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Discovery of orbital-selective Cooper pairing in FeSe

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Science  07 Jul 2017:
Vol. 357, Issue 6346, pp. 75-80
DOI: 10.1126/science.aal1575

A deeper look into iron selenide

In the past 10 years, iron-based superconductors have created more puzzles than they have helped resolve. Some of the most fundamental outstanding questions are how strong the interactions are and what the electron pairing mechanism is. Now two groups have made contributions toward resolving these questions in the intriguing compound iron selenide (FeSe) (see the Perspective by Lee). Gerber et al. used photoemission spectroscopy coupled with x-ray diffraction to find that FeSe has a very sizable electron-phonon interaction. Quasiparticle interference imaging helped Sprau et al. determine the shape of the superconducting gap and find that the electron pairing in FeSe is orbital-selective.

Science, this issue p. 71, p. 75; see also p. 32

Abstract

The superconductor iron selenide (FeSe) is of intense interest owing to its unusual nonmagnetic nematic state and potential for high-temperature superconductivity. But its Cooper pairing mechanism has not been determined. We used Bogoliubov quasiparticle interference imaging to determine the Fermi surface geometry of the electronic bands surrounding the Γ = (0, 0) and X = (π/aFe, 0) points of FeSe and to measure the corresponding superconducting energy gaps. We show that both gaps are extremely anisotropic but nodeless and that they exhibit gap maxima oriented orthogonally in momentum space. Moreover, by implementing a novel technique, we demonstrate that these gaps have opposite sign with respect to each other. This complex gap configuration reveals the existence of orbital-selective Cooper pairing that, in FeSe, is based preferentially on electrons from the dyz orbitals of the iron atoms.

The high-temperature superconductivity in iron-based superconductors is typically most robust where coexisting antiferromagnetic and nematic ordered states are suppressed by doping or pressure (13). However, FeSe appears to be distinctive for several reasons: (i) Although strongly nematic, it does not form an ordered magnetic state and is instead hypothesized to be a quantum paramagnet (46); (ii) it exhibits evidence for orbital selectivity (7, 8) of band structure characteristics (912); and (iii) a monolayer of FeSe grown on a SrTiO3 substrate has the highest critical temperature Tc of all iron-based superconductors (1316). It is therefore essential to understand the electronic structure and superconductivity of FeSe at a microscopic level; however, the Cooper pairing mechanism of FeSe has thus far been unknown. A quantitative determination of the momentum-space (Embedded Image) structure and relative sign of the superconducting energy gaps Embedded Image on each electronic band Embedded Image is necessary to identify this mechanism. So far, this has not been achieved because of the minute Fermi surface pockets, as well as the highly anisotropic Embedded Image requiring an energy resolution δE < 100 μeV. In this work, we used subkelvin Bogoliubov quasiparticle interference (BQPI) imaging (1719), an established technique for high-precision multiband Embedded Image determination (2022), to measure the detailed structure of the energy gaps in FeSe.

In the orthorhombic phase below the structural transition temperature TSEmbedded Image90 K, FeSe has a crystal unit cell with conventional lattice parameters a = 5.31 Å, b = 5.33 Å, and c = 5.48 Å. We parameterize the Fe plane of the same lattice by using the two inequivalent Fe-Fe distances aFe = 2.665 Å and bFe = 2.655 Å in the orthorhombic, nematic phase [Fig. 1A and section I of (23)]; we define the x axis (y axis) to always be parallel to the orthorhombic aFe axis (bFe axis), so that our x-y coordinate system rotates when a twin boundary is crossed. The FeSe Fermi surface is postulated to consist of three bands—α, ε, and δ (shown for kz = 0 in Fig. 1B)—and may be parameterized accurately using a tight-binding model (24, 25) that is fit simultaneously to several types of experimental observations [sections II and III of (23)]. Surrounding the Γ = (0, 0) point is an ellipsoidal hole-like α-band, whose Fermi surface Embedded Image has its major axis aligned to the orthorhombic bFe axis; surrounding the X = (π/aFe, 0) point is the electron-like ε-band whose “bowtie” Fermi surface Embedded Image has its major axis aligned to the orthorhombic aFe axis. At the Y = (0, π/bFe) point, a δ-band Fermi surface should also exist if its quasiparticles are coherent, but it has not been detectable by spectroscopic techniques. In this picture, the dyz orbital content of the α-band Fermi surface has its maximum value along the x axis (green in Fig. 1B), whereas its dxz orbital content peaks along the y axis (red in Fig. 1B) (25). Conversely, the dyz orbital content of the ε-band Fermi surface is maximum along the y axis (green in Fig. 1B), and its dxy orbital content reaches its highest point along the x axis (blue in Fig. 1B) [(2426) and section II of (23)]. These α-band and ε-band Fermi surface pockets (Fig. 1B) exhibit maximal simultaneous consistency with Fermi surface geometry from angle-resolved photoemission spectroscopy (ARPES) (26, 27), quantum oscillations (28, 29), and our BQPI imaging, as discussed below and in section III of (23).

