Observation of intertwined Fermi surface topology, orbital parity symmetries and electronic interactions in iron arsenide superconductors
L.A. Wray, D. Hsieh, Y. Xia, S.-Y. Xu, D. Qian, G. F. Chen, J. L. Luo, N. L. Wang, M.Z. Hasan
aa r X i v : . [ c ond - m a t . s t r- e l ] D ec Observation of intertwined Fermi surface topology, orbital parity symmetries andelectronic interactions in iron arsenide superconductors
L.A. Wray, D. Hsieh, Y. Xia, S.-Y. Xu, D. Qian,
1, 2
G. F. Chen, J. L. Luo, N. L. Wang, and M.Z. Hasan Department of Physics, Joseph Henry Laboratories of Physics,Princeton University, Princeton, NJ 08544, USA Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, Peoples Republic of China Beijing National Laboratory for Condensed Matter Physics, Institute of Physics,Chinese Academy of Sciences, Beijing 100080, Peoples Republic of China (Dated: April 22, 2017)We present a polarization and topology resolved study of the low energy band structure in op-timally doped superconducting Ba . K . Fe As using angle resolved photoemission spectroscopy.Polarization-contrasted measurements allow us to identify and trace all low energy bands expectedin models, revealing unexpected symmetry breaking and a surprisingly intertwined Fermi surfacetopology of hole-like bands near the Brillouin zone center. Band structure correlations across theΓ-M spin fluctuation wavevector are compared with the superconducting gap anisotropy to suggesta partial scenario for spin-mediated interband instability contributing to superconductivity in thehole doped regime. PACS numbers:
Despite intensive efforts, the Fermi surface topology ofpnictide high-T C superconductivity continues to be anunresolved but critically important issue. This is largelydue to the fact that it is a multi-band correlated sys-tem with nontrivial orbital texture and complicated spin-lattice interactions [1, 2, 3]. Here we present the lowenergy dynamics of the optimally doped pnictide super-conductor, using comprehensive orbital-polarization re-solved band structure mapping to provide an integratedanalysis of the orbital symmetries and electron kinet-ics. Our results reveal a multiplet of Fermi surfaces (FS)of which a pair around the Γ-point is intricately inter-twined with alternating orbital character, and show thatthere is hole-hole nesting between the pair of outermostFermi pockets along Γ-M. This Fermi surface topologyand the underlying band dispersions are interpreted inthe context of nonlinear electronic correlation-inducedcorrections to local density approximation (LDA) calcu-lations. Further, the band structure shows unexpectedhybridization (symmetry breaking), suggesting the pres-ence of antiferromagnetically ordered domains within thesuperconducting crystal. By correlating with Fermi sur-face dependent superconducting gap magnitude measure-ments, we observe that fine details of the gap structureare supported by ( π ,0) interband instability, which sup-ports a spin-fluctuation scenario for the pairing channel[4].Our previous angle resolved photoemission spec-troscopy (ARPES) investigations of iron arsenide bandstructure have strongly established the importance of in-cident photon polarization-resolved measurement to viewall low energy features [5]. In this Letter a more compre-hensive approach is adopted to perform separate map-pings of band structure and the full Fermi surface withpolarization directed along each of the available high- FIG. 1:
Complete Fermi Surface polarization mapping :(a) Polarization is kept fixed by moving the analyzer ratherthan the sample during Fermi Surface mapping. (b) Highsymmetry points in the 2D Brillouin zone are labeled on aFermi surface map. (c) Fermi surfaces measured at 34 eVincident energy are shown for polarization along the the Γ-Mand Γ-X high symmetry directions. symmetry crystallographic directions. Our presentationof the data begins by focusing near the Γ-point, usingmeasured reflection symmetries to identify all three lowenergy bands predicted by LDA. We then trace their dis-persion to the M-point to map all low energy bands con-tributing to the Fermi surface. Other ARPES investi-gations focusing on the hole-doped iron arsenide Fermisurface (e.g. Ref. [6, 7]) have neglected to perform com-plete polarization-resolved band mapping, and have not
FIG. 2:
