Importance of Fermi surface topology for high temperature superconductivity in electron-doped iron arsenic superconductors
Chang Liu, A. D. Palczewski, Takeshi Kondo, R. M. Fernandes, E. D. Mun, H. Hodovanets, A. N. Thaler, J. Schmalian, S. L. Bud'ko, P. C. Canfield, A. Kaminski
IImportance of Fermi surface topology for high temperature superconductivityin electron-doped iron arsenic superconductors
Chang Liu, A. D. Palczewski, Takeshi Kondo, R. M. Fernandes, E. D. Mun,H. Hodovanets, A. N. Thaler, J. Schmalian, S. L. Bud’ko, P. C. Canfield, and A. Kaminski
Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA (Dated: November 29, 2018)We used angle resolved photoemission spectroscopy and thermoelectric power to study the poorlyexplored, highly overdoped side of the phase diagram of Ba(Fe − x Co x ) As high temperature su-perconductor. Our data demonstrate that several Lifshitz transitions - topological changes of theFermi surface - occur for large x . T c starts to decrease with doping when the cylindrical, centralhole pocket changes to ellipsoids centering at the Z point, and goes to zero before these ellipsoidsdisappear around x = 0 .
2. Changes in thermoelectric power occur at similar x -values. Beyond thisdoping level the central pocket changes to electron-like and superconductivity does not exist. Ourobservations reveal the crucial importance of the underlying Fermiology in this class of materials.A necessary condition for superconductivity is the presence of the central hole pockets rather thanperfect nesting between central and corner pockets. PACS numbers: 79.60.-i, 74.25.Jb, 74.70.Dd
The phase diagrams of the newly-discovered iron ar-senic superconductors contain a number of intriguingfeatures. For the electron-doped A (Fe − x T x ) As series(122, A = Ca, Sr, Ba; T = Co, Ni, Pd, etc.), super-conductivity is found in both regions with and withouta long-range antiferromagnetic (AFM) order [1–7]. Thesuperconducting (SC) region extends to different dopinglevels for different dopants, but scales very well if the hor-izontal axis of the phase diagram was chosen to be thenumber of extra electrons [6, 7]. It is therefore likely thatchanges in the underlying electronic structure due to elec-tron doping are linked closely to their SC behavior. Onthe underdoped side, a recent angle-resolved photoemis-sion spectroscopy (ARPES) study on Ba(Fe − x Co x ) As [8] revealed that superconductivity emerges at a dop-ing level ( x on ) where a topological change of the Fermisurface (Lifshitz transition [9] at doping x ) reduces themagnetically reconstructed Fermi surface to its paramag-netic appearance, i.e. x (cid:39) x on . This transition exhibitsitself as a rapid change of Hall coefficient and thermo-electric power (TEP) in transport measurements [10]. Animmediate question is whether a similar change of Fermi-ology causes the collapse of the SC dome on the heavilyoverdoped regime. It is inevitable that the hole pocketssurrounding the central axis of the Brillouin zone (Γ- Z )will shrink in size and vanish at some higher doping x .The question is whether this Lifshitz transition correlateswith the offset of superconductivity on the overdopedside of the phase diagram ( x off ). Based on a solutionof the two-band BCS gap equations, assuming only in-terband coupling, Fernandes and Schmalian [12] showedthat the disappearance of superconductivity is directlylinked to the vanishing of the central hole pocket(s), i.e. x (cid:39) x off . Experimentally, the Hall coefficient vs. dopingon Ba(Fe − x Co x ) As [4] experiences a slight change ofslope around x off , hinting at a possible Lifshitz transition close to the high doping offset of superconductivity.In this Letter we study this issue in detail usingARPES and TEP measurements. We performed a com-plete survey of the electronic structure on the overdopedpart of the phase diagram of this material. This surveyreveals that topological changes of the Fermi surface linkdirectly to superconductivity in electron-doped pnictides.In the overdoped side, superconducting transition tem-perature T c starts to be suppressed around the dopinglevel ( x ) where the cylindrical hole pocket surround-ing the zone center (Γ- Z ) changes to ellipsoids centeringat Z . T c is driven to zero before the disappearance of k x [ p / a ] Exit slit
Z X k (1,-1,0) [ p / a ] -0.3-0.2-0.10.0 E n e r gy [ e V ] Z k x [ p / a ] k (1,-1,0) [ p / a ] k y [ p / a ( b )] x = 0.073 x = 0.42 k x [ p / a ] k (1,-1,0) [ p / a ] x = 0.166 FIG. 1: (Color online) Fermi maps and band dispersionaround the upper zone edge Z of Ba(Fe − x Co x ) As for x = 0 .
073 (optimal doping), x = 0 .
