures for 2 materials early idetical! Hole pocket ear, electro pocket ear M Kotliar et al, Cao et al: correlatios ca be importat 2D!

5 Are these ew materials differet? KFe 2 Se 2 strogly e-doped, o h pocket? T. Sato et al hole dispersio Y. Zhag et al H. Dig et al KFe 2 As 2 strogly hole doped, o electro pocket?

6 Multiorbital physics DOS ear Fermi due almost etirely to 5 Fe d-states Complicatios: calculatios will be harder Novelty: surprisig ew aspects of multiorbital/ multibad physics Total LaO Fe 3d As 4p LaOFeAs Total DOS LaO Bad structure Fermi surface

7 Outlie Experimetal overview of SC state Perspective o pairig by spi fluctuatios Evolutio with dopig: (T) ) ad (T) 3D effects ad trasport Evolutio of gap ad effective iteractios

8 Cotroversy: k-space structure of gap? Evidece for siglet, s-wave s type SC order, whose structure is very sesitive to details of iteractios, electroic structure, disorder Hope: gap symmetry optimize ew materials Experimets gap structure pairig theory Hi-T c

9 Cartoo of possible gap structures Paglioe ad Greee Nat. Phys (slightly modified) - + h + - (+/- isotropic) A 1g B 1g Also i discussio: S ++

10 Peetratio depth experimets Gordo et al 2008 Ba 1-x Co x Fe 2 As 2 T c,max =38K Fletcher et al 2008 LaFePO T c =6K Hashimoto et al 2009 Hashimoto et al 2009 BaFe 2 (As 1-x P x ) 2 T c,max =30K f ~ d N( ) ad for dirty clea odal SC N( ) N a 0 N( ) 2 so T T 2 dirty clea

11 Other peetratio depth experimets reported expoetial (T) ( full gap) K-doped Ba122 Hashimoto et al Phys. Rev. Lett

12 Thaks: KA Moler

13 Thermal coductivity (H=0) (bulk probe, lowest temperatures thus far) LaFePO: Yamashita et al axv: K-doped Ba-122: Luo et al axv: Big liear T term Tiy or zero liear T term Recall i theory of odal SC liear T term residual qp excitatios (metallic-like) for d-wave supercoductor this term is uiversal T ~ N 0 v F2 / 0

14 NMR spi-lattice relaxatio ~T 3 Yashima et al arxiv: Nakai et al. JPSJ (2008) lie odes N()~ T 3!

15 Resoat mode i ielastic eutro scatterig Remider: cuprates: Fog et al PRB 2000 Ba K 0.4 Fe Fe 2 As 2 : Christiaso et al Nature K 50K I Ba-122 resoace observed ear Q= folded BZ) Appears oly i SC state (like opt. doped cuprates) I 1-bad 1 models k+q = - k ucovetioal Multibad theory: Maier & Scalapio 2008, Korshuov & Eremi 2008, Maier et al 2009

16 Magetic field depedece of spec. heat L-1111 FeSe Mu et al (2008) (similar to d-wave Volovik effect) Zeg et al (2010)

17 BaFe 1.85 Co 0.15 As 2 Mystery: ARPES K. Terashima et.al. PNAS 2009 May ARPES measuremets, oe fid highly aisotropic gap

18 ? questios? What cotrols whether Fe-based material is odal or gapped supercoductor? Role of disorder? Ca we idetify order parameter structure i a give material? 3D effects? Are Fe-based SC itrisically sesitive to small chages electroic structure? Evolutio of gap structure with dopig,?

19 Why spi fluctuatios? Mazi et al, PRL 2008, see also Mu et al CPL (2008), Boeri et al. PRL 2008 Sigh & Du PRL 2008 Log rage magetic order is detrimetal to supercoductivity, but so is total absece of magetism. (but KFe 2 Se 2??) 1111-pictides T c =26-55K LaFePO T c =6K KFe 2 As 2 T c =3.6K omagetic Luetkes et al 08 Pratt et al 09

20 Spi fluctuatio theories of pairig Effective iteractio from spi fluctuatios (Berk-Schrieffer 1961) Recall: d-wave i cuprates from atiferromagetic spi fluctuatios d-wave takes advatage of peak i spi fluct. iteractio at! p(, ) p

21 Spi fluctutatio pairig theories i Fe-pictides Early electroic structure calculatios show e-ph weak Early calculatios of spi-fluctuatio pairig : Kuroki et al PRL 2008 Cvetkovic et al EPL 2009 We-Lee axv: Mazi et al PRL 2008 Zhag et al PRL 2008 Wag et al 2008 Y. Bag et al 2008 Seo et al PRL 2008 Graser et al NJP 2009 Zhag et al PRB 2009 Ikeda et al PRB 2009 Studies of odal-gapped trasitio: Maier et al PRB 2009 Chubukov et al PRB 2009 Kuroki et al PRB 2009 Thomale et al PRB 2009 Thomale et al axv 2010 Wag et al axv 2010 Graser et al axv 2010 Kemper et al axv 2010 Ikeda et al PRB 2010 Tight-bidig model +iteractios ivestigated by most authors: H=H 0 +H it H 0 =5-bad tight-bidig model most geeral 2-body Hamiltoia with itrasite iteractios oly!

