Antiferroic electronic structure in the nonmagnetic superconducting state of the iron-based superconductors.

A major problem in the field of high-transition temperature (Tc) superconductivity is the identification of the electronic instabilities near superconductivity. It is known that the iron-based superconductors exhibit antiferromagnetic order, which competes with the superconductivity. However, in the nonmagnetic state, there are many aspects of the electronic instabilities that remain unclarified, as represented by the orbital instability and several in-plane anisotropic physical properties. We report a new aspect of the electronic state of the optimally doped iron-based superconductors by using high-energy resolution angle-resolved photoemission spectroscopy. We find spectral evidence for the folded electronic structure suggestive of an antiferroic electronic instability, coexisting with the superconductivity in the nonmagnetic state of Ba1-x K x Fe2As2. We further establish a phase diagram showing that the antiferroic electronic structure persists in a large portion of the nonmagnetic phase covering the superconducting dome. These results motivate consideration of a key unknown electronic instability, which is necessary for the achievement of high-Tc superconductivity in the iron-based superconductors.

INTRODUCTION

One of the most intriguing properties of the iron-based superconductors (IBSCs) () is the high-transition temperature (Tc) superconductivity in balance with the multiple instabilities in lattice, spin, and orbital degrees of freedom. To understand the origin of high Tc, it is important to elucidate the nature of these electronic instabilities and their relations to the superconductivity. As represented by the phase diagram of Ba1−KFe2As2 (BaK122) in Fig. 1A (), most of the parent IBSCs exhibit the stripe-type antiferromagnetic (AFM) order at TN (, ). A tetragonal-to-orthorhombic structural transition occurs just at or slightly above TN (Ts). It accompanies a spontaneous difference in the occupation of Fe 3d and 3d orbitals being much larger than that expected from the orthorhombicity (–), namely, the ferro-orbital order (–). The structural transition has been suggested to be a nematic order (, ) driven by fluctuating antiferromagnetism (–) and/or orbital ordering (–).

Fig. 1

Temperature-dependent ARPES around X point for Ba0.59K0.41Fe2As2.

(A) Phase diagram of BaK122 (). TN and Ts are nearly equivalent in this system. (B) FSs of OP BaK122 obtained at 40 K with the photons of hν = 21.2 eV. (C) Schematic of (B). (D) E-k image divided by the Fermi-Dirac function taken at 40 K along cut 1 in (C). (E) Peak positions of the EDCs (filled diamonds) and momentum distribution curves (MDCs) (open diamonds) in (D). (F and G) The same as (D) and (E), but obtained at 15 K. (H) T dependence of the peak plots around X point from 15 to 90 K. (I) Schematic of (H). Δe and Ebot represent the SC gap magnitude of the electron band and energy level of the band bottom, respectively. (J and K) T dependence of the EDCs divided by the Fermi-Dirac functions at X point and kF of the electron band (k = 0.06 Å−1), respectively.

Whereas these orders are suppressed by carrier doping, many indications of electronic instabilities have been found in the normal state of IBSCs. Twofold symmetric physical properties were observed above TN/Ts in the underdoped regime, as represented by in-plane electronic resistivity () for Ba(Fe1−Co)2As2 (FeCo122) and magnetic torque measurements () for BaFe2(As1−P)2. AFM fluctuations and nematic fluctuations were reported to extend over the whole superconducting (SC) dome of BaK122 by the neutron magnetic resonance (NMR) () and shear modulus measurements (), respectively. In addition, the ferro-orbital order/fluctuation detected by x-ray linear dichroism measurement was found to persist in the optimally doped (OP) regime of FeCo122 (). These observations indicate that superconductivity in IBSCs, especially the 122 system, is subject to the influence of multiple electronic instabilities. However, the normal-state electronic structure in the OP regime has been reported to exhibit the tetragonal symmetry without any sign of electronic instability. Here, we report the spectral evidence for the antiferroic electronic structure in the normal state of the OP BaK122. Previous angle-resolved photoemission spectroscopy (ARPES) measurements on BaK122 mainly focused on the SC gap distribution in the multiorbital Fermi surfaces (FSs) (–). Here, we systematically investigate fine electronic structures at both the Brillouin zone (BZ) center (Γ) and corner (X) of the BaK122 system by using high–energy resolution ARPES. Across the SC transition of the OP sample, we observe a drastic change in the electron band at X point, together with the evolution of an unusual intensity distribution around Γ point. Striking resemblances in E, k, and T dependences between these two electronic features suggest that the latter is a replica of the former. We establish the x-T phase diagram (0.18 ≤ x ≤ 0.69 and 5 K ≤ T ≤ 200 K) showing that this antiferroic electronic instability persists in a large portion of the nonmagnetic phase covering the SC dome.