166 (edge of SC dome)and x = 0 .
42. Upper Row: Fermi mappings for the threedoping levels, taken with incident photon energy hν = 35 eVat temperature T = 20 K. Red arrows show the exit slit direc-tion of the hemispheric analyzer and the cutting direction ofthe band dispersion maps (Lower Row). The same directionis also used in Fig. 2. a r X i v : . [ c ond - m a t . s up r- c on ] N ov c -0.4 0.0 0.4 i x = 0.27 b x = 0.195 x = 0.166 -0.4 0.0 0.4-0.3-0.2-0.10.0 g x = 0.313 -0.4 0.0 0.4 e x = 0.37 -0.4 0.0 0.4 f x = 0.42 I n t e n s it y [ a r b . un it ] -0.3 -0.2 -0.1 0.0 Energy [eV] j x = 0.166 (180 K) x = 0.195 (180 K) x = 0.27 x = 0.313 x = 0.37 x = 0.42 k (1,-1,0) [ p / a ] E n e r gy [ e V ]
20 K180 K -0.4 0.0 0.4 d -0.3-0.2-0.10.0 Z a -0.4 0.0 0.4 h -0.10.0 E n e r gy [ e V ] k hole band top electron band bottom
35 eV ( Z ) -0.10.0 E n e r gy [ e V ] Co doping x l
49 eV ( G ) h n = 35 eV FIG. 2: (Color online) Band location analysis for the Lifshitz transitions. (a)-(i): Band dispersion maps along the directionshown in Fig. 1 for six different doping levels (top of each column) at low and high temperatures (left of each row). All data istaken with 35 eV photons. The high temperature data is divided by the resolution convoluted Fermi-Dirac function for betterpinpointing the band positions above the Fermi level. The red vertical line indicates that a Lifshitz transition happens between x = 0 .
195 and x = 0 .
27 at Z . (j) Energy distribution curves (EDCs) at Z for the doping levels in panels (a)-(i). Measurementtemperature is T = 20 K unless specifically mentioned in the graph. (k),(l): Evolution of binding energy for the top of thehole band and the bottom of the electron band with respect to cobalt doping. Data is extracted from ARPES intensity mapstaken with (k) 35 eV and (l) 49 eV photons, corresponding to k z values of Z and Γ points, respectively. Data points in (k) areextracted from the EDCs at (j) by fitting with two Lorentzian functions (times the Fermi function for low temperature data).Raw data for extracting panel (l) is not shown. Z -ellipsoids and the change in TEP at x Z ∼ .
2. Inshort, we find that x < x off < x Z . Our data demon-strated that superconductivity in the pnictides is veryrobust with respect to doping; the whole Γ Fermi sheethas to be almost completely eliminated in order to drive T c to zero. A necessary condition for superconductivitythen is the existence of the central hole pockets ratherthan a perfect nesting between the Γ and X pockets [11].The dominant contribution to the pairing interaction isbelieved to come from inter-band coupling [12].Single crystals of Ba(Fe − x Co x ) As were grown outof a self-flux using conventional high-temperature solu-tion growth techniques [1]. The doping level x was de-termined using wavelength dispersive X-ray spectroscopyin a JEOL JXA-8200 electron microprobe [1]. Longrange antiferromagnetism was observed below a transi-tion temperature T N ( x ) up to x ∼ .
06. Superconduc-tivity appears around x on = 0 .
038 and vanishes between0 . < x off ≤ .
166 (see Fig. 4) [7]. The ARPES mea-surements were performed at beamline 10.0.1 of the Ad-vanced Light Source (ALS), Berkeley, California usinga Scienta R4000 electron analyzer. Vacuum conditionswere better than 3 × − torr. The energy resolutionwas set at ∼
25 meV. All samples were cleaved in situ yielding mirror-like, fresh a - b surfaces. High symmetrypoints were defined the same way as in Ref. [8]. TEPmeasurements were made as described in Ref. [10]. Fig. 1 shows the ARPES Fermi maps and correspond-ing band dispersion data for three different doping levelsof Ba(Fe − x Co x ) As [13]. The incident photon energyis hν = 35 eV, corresponding to k z (cid:39) π/c , the upperedge of the first Brillouin zone ( Z ) [14]. From data inFig. 1 it is clear that, as electron doping initially in-creases, the Fermi contours around Z shrink in size. At x = 0 . Z -pocket shrinksto almost a single point, meaning a complete vanishing ofthe hole pocket. This observation is consistent with thedata in Refs. [8, 15, 16]. As x increases, the Z pocketexpends again, yielding a diamond shape at x = 0 . X pocket, on theother hand, keeps expanding from x = 0 .
