Superconductivity in the Iron Age Zlatko Tesanovic, Johns Hopkins University [email protected] http://www.pha.jhu.edu/~zbt Saturday, March 23, 13 Superconductivity in the Iron Age Zlatko Tesanovic, Johns Hopkins University [email protected] http://www.pha.jhu.edu/~zbt Science Blockbuster of 2009 Saturday, March 23, 13 Superconductivity in the Iron Age Zlatko Tesanovic, Johns Hopkins University [email protected] http://www.pha.jhu.edu/~zbt Science Blockbuster of 2009 Saturday, March 23, 13 Superconductivity in the Iron Age Zlatko Tesanovic, Johns Hopkins University [email protected] http://www.pha.jhu.edu/~zbt #6- Iron-based Superconductors, which rivaled swine-flu for citations among scholars… Science Blockbuster of 2009 Saturday, March 23, 13 Superconductivity in the Iron Age Zlatko Tesanovic, Johns Hopkins University [email protected] http://www.pha.jhu.edu/~zbt o $ 1,000,000,000 question: How to make a 100 K iron-based superconductor #6-? Iron-based Superconductors, which rivaled swine-flu for citations among scholars… Science Blockbuster of 2009 Saturday, March 23, 13 Superconductivity in the Iron Age Zlatko Tesanovic, Johns Hopkins University [email protected] http://www.pha.jhu.edu/~zbt o o $ 1,000,000,000 question: o$ 100 question: What is the Howtheory to make of iron-pnictidesa 100 K iron-based ? superconductor #6-? Iron-based Superconductors, which rivaled swine-flu for citations among scholars… Science Blockbuster of 2009 Saturday, March 23, 13 PHYSICAL REVIEW B 80, 024512 ͑2009͒ Valley density-wave and multiband superconductivity in iron-based pnictide superconductors Vladimir Cvetkovic and Zlatko Tesanovic Institute for Quantum Matter and Department of Physics & Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA ͑Received 5 September 2008; revised manuscript received 22 June 2009; published 20 July 2009͒ The key feature of the Fe-based superconductors is their quasi-two-dimensional multiband Fermi surface. By relating the problem to a negative U Hubbard model and its superconducting ground state, we show that the defining instability of such a Fermi surface is the valley density-wave ͑VDW͒,acombined spin/charge density- wave at the wave vector connecting the electron and hole valleys. As the valley parameters change by doping or pressure, the fictitious superconductor experiences “Zeeman splitting,” eventually going into a nonuniform “Fulde-Ferrell-Larkin-Ovchinikov” ͑FFLO͒ state, an itinerant and often incommensurate VDW of the real world, characterized by the metallic conductivity from the ungapped remnants of the Fermi surface. When Zeeman splitting exceeds the “Chandrasekhar-Clogston” limit, the “FFLO” state disappears and the VDW is destabilized. Near this point, the VDW fluctuations and interband pair repulsion are essential ingredients of high-Tc superconductivity in Fe pnictides. RAPID COMMUNICATIONS DOI: 10.1103/PhysRevB.80.024512PHYSICAL REVIEWPACS B number83, 020505(R)͑s͒: 74.20. (2011)Ϫz, 71.45.Lr, 74.70.Dd, 75.30.Fv TheoryI. INTRODUCTION of the valley-density wave and͑xc͒, the hidden “superconducting” order in state iron is pnictides completely destroyed and so is the VDW in a true material. However, for ␦kF above but Recently, the superconductivity below 7 KJian in LaOFeP Kang and Zlatkonear ␦k Tec,sanoviˇ we considerc´ strong “superconducting” fluctuations ͑Ref. 1͒ led to the discovery of high Tc ϳ26 K in its doped and find that these VDW fluctuations can induce real super- Institute for Quantum Matter and Department2 of Physics & Astronomy, The Johns Hopkins University, Baltimore, Maryland 21218, USA sibling LaO1−xFxFeAs͑xϾ0.1͒. Even higher Tc’s were conductivity in Fe pnictides ͑see Fig. 1͒. In principle, one found by replacing(Received La 20 with November other rare 2010; earths, revised up to manuscript the cur- receivedcould 22 avoid December the mapping 2010; published to the negative 31 JanuaryU Hubbard 2011) model 3 rent record ofInT thec =55 limit K. ofThese perfect are nesting, the first the noncuprate physics of ironsu- pnictidesand argue is governed that the by VDW the density instability wave in formation pnictides at occurs the for 9 perconductorszone-edge͑SCs͒ exhibiting vector M. At such high high energies,Tc’s and various their spin- dis- (SDW),the same charge-, reasons and orbital/pocket- as the SDW instability (PDW) density found waves, in, say, Cr. covery has touched off a storm of activity.4 We find, however, that our “fictitious superconductivity” de- and their linear combinations, all appear equally likely, unified within the unitary order parameter of U(4) U(4) In this paper, we introduce a notable element into the scription is more appropriate to pnictides not only× due to its theoreticalsymmetry. debate by Nesting considering imperfections a unified and model low-energy of spin interactionsillustrative reduce purposes this symmetry but also because to that of it real allows materials. us to extend density-wave,Nevertheless, orbital density-wave, the generic ground structural state deformation, preserves a distinctthe analogy signature to of the its “FFLO” highly symmetric state and origins: multiband A SDW “SC,” i.e., and superconductivityalong one axis in of Fe the pnictides. iron lattice The is model predicted is simple to coexist with a perpendicular PDW, accompanied by weak charge but it containscurrents. the necessary This “hidden” physical order features. induces The the structural essential transition in our theory, naturally insures Ts ! TN ,andleads ingredientsto are orbital electron ferromagnetism and hole pockets and other͑valleys observable͒ of consequences. the Saturday,quasi-two-dimensional March 23, 13 ͑2D͒ multiply connected Fermi sur- face ͑FS͒.5DOI:–7 To10.1103/PhysRevB.83.020505 extract the basic physics we consider spin- PACS number(s): 74.70.Xa, 75.30.Fv, 75.25.Dk less electrons first and only a single electron and a single hole band with identical band parameters. We then show that Thethis model discovery can be related of high-temperature to a 2D negative U superconductivityHubbard model, vector Q,withallofitsdifferentreincarnations—various 1,2 3 (HTS)the in ground iron pnictides state of whichhas sparked is known intense exactly—it research. isLike a spin-, charge-, and orbital/pocket-density waves (SDW, CDW, thesuperconductor. cuprates, the8 pnictidesIn real FeAs are materials, layered systems this fictitious and super- exhibit PDW, respectively), as well as their mutually orthogonal linear antiferromagnetismconductivity translates (AF) into at zero a fully doping gapped (x valley0), density- followed combinations—unified within a unitary U(4) U(4) order bywave HTS͑ beyondVDW͒, a some unified finite statex. representing3,4 Magnetic a combination order= in parent of parameter.22 At yet lower energies, however, as× the U(4) compoundsspin, charge, consists and orbitalof an AF density-waves spin chain along͑SDW/CDW/ODW the wave vector͒ U(4) symmetry-breaking interactions and the deviations from× (π,0)at orthe (0commensurate,π)intheunfoldedwave vectorBrilliouinM connecting zone (UBZ) the and two an val- FM perfect nesting come into play, the symmetry is reduced down leys. Next, we introduce two different fictitious5 “chemical spin chain alonge the perpendicularh direction. The dynamical to that of real materials. Nevertheless, provided there is a originpotentials,” of this AF␮ ! state␮ for is the hotly electron debated: and Within the hole the valleys, itinerant as significant segregation of scales in the effective Hamiltonian measured from the bottom and the top of the bands, electron model, the magnetic transition is ascribed to the of iron pnictides between the high-energy U(4) U(4)- respectively—this describes the effect of doping the parent FIG. 1. ͑Color online͒ Phase diagram of Fe pnictides, depicting× SDWiron-pnictide instability, compounds enhanced by and the corresponds near-nesting to among the external electron symmetric and the low-energy symmetry-breaking terms, the and hole pockets of the Fermi surface (FS).6–9 To ensure theground evolution state of our and fictitious its excitations superconductor bear a from distinct the fully signature gapped of their Zeeman splitting in our fictitious attractive Hubbard model. VDW insulator to the “FFLO superconductor”—a partially gapped “striped” spine order,h only one electron pocket is involved in highly symmetric origin. As ␦␮=␮ −␮ increases, so does this Zeeman splitting, and metallic VDW—to the real SC under the influence of the Zeeman SDW,eventually and the our spin-wave fictitious anisotropy superconducting arises state from approaches the electron to Our␦␮ picture is based on the itinerant model and re- 10,11 splitting ͑doping or pressure͒. The red dot on the vertical axis pockets’and exceeds finite ellipticity. the “Chandrasekhar-Clogston”In contrast, within limit, the giving localized way symbolizeslies on the the parent hierarchy compounds of and energy the regime scales below that it might separate be the 12,13 Heisenberg-typeto a nonuniform modelFulde-Ferrell-Larkin-Ovchinikovvarious frustrated couplings͑FFLOJ͒1a, physically“flavor”-conserving inaccessible. Insets: from FS the of ͑ “flavor”-changinga͒ the normal state in interactions the J1b,groundJ2 between state at neighboring an incommensurate spins conspire͑IC͒ wave to produce vector q the, folded ͑⌫ M͒ BZ ͑Ref. 18͒, ͑b͒ the VDW metal ͑computed with e h of quasiparticles↔ on the FS, composed of two hole (h1,h2) where ͉q͉ is set by ␦kF =kF −kF, and thus by doping 14x.,15 This the interband interaction set to unity͒—this is the C version of ͑c͒ observed magnetic order and the magnon anisotropy. and two electron (e1,e2)pockets(orvalleys)(Fig.4 1). This “FFLO state” is nothing but an IC VDW at the wave vector the continuum FFLO state Ref. 21 . The remaining states are fully In addition, the tetrahedral-to-orthorhombic structural hierarchy is further͑ assisted͒ by the differences in area and M+q. Finally, as ␦k ͑x͒ exceeds certain critical value ␦k gapped. transformation is observed,F accompanied by the AFc shape of different pockets being much smaller than their transition.16,17 The AF-ordered moment is linearly 1098-0121/2009/80͑2͒/024512͑8͒ 024512-1 common overall features;©2009 hence The American the U(4) Physicale U(4) Societyh symmetry.