RESULTS

Electronic structure around X point

Figure 1B shows the FSs of OP BaK122 obtained in the normal state (T = 40 K). The schematic in Fig. 1C shows two hole pockets centered at Γ point and a small electron pocket with flower-like hole pockets around X point (section S1), as similarly reported in a previous ARPES study (). Here, we start with a description of the electronic structure around X point for the OP x = 0.41. As indicated in the E-k images along the momentum cut 1 (Fig. 1C) divided by the Fermi-Dirac function (Fig. 1, D and F), the electron band at X point shows a drastic change in its shape across Tc (36 K). Above Tc, the bottom of the parabolic electron band locates at a binding energy of ~8 meV. The shallow electron band is consistent with the rigid band picture, which predicts the band shift of ~40 meV toward lower binding energy with respect to the parent Ba122 (). As indicated by the peak positions of the energy distribution curves (EDCs) in Fig. 1 (E, G, and H) (section S2), the electron band becomes anomalously flat in the SC state. This result is understood by considering the SC gap (Δe) formation at the Fermi momentum (kF) with an energy scale comparable to that of the electron band bottom (Ebot), as depicted in Fig. 1I. The condition of Δe ≈ Ebot can be regarded as a SC state in the Bardeen-Cooper-Schrieffer (BCS)–Bose-Einstein condensation crossover regime where the Fermi energy and SC gap magnitude are comparable, as has been discussed in the FeSe family (–). In the Ba122 family, this circumstance is realized only in the hole-doped system because Ebot for the parent Ba122 (~50 meV) is much larger than Δe of any ion-substituted Ba122 ().

In addition to the drastic change of the band shape, we observed the shift of Ebot to the higher binding energy below Tc. For the quantitative analysis, we show the EDCs at X point in Fig. 1J. The peaks of the EDCs, representing the electrons at the band bottom, are remarkably enhanced below Tc and simultaneously shift toward higher binding energy by ~6 meV. On the other hand, the EDCs at the kF of the electron band exhibit finite SC gap formation below Tc (Fig. 1K). The characteristic shift in the band bottom seems to occur when Δe becomes comparable to Ebot with decreasing T (Fig. 1I), which implies that the superconductivity modifies the band structure.

Electronic structure around Γ point

Next, we performed detailed T-dependent ARPES at Γ point by using laser-ARPES (, ) along the momentum cut 2 in Fig. 1C. In the normal state, we observed an inner hole band around Γ point crossing the EF in the E-k image (Fig. 2, A and E). To clearly see the T dependence, we show the EDCs at the kF of the inner hole band in Fig. 2I (along the dashed lines in Fig. 2, A to D) and those divided by the Fermi-Dirac function and further normalized by that at 60 K in Fig. 2J. As T decreased, we observed the evolution of a peak and a gap structure near EF below Tc. The counterparts of the peak in the unoccupied state (Fig. 2, I and J) and its T dependence characterized by the BCS curve (Fig. 2K) suggest that these spectral features represent the SC gap formation in the inner hole band (Δh ≤ 5 meV). We further observed a flat intensity distribution appearing at Eflat = ~10 meV around Γ point (Fig. 2, A to D), as similarly observed in previous ARPES studies (–, ). We note that the flat feature cannot be explained by the first-principles band calculations assuming the paramagnetic state and tetragonal lattice (). Peak plots obtained from EDCs and MDCs in Fig. 2 (E to H) exhibit the evolution of the SC gap and flat feature across Tc (section S3). In addition to the SC peaks, the EDCs in Fig. 2I exhibit a sharp peak at Eflat. Note that the flat feature becomes apparent below Tc and exhibits an energy shift toward higher binding energy with decreasing T, as shown by the red markers in Fig. 2J (section S4). Because the flat feature responds to the onset of the superconductivity, it should reflect the bulk electronic properties of OP BaK122.

