Main

Previous studies demonstrated that the presence of the long-range AFM order leads to a substantial reconstruction of the Fermi surface at low temperature in the undoped pnictides8,9,10,11,12,13,14, as well as in the hole-doped Ba1−xKxFe2As2 system15. Here we report a systematic study of electron-doping effects on the reconstructed Fermi-surface sheets and relate it to the emergence of superconductivity. In Fig. 1a,b we present the Fermi-surface maps of Ba(Fe1−xCox)2As2 at T=20 K for two extreme doping levels: x=0 where AFM order is present and x=0.114 where it is fully suppressed by cobalt doping. In the undoped samples the X-pocket Fermi surface looks like four flower petals—high-intensity peaks are visible along the diagonal k(110) and directions. For x=0.114 samples, the X-pocket Fermi surface changes to an oval shape and the peaks along the k(110) direction are absent. In Fig. 1c–j we point out the magnetic origin of this Fermi-surface reconstruction by comparing the X-pocket details to the prediction of a model calculation. We use a five-band tight-binding model (see Supplementary Information) with and without an AFM order. The presence of the AFM order is measured by mean-field order parameters ΔAF and Δ′ that represent intra-orbital and inter-orbital magnetic interactions, respectively, and lead to opening of gaps in the AFM state. The observed Lifshitz transition (detailed later) occurs only as a consequence of Δ′ and is evidence for the importance of inter-orbital magnetic interactions, which were argued to be essential for spin-fluctuation-induced superconductivity16. The comparison shown in Fig. 1 clearly demonstrates that the observed Fermi-surface reconstruction is consistent with the effects of a long-range AFM order and inter-orbital coupling on the electronic structure. In the undoped sample with AFM order, the four Fermi peaks that make up the ‘flower petals’ appear in both the experimental data and the theoretical calculation, and they are hole-like— increasing the binding energy results in a larger size of the petals in the constant-energy cuts. In the overdoped paramagnetic state, however, these petals are absent in both the experiment and theory. The main X-pocket is electron-like—increasing the binding energy results in smaller pockets. We will use these features to study the effects of doping on the Fermi surface and its relation to superconductivity in electron-doped pnictides.

Figure 1: The Fermi-surface reconstruction and its magnetic origin.
figure 1

a,b, Fermi-surface mappings of Ba(Fe1−xCox)2As2—intensity of the photoelectrons integrated over 10 meV about the chemical potential. Data are taken with 105-eV photons in the AFM (x=0) and paramagnetic (x=0.114) phases at T=20 K. The bright areas indicate higher intensity. The orange arrows in a emphasize the Fermi peaks along the k(110) direction. c–f, Expanded ARPES intensity plots in the vicinity of the X-points for two different binding energies indicated at the top of each graph. g–j, Results of a five-band tight-binding model calculation for the same binding energies. ΔAF is a measure of the AFM order parameter; Δ′ is a measure of the inter-orbital coupling strength.

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In Fig. 2 we plot the angle-resolved photoemission spectroscopy (ARPES) Fermi-surface maps at T=13 and 150 K for several different cobalt doping levels obtained with a photon energy of 21.2 eV (He–I line). It is clear that the reconstructed hole pockets are present for x<0.034 at low temperatures and vanish at T=150 K, above the magnetic transition temperature T*. It is worth noting that the temperature dependence of the Fermi surface is not due to thermal broadening, because the low- and high-temperature data for higher doping levels are very similar. The first and most important observation in Fig. 2 is that the small hole-like pockets vanish from the Fermi level rather rapidly at intermediate doping levels. At low temperature the intensity of those petals starts to decrease at a doping level of x=0.024, and effectively the intensity has vanished by x=0.038. This is due to the fact that the top of the hole bands moves below the Fermi energy, which is a classic signature of a Lifshitz transition7 (see Fig. 3c), and it coincides with the emergence of superconductivity in the phase diagram. ARPES data consistent with this picture are also taken with a linear polarized synchrotron beam (see Supplementary Information). In Fig. 2b we quantify this transition by plotting the maximum intensity around the X-pocket Fermi surface (from panels in Fig. 2a) as a function of the angle (α) with respect to the k(110) direction. With hole pockets present (0<x<0.024) there is a strong peak at α=0∘. This peak decreases as x changes from 0.024 to 0.034 and vanishes by x=0.038. Beyond this doping these small hole pockets are absent. Neutron scattering experiments5,17 clearly demonstrate that long-range AFM order coexists and competes with superconductivity beyond x=0.04, and probably extends up to x∼0.06. Indeed, in ARPES data the reconstruction of the electronic structure is observed up to x=0.058, but only at higher binding energies (see Supplementary Information). As the doping increases beyond x∼0.03, the small hole pockets disappear and superconductivity can take place even in the AFM state.