Fig. 1 Bogoliubov quasiparticle interference (BQPI) model for FeSe.

(A) Top view of FeSe crystal structure. Dashed lines represent the 1-Fe unit cell, and solid lines show the actual unit cell. The unit cell of FeSe is distorted in the nematic phase with aFe > bFe. Throughout, we define the Embedded Image axis, Embedded Image axis, and Embedded Image axis to all be parallel to the aFe axis, so that labels of orbitals such as dxy or dyz, or Embedded Image locations and states, are equally valid in both orthorhombic, nematic domains. (B) In the nematic phase with orthorhombic crystal symmetry, the FeSe Fermi surface consists of a hole-like α-band around Γ = (0, 0) and an electron-like ε-band around X = (π/aFe, 0); the color code indicates the regions of Fermi surface dominated by states with primarily dyz (green), dxz (red), and dxy (blue) orbital character. An anticipated third band, the δ-band around Y = (0, π/bFe), has not been observed by spectroscopic techniques. (C) Constant-energy contours (CECs) of Bogoliubov quasiparticles for the gapped α-band around Γ = (0, 0). The CECs are color-coded to indicate increasing energy (red to purple). A schematic ellipsoidal normal-state Fermi surface is shown using a gray dashed contour. Predominant scattering interference occurring between the “tips” of the banana-shaped CECs should produce a triplet of characteristic BQPI wave vectors: Embedded Image, Embedded Image, and Embedded Image (black arrows). (D) Same as (C), but for the gapped ε-band around X = (π/aFe, 0). (E) The expected energy dependence of the α-band wave vector triplet [Embedded Image, Embedded Image, and Embedded Image] in (C); points are color-coded to indicate decreasing energy. The black diamond symbolizes the starting point of Embedded Image, where Δα = max. (F) The expected energy dependence of the ε-band wave vector triplet [Embedded Image, Embedded Image, and Embedded Image] color-coded by energy. The black diamond symbolizes the end point of Embedded Image, where Δε = min.

A fundamental issue in iron-based superconductivity research is whether conduction electrons are weakly or strongly correlated and what the consequences thereof are for enhancing the superconductivity. The situation is complex because multiple Fe orbitals (e.g., dxz, dyz, and dxy) are involved. One limit of theoretical consideration is an uncorrelated metallic state where “nesting” features of the Fermi surface geometry generate antiferromagnetic spin fluctuations, which then mediate Cooper pairing and superconductivity (2). In contrast, the ordered magnetic states of these same materials are often modeled using frustrated multi-orbital Heisenberg (J1-J2) models in which electrons are essentially localized, with the metallicity and spin fluctuation–mediated superconductivity appearing upon doping this magnetic insulator (5). Intermediate between the two is the Hund’s metal viewpoint (7) in which strong Hund’s coupling, while aligning the Fe spins, also suppresses the interorbital charge fluctuations. This generates orbital decoupling in the electronic structure, which allows “orbital selectivity” to occur in the effects of correlations (7, 8). In theory, the result can be Mott-localized states associated with one orbital coexisting with delocalized quasiparticle states associated with others. Under such circumstances, the pairing itself can become orbital-selective (30, 31), meaning that the electrons of predominantly one specific orbital character bind to form the Cooper pairs of the superconductor. If this occurs, the superconducting energy gaps should become highly anisotropic (30, 31), being large only for those Fermi surface regions where a specific orbital character dominates. Such phenomena have remained largely unexplored because orbital-selective Cooper pairing has never been detected in any material.