Fig. 2

Temperature-dependent ARPES around Γ point for Ba0.59K0.41Fe2As2.

(A to D) T dependence of E-k images divided by the Fermi-Dirac functions obtained by laser-ARPES (hν = 6.994 eV) along cut 2 in Fig. 1C. (E to H) Peak plots obtained from EDCs (filled circles) and MDCs (open circles) in (A) to (D). Gray curves are guides to the eye. Δh and Eflat represent the SC gap magnitude of the inner hole band and the energy level of the flat intensity distribution at kF, respectively. (I) T dependence of the EDCs at kF of inner hole band. (J) The EDCs in (I) divided by the Fermi-Dirac functions and further normalized by that at 60 K. The data set shown in (I) and (J) was taken from Shimojima et al. (). (K) T dependences in the energy levels of Δh, Δe, Ebot, and Eflat. Black solid curves represent the BCS curves for hole and electron bands.

Temperature dependences of the electronic features in Γ and X points

Here, we compare the energy levels of Δh, Δe, Ebot, and Eflat in Fig. 2K. In the SC state, both Δh and Δe follow the BCS-like T dependence, as indicated by the black solid curves. Ebot exhibits the energy shift comparable to that of Δe, resulting in the flat electron band at X point below Tc. We further found that the energy shift in Eflat is also in good agreement with those of Δe and Ebot, suggesting that the unidentifiable flat feature around Γ point has a close relation to the electronic structure around X point. Because the flat feature around Γ point shows a striking resemblance to the flat electron band at X point in its k, E, and T dependences, we here assign the former as a replica of the latter (section S5). This replica indicates the antiferroic band folding between Γ and X points, characterized by the same wave vector as the AFM order in the parent Ba122 [denoted as (π,π) folding in Fig. 3A] ().

Fig. 3

Schematic of the (π,π) folding.

(A) Schematic of the (π,π) folding in the BZ for x = 0.41. Folded FSs are indicated in light colors. k and k represent the momentum axes with the tetragonal settings. (B) Simplified schematic of the hole and electron bands above Tc for x = 0.41. (C) The same as (B) but far below Tc. Δe and Δh represent the SC gaps of the electron and hole bands, respectively. (D) The same as (C) but in the presence of the (π,π) folding.

We summarize our observations in the simplified schematic images. According to the E-k images in Figs. 1D and 2A, the electronic structure in the normal state can be depicted by a hole band and an electron band in Fig. 3B. Far below Tc, the SC gaps were observed in both hole and electron bands with Δh = 5 meV and Δe = 14 meV, respectively (Fig. 3C). In the presence of the (π,π) folding, the electron band at X point will be overlapped with the hole band at Γ point (Fig. 3D), which should correspond to the appearance of the flat feature around Γ point in the present ARPES data. This picture is consistent with two main observations in the present study for OP BaK122 as follows. First, the flat feature around Γ point becomes clearly visible below Tc. Assuming the (π,π) folding, this can be attributed to the coherence of the electrons around X point being significantly enhanced by the onset of the superconductivity, as observed in the development of the EDC peaks in Fig. 1 (J and K). Second, the shift of Eflat (~6 meV) was observed just below Tc. This might be caused by the energy shift in the flat electron band under the condition of Δe/Ebot ≈ 1.

x-T phase diagram

Finally, we show that the indication of the antiferroic electronic instability is commonly observed from x = 0.18 to 0.6 in the BaK122 system. The x dependence of the E-k images around Γ point in the SC state is shown in Fig. 4A. The magnitudes of Δh and Eflat gradually decrease with increasing x. The characteristic x dependence was highlighted in the EDCs at the kF of the inner hole band where the flat feature is clearly observed. As represented by the red circles in Fig. 4B, the flat feature shows continuous decrease in both energy and intensity with increasing x and almost disappears at x ≥ 0.6. These behaviors support the scenario that the condition of Δe ≈ Ebot is necessary for clearly detecting the replica of the electron band. With increasing x, Δe will decrease toward overdoped (OD) regime. At the same time, the electron band bottom at X point moves to the unoccupied state above x ≈ 0.5 according to the rigid band picture reported by Neupane et al. (). Therefore, the signature of the antiferroic electronic structure will be invisible above this threshold x, even if the electronic state still has a potential to exhibit the antiferroic instability.