Figure 2: The vanishing of the marked Fermi-surface reconstruction coincides with the onset of superconductivity.
figure 2

a, Fermi-surface mappings of Ba(Fe1−xCox)2As2 for temperatures T=13 and 150 K measured at various cobalt doping levels. The incident photon energy is 21.2 eV. (Note: the image slice is rotated by 45∘ with respect to Fig. 1.) b, Maximum intensity of electrons around the X-pocket for the low-temperature data, shown as a function of an angle α defined in the inset. The intensities are normalized at α=90∘ and symmetrized with respect to α=0∘. c, Γ- and X-pocket location of the low-temperature data extracted through the peak position of the momentum distribution curves for 0.038≤x≤0.114. The X-pocket is shifted to the Γ-pocket by rescaling the k(110) axis through for easier comparison of their areas.

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Figure 3: Summary.
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a, Left axis: the a–b-plane Hall coefficient RH≡ρH/H versus x of Ba(Fe1−xCox)2As2 with magnetic field H=90 kOe∥c, T=25 and 150 K (ref. 19). Right axis: ARPES intensity IARPES at α=0∘ extracted from both helium lamp and synchrotron data, minus IARPES at x=0.114. b, Schematic phase diagram of Ba(Fe1−xCox)2As2 based on ARPES and transport measurements 19. Both the magnetic transition temperature T* and the onset temperature of superconductivity are determined by resistivity measurements. c, Schematic band dispersion for three different doping levels at the vicinity of the X-point. In the AFM state (0<x<0.058) the electron bands and hole bands fold back onto each other, and hybridize because of the existence of inter-band coupling. The Lifshitz transition takes place when the tip of a hybridized band sinks below the Fermi level because of increasing electron occupation.

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In Fig. 2c we focus on the doping evolution of the nesting condition by examining the contours of the X- and Γ-pocket Fermi-surface sheets in the doping region where the petals are absent. For 0.038<x<0.073, both pockets are roughly similar in shape and size, indicating reasonably good nesting conditions. For x=0.114, however, the X-pocket is significantly larger than the Γ-pocket, yet the sample is still superconducting (TC=12.8 K). Thus, superconductivity can exist in these materials even in the absence of perfect nesting, in contrast to what was previously suggested18.

Our ARPES results explain the marked changes with doping reported from Hall effect and thermoelectric power (TEP) measurements19,20,21. In Fig. 3a we plot the Hall coefficient RH as a function of doping at T=25 and 150 K (ref. 19) measured on samples from the same batch as those used for the ARPES measurements. We compare this with the maximum ARPES intensity of the reconstructed Fermi surface at the chemical potential (defined in the caption) for the data from both the helium lamp and the synchrotron, which is a way to quantify the changes in the Fermi-surface topology. The two ARPES data sets are qualitatively consistent with each other. From the helium lamp data, one can observe that not only does the change in the above-defined ARPES intensity correlate with the marked increase in the Hall coefficient, it also coincides with the onset of superconductivity at 0.024<x<0.028. In a similar manner to the Hall coefficient, the TEP (ref. 19) (not shown) changes abruptly with doping between x=0.02 and x=0.024 (right at the onset of the changes in the Hall coefficient) for a surprisingly wide range of temperatures (25 K<T<300 K). This implies that TEP is much more sensitive to the underlying electronic properties. The Hall effect and TEP measurements together set a finer range for the Lifshitz transition as they reflect the effects of the electronic structure on the macroscopic physical properties of the sample. It is also noteworthy that other electron-doped 122 systems show essentially the same phase diagram as that of the cobalt-doped samples22,23 and similar changes in Hall coefficient and TEP are also observed (for Cu-doped BaFe2As2(ref. 22) and for Ni-doped SrFe2As2 where the onset of the Hall coefficient and TEP anomaly also occurs right at the onset of superconductivity23). This suggests that the Lifshitz transition reported here is a general property for the electron-doped 122 systems. It is not clear whether or not this conclusion can be extrapolated to the hole-doped side of the phase diagram. On one hand, assuming a simple rigid band shift, one would expect the petals to be present in the hole-doped 122 system and indeed they were observed by ARPES in Ba1−xKxFe2As2 (refs 15, 24). On the other hand, the situation in Ba1−xKxFe2As2 is significantly complicated by spatial inhomogeneity24 and evidence from local probes (for example, nuclear magnetic resonance) suggests that AFM and superconductivity are microscopically separated25,26. In this case the impact of down folding on the superconducting state is not an issue and superconductivity is suppressed at low hole doping by the emergence of a first-order phase boundary between the two states27. The question of why superconductivity is compatible with the petals in the hole-doping regime is an important one and requires further detailed experimental investigation.