22 Similar argumet from Mazi et al PRL 2008 for pictides: cosider oly pair scatterig also: Kuroki et al 2008 Seo et al Chubukov et al estig peaks iteractio V s at,0 i 1-Fe zoe. - iteractio is costat over sheet sice they are small. - therefore isotropic sig-chagig s +/- state solves gap eq

23 Realistic theories: gaps display strog aisotropy/ odes aisotropic exteded-s -wave close: d x 2 -y 2 similar: (k) Kuroki et al 08, 09, Ikeda et al 09, 10, Graser et al 09,10, Wag et al. 08,09 (x=0.125 e-doped) e U=1.54 J=0.3 Two pairig chaels early degeerate a) Ca differet FeAs materials have differet symmetries? b) More likely: s-wave s symmetry,, differig gap structures for differet materials

24 What is the origi of the gap aisotropy [Maier et al PRB 09]? 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 (bad picture), Zhag et al 2009 Thomale et al 2010, Kemper et al 2010 Fermi surface w/ orbital character Gap

25 Itra- vs. iterorbital pairig: RPA aalytical results itra iter Largestdrive by U,J U,J drive istability mixed small due to mat elts.

26 Importace of pocket Kuroki et al 2009 foud that pocket at (,) promotes a odeless gap Presece of pocket ca be cotrolled by dopig AND by tuig the height of As above the Fe plae Tedecy of hole-doped systems to be more isotropic

27 Nodal-gapped trasitio as fuctio of hole dopig RPA: Kemper et al. NJP 2010 LaOFeAs Fermi surface (k) U=1.3 J=0.2 Gapped odal

28 So small chages i electroic structure due to strai, defects, surfaces ca chage pair state Implicatios for ARPES? A. Kemper 2010

29 sesitivity to small chages i electroic structure Kemper et al 2010 a) chages to small Fermi pockets big chages i gap b) ay odes are accidetal rather tha symmetry-eforced i ext.-s states a) isotropic s +/- b) odes c) deep miima ) N() N() N() ) )

30 Big picture? How does SC state vary with dopig?

31 Thermodyamics & trasport evidece for Ba-122 system odes Full gap odes odes Full gap odes KFe 2 Se 2 : No hole pockets: d-wave Wag et al axv: Graser et al axv: KFe 2 As 2 : No electro pockets: d-wave Thomale et al axv:

32 Evidece: low-eergy quasiparticle desities icrease away from optimal dopig Marti et al 2010 Reid et al 2010

33 Graser et al PRB 2011 odeless d-wave state for KFe 2 Se 2 Similar: F. Wag et al 2011, Das ad Balatsky Iter-orbital pairig ecessary! Kight shift 77 K cosistet with full gap Ma et al 2011 U Aisotropic but odeless d-wave Neutro scatterig resoace ear

34 Agular harmoic represetatio of RPA results Maiti et al 2011 S-wave (A 1g ) chael k - k p - p (k, p), m (k),m m (p) ( k) cos k x cos k y, cos k x cos k y... ( k x, k y),m( k y, k x ), m Near k=0, pure s-wave Near p=(,0), (D ( k) A B cos 4 C (p) (A ~ B ~ cos 2 E cos 4 C ~ cos 6...) cos 8... cos 8...) alog hole FS alog electro FS

35 keep oly the leadig terms i the series: ( 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 effective iteractios: h,h e1,e1 (k,p) (k,p) u h,h u, e,e (1 e,h (k,p) 2 ee u e,h (1 (cos he cos 2 ), cos 2 ) 4 2 ee cos 2 cos solve gap equatio aalytically

36 fits to RPA determie direct bad iteractio coefficiets i harmoic space

37 results of harmoic aalysis Geeric case: as log as both hole ad electro pockets are preset, the drivig force is electro-hole iteractio. Poor estig suppresses isotropic s+/- away from optimal dopig for strogly electro doped FeSCs, strog direct d-wave attractio betwee electro pockets develops (Graser et al, Wag et al, Das/Balatsky 2011) for strogly hole-doped FeSCs, d-wave chael probably agai wis. There is d-wave attractio withi hole pocket at () ad strog attractio betwee the two hole pockets at (0,0), both effects leads to d >0 (Thomale et al 2011)

38 Coclusios Order parameter form cotroversial, experimets disagree. Symmetry A 1g ( s-wave ), probably with overall sig chage-- odes i some systems, ot i others. d-wave d possible for extreme electro, hole dopig. aisotropic s +/- odal structures show strog sesitivity to small chages i electroic structure (pictoge( height, surfaces, strai, defects) 122 experimets ow idicate systematic tred of gap structure ~ spi fluctuatio theory across dopig rage, supported by lowest order harmoic aalysis. Ed poits KFe2As2 ad KFe2Se2 may be differet Challege: use such theories to predict systematics of T c withi family