Fig. 4

x and T dependences of the flat intensity at Γ point.

(A) E-k images around Γ point in the SC state for x = 0.30, 0.51, and 0.57 obtained by laser-ARPES (hν = 6.994 eV). White circles represent the peak positions of the EDCs corresponding to the flat feature around Γ point. White horizontal lines show the location of the SC peak. (B) x dependence of the EDCs at the kF of the inner hole band. Red and black markers represent the energy levels of the flat feature and SC gap, respectively. (C) Contour plot of the spectral weight derived from the flat feature around Γ point in the x-T phase diagram of the BaK122 system. The spectral weight was integrated between −5 and +5 meV around Eflat in the EDC at kF of the inner hole band (section S5). The measurement points are indicated by black dots.

In Fig. 4C, we present a x-T phase diagram showing the area where the signature of the replica electronic structure appears. The contour plot was obtained from the spectral weight at Eflat integrated with the energy window of ±5 meV in the EDCs divided by the Fermi-Dirac function at the kF of the inner hole band (section S6). We note that the contour plot represents the inherent antiferroic electronic instability appearing through the replica structure being enhanced because of the condition of Δe ≈ Ebot at X point. Figure 4C shows that the indication of the antiferroic replica structure clearly appears in the SC state, and its remnant is further observed above Tc (section S7).

DISCUSSION

The present results suggest that the influence of the antiferroic electronic instability appears in a wide area of the nonmagnetic phase in the BaK122 system, which should be distinguished from the signatures of the long-range AFM order exhibiting a strong competition with superconductivity (, –). Alternatively, this instability may be related to the AFM fluctuations detected from underdoped to OD regime by the NMR measurements (). The evolution of the AFM fluctuations () and transport property () of BaK122 show an anomaly around 100 K from OP to OD regime, which may be associated with the observed antiferroic instability (Fig. 4C). On the other hand, the elastic shear modulus indicating the nematic fluctuations [ ≈ (0,0)] was also observed in a wide range of x for BaK122 (, ), which supports the presence of the nematic spin fluctuations (). From the viewpoint of the orbital degrees of freedom, multiple orbital orders/fluctuations [ ≈ (π,π) and (0,0)] can simultaneously develop with spin fluctuations, according to the theoretical studies based on the self-consistent vertex correction method (). The antiferroic electronic instability observed in the present work suggests the presence of an as-yet-unknown electronic order, such as antiferroic orbital order, or some form of the nematic spin and/or orbital fluctuations, whose origin and relation to the high-Tc superconductivity should be further elucidated.

MATERIALS AND METHODS

Laser-ARPES measurements were performed on the spectrometer built using a VG-Scienta R4000WAL electron analyzer and a 6.994-eV vacuum ultraviolet laser as a photon source (, ). Using the λ/2 (half-wave) plate, we could rotate the light polarization vector and obtain s- or p-polarized light. The energy resolution was set to 3 meV to obtain high count rate. ARPES measurements at the BZ corner were performed on the spectrometer built using a VG-Scienta R4000WAL electron analyzer, a motor-controlled six-axis manipulator, and a helium discharge lamp of hν = 21.2 eV at the University of Tokyo. The energy resolution was set to 4 meV. The spectra were reproducible over measurement cycles (5 K ≤ T ≤ 200 K) of 24 hours. The EF of samples was referenced to that of a gold film evaporated onto the sample substrate. All measurements were carried out on surfaces cleaved at 200 K in ultrahigh vacuum better than 5 × 10−11 torr. Single crystals of BaK122 (0.18 ≤ x ≤ 0.69) were grown by the self-flux method as described in detail by Ohgushi and Kiuchi () and Kihou et al. (). The samples were mounted on the copper plate with a silver paste without applying pressure.