Band symmetries near the Γ point : (a) Measured polarization sym-metries are labeled on a diagram of theintertwined Fermi surface, and LDA or-bital symmetries are summarized in theinset. (b) Momentum dependence of theFermi surface along the ˆ z axis, usingsecond derivative images. (c-h) ARPEScuts measured through the 3D Brillouinzone center (K z ∼ o (even),90 o (odd) and at 45 o (mixed reflectionsymmetry) relative to the cut. (i) Elec-tronic correlation effects raise the G-XDirac node, beneath which the α and α Fermi surfaces are intertwined (Numer-ics from Ref. [15]). (j,k) Second deriva-tive images from panels (c,g) are overlaidwith (left) the experimental band struc-ture and (right) LDA dispersions fromRef. [7] linearly renormalized by a fac-tor of 0.63 and shifted up by 40 meV. experimentally traced the low energy bands along the en-tire Γ-M axis, therefor missing significant features.The optimally doped superconductingBa − x K x Fe As system was chosen for detailed in-vestigation due to the extremely high sample qualityavailable, as noted in other angle resolved photoemissionspectroscopy (ARPES) studies [7, 8, 9, 10, 11] anddocumented in detail in our previous work [8] using acombination of scanning tunneling microscopy ( ∼ A rmssurface roughness), magnetic susceptibility and ARPESmeasurements.Momentum space mapping was performed by orient-ing the high symmetry Γ-M or Γ-X crystallographic axisin parallel to incident photon polarization, and movingthe analyzer slit to detect ejected electrons with mo-menta covering a full two dimensional Brillouin zone(Fig-1(a,c)). Out of plane momentum is varied by tuningthe incident photon energy. The Brillouin zone mappingconvention is labeled in Fig-1(b), with the ˆ x axis (Γ-M) defined as the nearest neighbor iron-iron direction.The Fermi surface is composed of three hole-like pocketscentered on the Γ-point and a combination of hole- andelectron-like quasiparticle features at the M-point.Single crystals of Ba . K . Fe As (T C =37 K) weregrown using the self-flux method [12]. ARPES mea-surements were performed at the Advanced Light Sourcebeamline 10.0.1 using 34-51 eV photons with better than10-15 meV energy resolution, respectively, and overallangular resolution better than 1% of the Brillouin zone(BZ). Samples were cleaved and measured at tempera-tures below 15 K, in a vacuum maintained below 8 × − Torr.Momentum along the ˆ z axis is parameterized in unitsof 4 π /c, which has been observed to represent the fullperiodicity in studies of the electron doped compound BaFe − x Co x As . An inner potential of 15eV is usedto determine K z , consistent with the value used forBaFe − x Co x As [13]. The linear dimensions of Fermisurface contours, as estimated from Fig-2(b) and similardata near the M-point, increase by roughly 10% as mo-mentum is varied across the Brillouin zone along the ˆ z axis, suggesting that the ARPES signal is representativeof bulk electronic properties. The full two dimensionalLuttinger count ( F S areaBZ area ) varies from ∼
18% hole densityin the K z =4 rlu (Γ-point) plane to ∼
22% at the zoneboundary (K z =3.5 rlu), in agreement with nominal 20%hole doping.Measurements revealing band structure near the threedimensional Γ-point are shown in Fig-2(c-l). When po-larization is 45 o from the cut direction (e.g. E k ˆ x + ˆ y for K k ˆ x ) the mixed matrix element allows all threehole-like bands surrounding the Γ-point to be observedsimultaneously, however it is difficult to trace them. Cutsparallel or perpendicular to the photon polarization (Fig-2(c-d,f-g)) are observed to selectively suppress at leastone band, allowing the remaining bands to be clearlydistinguished. Second derivative images in Fig-2(j,k) areused to enhance contrast under geometries for which twobands are visible simultaneously. All bands along the Γ-X direction follow typical hole-like dispersions, howeverthe two outermost bands in the Γ-M cut fold upwardsas they approach the M-point. The outermost band hasa much weaker emission signal than the inner two, butis also less broad, allowing it to show up clearly in thesecond derivative images.Measured reflection symmetries at the Fermi surfaceare summarized in Fig-2(a). Under the scattering ge-ometry used, bands with odd mirror symmetry relativeto the momentum cut direction are probed when polar-ization is perpendicular to the cut, and even symmetry FIG. 3:
Band structure near M : (a) A symmetrized second derivative image of the Fermi surface is shown near K z =3.5rlu. (b) Second derivative images of the dispersion cuts labeled on panel (a) are shown with cartoons of the apparent bandstructure. (c) Two bands near the M-point along the Γ-M cut are only seen with parallel (even) polarization. (d) A diagramof the M-point Fermi surface is superimposed above data from panel (a). (e) ARPES Fermi surface maps are shown withpolarization (left) perpendicular and (right) parallel to the ˆ x axis. (f) The full experimentally derived Γ-M dispersion (belowE F , K z =3.5 rlu) of all low energy bands predicted by paramagnetic LDA is presented, with thick lines representing the oddsymmetry bands visible in cut-1(odd) and thin lines representing the even symmetry sections observed in cut-1(even). Thelocation of a proposed hybridization gap between the α and α bands is indicated in black. bands are observed when polarization is parallel to thecut. LDA predicts three hole-like bands with dominant3d xz /3d yz (mixed) and 3d xy orbital character near the Γ-point [14]. For a one-to-one identification of these bandswith our data, it is necessary to look at details of the re-flection symmetry along both high symmetry directions(Γ-M and Γ-X).Along the Γ-X direction, the reflection symmetryprobed by ARPES is also a symmetry of the crystal,meaning that measured bands must be fully symmetric orantisymmetric. The three bands predicted by LDA haveeven ( α , strong 3d xz +3d yz ), odd ( α , strong 3d xz -3d yz )and even ( α , strong 3d xy ) symmetry in this direction.Our data also show two even bands and one odd sym-metry band, meaning that the innermost, odd symmetryband can be identified with α from LDA.Along Γ-M, reflection symmetry is influenced by thecorrugated As lattice, allowing some mixing between 3dorbitals that have different reflection symmetries acrossthe Fe-Fe axis. According to LDA calculations, the α band has predominant 3d xz character (even), α is pre-dominantly composed of 3d yz (odd) and α of 3d xy (odd).The band dispersion that most closely matches LDA,with α dispersing downwards and α and α bendingupwards (see Fig-2(k)), also matches these d-orbital re-flection symmetries. Reconciling band structure alongthe Γ-M and Γ-X axes requires an intertwined Fermi sur-face, as drawn in Fig-2(a). A more detailed analysis ofmeasurements showing the intersection of α and α isincluded as online supplementary information. An in-tertwined Fermi surface topology can be achieved withselective renormalization (bending) of LDA bands, but not with the sort of global renormalization constant thathas been suggested in some recent literature [9, 16]. Newtheoretical investigations show that this bending may becaused by charge correlation effects [15], which raise theenergy of the α - α Dirac node (intersection) along theΓ-X axis, beneath which the band topology is intertwinedas we observe (Fig-2(i)).A second derivative image of the M-point Fermi sur-face (Fig-3(a,d)) resembles a baseball diamond with out-ermost dimensions closely matching the size of the out-ermost Γ-point Fermi surface ( α band). In the parallelcuts labeled α and α bands ap-proach one another closely between the Γ- and M- points.The point of closest proximity between the bands alongarbitrary momentum space cuts is generally well beneaththe Fermi level (as seen in cut-2), but approaches theFermi surface exactly along the Γ-M axis, at the loca-tions for which hole pockets are observed (cut-1(odd),-3). Rotating polarization to the ˆ x -axis (cut-1(even), evensymmetry) reveals the dispersion of two bands near theM-point, one of which is a large electron-like pocket, witha diameter along the Γ-M axis roughly two thirds aslarge as the ˆ x axis separation of the satellite hole pockets(.36 π /a vs. 0.52 π /a), and similar in size to the inner Γ-point Fermi surface. The location of the other band seenin cut-1(even) is appropriate to connect it with α .These observations conflict in several key ways withother experimentally motivated analyses of the bandstructure. Following the course of the α band along Γ-Mreveals that it does fold up to form the outer hole pockets(“propeller” pockets) around the M-point, in agreementwith a ( π ,0) reconstruction scenario [7], and strongly dis- α1 fitα2 fitα3 fitα1,α2α3 Γ M K y ( / a ) π D α π3 ( ,0) FoldingKx ( /a)π Polar Gap Map D (K) | FS G ap ( m e V ) D (a) FIG. 4:
Interband correlation and gap anisotropy. (a)The outermost Γ- and M-point Fermi surfaces are geometri-cally nested by a ( π ,0) wavevector. (b) Extensive measure-ments of the superconducting gap ∆( K ) from Ref. [11] arecompared with fit curves from a cos(K x ) × cos(K y ) model. Ar-rows mark points with ( π ,0) correlation to satellite hole pock-ets at the M-point. agreeing with the suggestion that what appear to be pro-peller pockets are an artifact of intensity from the α band [6]. However, our Fermi surface map in Fig-3(a,d)suggests that the inner edge of the propeller pockets is farremoved from the electron-like β band, a situation thatdoes not emerge from ( π ,0) reconstruction. The Fermisurface we have traced in Fig-3(d) includes more pocketsthan are expected in either picture.One scenario that may self-consistently explain theband maps from cuts α band is suggested to result from hybridization with α , rather than direct folding across a ( π ,0) wavevectorfrom the Γ-point as in Ref. [7]. Hybridization between α and α is not allowed by symmetry in paramagneticLDA models, but the relevant symmetry can be brokenby type-1 antiferromagnetic spin order, which is presentin the undoped compound [4] and may persist in localdomains of the superconducting crystal.Careful tracing of the Fermi surface reveals that thesystem is too strongly hole doped for there to be per-fect ( π ,0) nesting between hole- and electron-like Fermisurfaces. However, as shown in Fig-4(a), the outermost“propeller” hole pockets surrounding the M-point are ge-ometrically nested with the largest hole pocket surround-ing the Γ-point. Because both pockets come from the α band, there is no symmetry argument that would pre-vent superconducting pairing between their Fermi sur-faces. Nesting between two hole-like Fermi surfaces doesnot lead to strong spin-fluctuations, and is almost cer-tainly not the primary mechanism for superconductivity.Nonetheless, ( π ,0) spin fluctuations present for other rea-sons, such as exchange induced local spin interactions[17], could mediate a pairing interaction between thenested hole pockets and allow them to strengthen thesuperconducting ground state.Such interactions also provide a plausible answer to the long-standing puzzle of why the measured α supercon-ducting gap function is isotropic [8, 11]. In theoreticalmodels of phase shifting s-wave superconductivity, thesuperconducting order parameter is generally required todisappear midway between the Γ- and M-points, lead-ing to a reduction in the expected α gap size along theΓ-M axis. A theoretical prediction for the gap distri-bution based on the lowest order term in such models(cos(K x ) × cos(K y )) is drawn with solid lines on a polarplot in Fig-4(b).The isotropic gap observed in experiments could bestrengthened near (but not at) the nodal line by a ∼ ( π ,0)pairing interaction with the M-point hole pockets (Fig-4(a)). Unlike hole-electron nesting, interactions betweentwo hole-like Fermi surfaces are robust against hole dop-ing, and could play a role in stabilizing superconduc-tivity through the large part of the phase diagram inwhich overdoped superconductivity is found. ( T C > . < x ≤ π ,0) interband insta-bility of the M-point satellite hole pockets are character-istics that distinguish optimally doped superconductingBa − x K x Fe As from underdoped crystals.The results presented in this paper strongly emphasizethe need for more sophisticated first principles numericalmodeling that can comprehensively address short rangespin order and ARPES matrix elements. Our data showseveral features that are not present in typical paramag-netic LDA calculations, such as the intertwined Γ-pointFermi surface and hole pockets near the M-point appar-ently resulting from hybridization of the α and α bands.We note that interactions between spin and the latticedimensions are unusually strong for iron pnictides, andsymmetry breaking spin correlations in the pnictide planeare necessary to reconcile first principles theories withthe crystal structure and phonon spectrum [2]. With re-spect to experimental methodology, we emphasize thatdue to the distribution of matrix elements and the weakphotoemission intensity of some bands, a detailed, com-prehensive comparison with LDA is only possible if theband dispersions are separately traced. It is not suffi-cient to simply establish a correlation between the LDAdispersions and regions of intensity in the ARPES spec-trum.In summary, we present a polarization resolvedARPES study of the Fermi surface and band structurein optimally doped Ba − x K x Fe As . We observe the dis-persion of three hole-like Fermi sheets surrounding theΓ-Z axis and demonstrate that two of them intersect,providing the finely resolved Fermi surface topology inthat region of momentum space and emphasizing the im-portance of electronic correlation effects in shaping bandstructure near the Fermi level. Polarization-symmetrycharacterized mapping enriches this picture with respectto theoretical models, by revealing the momentum spacedistribution of band symmetries. 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