We summarize our main findings in Fig. 3b, where we plot the locations of each ARPES spectrum on the x–T phase diagram. Figure 3b shows that the emergence of superconductivity in Ba(Fe1−xCox)2As2 coincides with the disappearance of the reconstructed pieces of the Fermi surface. Our observation explains that the changes in Hall coefficient, namely the rapid increase of RH, are caused by rapid changes of the Fermi-surface topology with doping. As shown in Fig. 3c, a Lifshitz transition takes place close to the emergence of superconductivity, when the hybridized petal-like hole pockets fill up because of an increase in electron occupation. Long-range magnetic order has a particularly strong impact on the pairing interaction in the case of unconventional superconductivity because of magnetic fluctuations. The pairing interaction resulting from spin fluctuations on the reconstructed Fermi surface is reduced because of the requirement that the quasiparticle-induced spin wave damping vanishes at the ordering vector28. In the context of the pnictides, this effect leads to the reduced pairing interaction of the magnetically ordered state because the modified wavefunctions in the magnetically ordered state couple less efficiently to magnetic fluctuations29. This effect is strongest for large magnetization with pronounced down folding and demonstrates the sensitivity of an electronic pairing mechanism with respect to an AFM Fermi-surface reconstruction. The finding of the present letter demonstrates that avoiding the Fermi-surface reconstruction may be the key to establishing the superconductivity in electron-doped iron arsenic high-temperature superconductors.

Methods

Single crystals of Ba(Fe1−xCox)2As2 were grown by self-flux using conventional high-temperature solution growth techniques. The doping level x for each sample batch was determined using wavelength dispersive X-ray spectroscopy in a JEOL JXA-8200 electron microprobe; the doping inhomogeneity is kept as low as Δ x/x<7% (ref. 3). Transport and magnetization measurements report a tetragonal to orthorhombic structural transition with a paramagnetic to AFM transition at TS≈T*≈135 K for the undoped (x=0) samples. Increasing the doping significantly suppresses and splits the two transition temperatures3,4,5; superconductivity appears around x∼0.025 and a maximum onset TC of ∼24 K was observed for the x=0.058 samples3. The ARPES measurements were carried out at a laboratory-based ARPES system consisting of a Scienta SES2002 electron analyser, GammaData ultraviolet lamp and custom-designed refocusing optics at Ames Laboratory, as well as beamline 7.0.1 of the Advanced Light Source (ALS), Berkeley, California with a Scienta R4000 electron analyser. Vacuum conditions were better than 3×10−11 torr. The energy resolution was set at ∼25 meV for Fig. 1 and ∼9 meV for Fig. 2. All samples were cleaved in situ yielding mirror-like, clean a–b surfaces. Cleaved surfaces of all samples were stable for at least 24 h. Results were reproduced at the ALS beamline 7.0.1 as well as Ames Laboratory on several samples. The high symmetry point X is defined to be (±π/a,±π/a(b),0) with the kx and ky axes along the Fe–As bonds.