073 to x = 0 . Z -pocket undergoes a drastic topolog-ical change from hole-like to electron-like at roughly thedoping level where superconductivity vanishes. Based onthis observation we perform two independent data analy-sis procedures with finer doping steps to further pinpointthe doping level at which the Lifshitz transition takesplace.First, to obtain a more accurate value for x , we ex-tract the energies for the hole band top and the electronband bottom at the zone center, and examine them as Z po c k e t a r ea [ p / a ] Co doping x SC non SC hole pocket electron pocket -0.4-0.20.00.20.4 k y [ p / a ( b )] -0.4 -0.2 0.0 0.2 k x [ p / a ] hole pocket -0.4 -0.2 0.0 0.2 0.4 k x [ p / a ] electronpocket k y [ p / a ( b )] x = 0.073 x = 0.166 x = 0.195 x = 0.27 x = 0.313 x = 0.37 x = 0.42 Z C o dop i ng x k x [ p / a ] x ~ 0.2 ab c FIG. 3: (Color online) Pocket size analysis for the Lifshitztransition at upper zone boundary Z . (a) Z pocket extrac-tion for seven doping levels, done by fitting the momentumdistribution curves (MDCs) at the chemical potential withseveral Lorenzian functions. Positions of hollow circles aresymmetrized from experimental data points (solid circles),proposing the band positions where ARPES intensity is sup-pressed by the transition matrix element. (b) Evolution of Z pocket area with cobalt doping. Green shaded area indicatesthe boundary of the SC dome. (c) Visualization of the Lifshitztransition. Data in (a) is plotted against the cobalt doping x as a third dimension. Shaded areas are approximate sizeand shape of the pockets. Panels (b) and (c) show a Lifshitztransition at x Z ∼ . a function of cobalt doping. As shown in Fig. 2, weplot the band dispersion maps along the same directionas in Fig. 1 for six different doping levels ranging from x = 0 .
166 to x = 0 .
42, and use the energy distributioncurves (EDCs) in Fig. 2(j) [17] to see that both the holeband and the electron band shift to higher binding en-ergies as x increases. The shape of these bands remainthe same during the process. There is a small gap ( ∼ . < x < . E F . Figs. 2(a)-(k) illustrate that, at the Z point of theBrillouin zone, the Lifshitz transition takes place between0 . < x Z < .
27, higher than x off ∼ . x values for different k z . In Fig. 2(l) we investigate this effect by performingthe same analysis to the data taken with 49 eV photons(raw data not shown). This incident photon energy cor- responds to k z (cid:39)
0, the central point of the Brillouin zone(Γ). We see that indeed the Lifshitz transition shifts toa lower doping, i.e. x ∼ .
11. We note that this isthe doping level where T c starts to decrease in the phasediagram. This observation also supports the theoreticalprediction that three dimensionality of the Fermi surfaceleads to a more gradual decrease of T c in the overdopedside [12].In Fig. 3 we perform a pocket size analysis at Z tofurther pinpoint x . This second procedure is indepen-dent from the above energy extraction method. To dothis we first find the Z pocket location for seven dopinglevels (ranging from x = 0 .
073 to x = 0 .
42) by fitting themomentum distribution curves (MDCs) at the chemicalpotential with several Lorenzian functions. From Fig.3(a) we see a clear evolution of the Z pocket size withdoping. As x increases, the hole pocket shrinks in sizeup to x = 0 . x = 0 .
2. This Lifshitz transitionis best visualized in Fig. 3(c) where data in Fig. 3(a)is plotted against the cobalt doping x as a third dimen-sion. This figure reveals that, as cobalt concentrationincreases, the Fermi sea level rises and the Z hole bandsgradually drop below it. At x ∼ . Z pocket changes to electron-like,and superconductivity vanishes.Fig. 4 summarizes our systematic ARPES surveyon the Fermi surface topology of Ba(Fe − x Co x ) As for0 ≤ x ≤ .
42 and compares it with TEP data over thesame doping range. The most important finding of thisstudy is that the low- and high-doping onset of the SCregion link closely to topological changes of the Fermisurface. The first Lifshitz transition at the low dopingonset of superconductivity is described in detail in Ref.[8, 10]. The second and third Lifshitz transitions occurfor 0 . (cid:46) x (cid:46) . x (cid:39) .
11 corresponds tothe doping level where the shape of the quasi-cylindricalouter Γ contour changes to an ellipsoid centering at Z .Also at x (cid:39) .
11 the superconducting T c starts to sup-press. As doping is increased, this Z ellipsoid shrinks insize until it disappear altogether at x Z (cid:39) .
2. On theother hand, superconductivity vanishes at x off (cid:39) . x > .
2, the region of the highest doping, the centralpocket changes to electron-like, and superconductivitydoes not exist. Our TEP data, plotted as S ( x ) | T =const forseveral temperatures in Fig. 4(b), show clear step-like orchange-of-slope anomalies at Co-concentrations that arein an excellent agreement with those at which the theLifshitz transitions were detected by ARPES [Fig. 4(a)]. T e m p e r a t u r e [ K ] SC Ba(Fe x Co x ) As x x G x x -50-40-30-20-100 T h e r m o e l ec t r i c po w e r [ m V / K ] Co doping x Hole pocket Electron pocket T N T c by resistivity TEP at 25 K TEP at 50 K TEP at 150 K TEP at 200 K Lifshitz transition (a)(b) X X G, Z X Z
G G
XZ ZZ ZZ Z a-b a-c a-b a-c a-ba-b
FIG. 4: (Color online) (a) location of the known Lifshitz tran-sitions in the phase diagram. T N and T c data is taken fromRefs. [1] and [8]. Top insets show schematic Fermi surfacetopology in the a - b and a - c plane for each region in the phasediagram. (b) Thermoelectric power vs. doping for four dif-ferent temperatures. These results, taken together, confirm extreme sensitivityof TEP to the changes in FS topology [21].Importantly, the above conclusion most likely also ap-plies to other electron doped 122 systems. We are spe-cially interested in A (Fe − x Ni x ) As where each nickelatom gives two extra electrons per Fe site compared toone in the cobalt doped system [7]. There, similar tothe cobalt doped system, the Hall coefficient and ther-moelectric power anomaly occurs right at the onset ofsuperconductivity [8, 22]. Based on a similar ARPESsurvey [23] we indeed find Lifshitz transitions at closevicinity to the boundaries of superconductivity, the onlydifference being that the corresponding doping levels areroughly one half as those of the cobalt system. As thephase diagram changes to T vs. e , the extra electroncount, these two systems match perfectly.Our findings have important implications on the na-ture of superconductivity of the pnictides. First, ourobservation reveals the crucial importance of the under-lying Fermi surface topology: a necessary condition forthe emergence of superconductivity is the existence of the non-reconstructed central hole pockets rather thana perfect nesting condition between the central and cor-ner pockets. Superconductivity is not supported onlywhen either one set of these pockets (central or cor-ner) vanishes, changes its carrier nature or shows con-siderable reconstruction. Second, our results imply thatthe suppression of superconductivity on the underdopedside is related to the competition between the AFM andSC phases [7], whereas on the overdoped side the dis-appearance of the central hole pocket plays a more im-portant role than the decrease of the pairing interactionmagnitude [12]. Electron doped 122 systems are, there-fore, clear examples of high temperature superconductorswhose superconducting behavior is controlled primarilyby the underlying Fermiology.We thank Sung-Kwan Mo and Makoto Hashimoto fortheir grateful instrumental support at the ALS. AmesLaboratory was supported by the Department of Energy- Basic Energy Sciences under Contract No. DE-AC02-07CH11358. ALS is operated by the US DOE under Con-tract No. DE-AC03-76SF00098. [1] N. Ni et al. , Phys. Rev. B , 214515 (2008).[2] J.-H. Chu, J. G. Analytis, C. Kucharczyk, and I. R.Fisher, Phys. Rev. B , 014506 (2009).[3] F. L. Ning et al. , J. Phys. Soc. Jpn. , 013711 (2009).[4] L. Fang et al. , Phys. Rev. B , 140508(R) (2009).[5] S. Nandi et al. , Phys. Rev. Lett. , 057006 (2010).[6] P. C. Canfield et al. , Phys. Rev. B , 060501(R) (2009).[7] P. C. Canfield and S. L. Bud’ko, Annu. Rev. Condens.Matter Phys. :11.1-11.24 (2010).[8] C. Liu et al. , Nature Physics , 419 (2010).[9] I. M. Lifshitz, Sov. Phys. JETP , 1130 (1960).[10] E. D. Mun, S. L. Bud’ko, N. Ni, and P. C. Canfield, Phys.Rev. B , 054517 (2009).[11] K. Terashima et al. , Proc. Natl. Acad. Sci. USA ,7330 (2009).[12] R. M. Fernandes and J. Schmalian, Phys. Rev. B ,014521 (2010).[13] Direction of the band dispersion maps is perpendicularto the exit-slit because the ARPES intensity of the Z electron pocket along the exit-slit direction is suppressedby the transition matrix element.[14] T. Kondo et al. , Phys. Rev. B , 060507(R) (2010).[15] Y. Sekiba et al. , New J. Phys. , 025020 (2009).[16] V. Brouet et al. , Phys. Rev. B , 165115 (2009).[17] In Fig. 2(j) high temperature data divided by the Fermifunction is used for x = 0 .
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