To search for such pairing in FeSe, we applied BQPI imaging of impurity-scattered quasiparticles that interfere quantum-mechanically to produce characteristic modulations of the density of states, Embedded Image (where Embedded Image is location), surrounding each impurity atom. When a Embedded Image energy gap Embedded Image is anisotropic, the Bogoliubov quasiparticle dispersion Embedded Image will exhibit closed constant-energy contours (CECs), which are roughly banana-shaped and surround Fermi surface points where Embedded Image is minimum (2022). Then, at a given energy E, the locus of the “banana tips” can be determined because the maximum-intensity BQPI modulations occur at wave vectors Embedded Image connecting the tips, thanks to their high joint density of states for scattering interference. The superconductor’s Cooper-pairing energy gap Embedded Image and the Fermi surface on each band are then determined directly (2022) by geometrically inverting the measured BQPI wave vector set Embedded Image in the energy range Embedded Image. Because these techniques can be implemented at temperatures T ≤ 300 mK, the Embedded Image on multiple bands can be measured with an energy resolution δE ≈ 75 μeV (21, 22), a precision unachievable by any other approach.

However, no BQPI measurements have been reported for bulk FeSe, although photoemission data for the equivalent of the α-band do exist for a related compound, Fe(Se,S) (32). For guidance, we first consider a pedagogical model, while recalling that Fermi surfaces and energy-gap structures derived using BQPI imaging do not depend on any particular model (2022). Given the α-band Fermi surface (dashed gray contour in Fig. 1C), supporting an anisotropic Embedded Imagethat has C2 symmetry (32, 33), the CECs would be as shown by the colored curves in Fig. 1C, with quasiparticle energy increasing as indicated by the color code. The tips of each Bogoliubov CEC “banana” are indicated by colored dots, similarly representing increasing energy. Thus, we expect that a triplet of inequivalent BQPI wave vectors Embedded Image (i = 1 to 3) should exist (black arrows in Fig. 1C). The anticipated energy dependence of Embedded Image is shown schematically in Fig. 1E. For each energy Embedded Image, the positions of the four CEC banana tips [±kx(E), ±ky(E)]α can be determined by inverting

Embedded Image(1)Embedded Image(2)Embedded Image(3)

If a C2-symmetric energy gap Embedded Image existed on a coherent δ-band surrounding Y = (0, π/bFe), it might be expected to behave comparably. A similar analysis (Fig. 1, D and F) applies to the “bowtie” ε-band Fermi surface surrounding X = (π/aFe, 0) (dashed gray contour in Fig. 1D), with the anticipated energy dependence of Embedded Image shown schematically in Fig. 1F.

To measure the Fermi surface and the superconducting gap structure and sign, we imaged differential tunneling conductance Embedded Image at T = 280 mK (where I is current, V is voltage, and e is the electron charge) both as a function of location Embedded Image and electron energy E. Because the Fermi surface pockets are so small in area (Fig. 1B), the expected range of dispersive intraband BQPI wave vectors is very limited—Embedded Image—whereas the interband BQPI necessitates resolving wave vectors ≥π/aFe. To achieve the Embedded Image resolution Embedded Image required to discriminate the energy evolution of BQPI on both the α-band and ε-band necessitates high-precision Embedded Image imaging in very large fields of view. We typically used fields between 60 by 60 and 90 by 90 nm [section IV of (23)]. Local maxima of Embedded Image, the amplitude Fourier transform of Embedded Image, were then used to determine the characteristic wave vectors Embedded Image and Embedded Image of dispersive modulations of BQPI. Figure 2A shows a typical example of measured Embedded Image with its Embedded Image in Fig. 2C. In this case, by using a low-resolution scanning tunneling microscope (STM) tip, we predominantly detected the BQPI signal corresponding to the α-band surrounding Γ = (0, 0) [a complete data set is shown in movie S1 and section IV of (23)]. The evolution of the BQPI triplet Embedded Image (black crosses in Fig. 2C) in the range 2.3 meV > |E| > 0.8 meV at 280 mK is plotted in Fig. 2E. Analogous images for the ε-band, obtained using tips with very high spatial resolution that are sensitive to states at high Embedded Image, are shown in Fig. 2, B, D, and F [a complete data set is shown in movie S2 and section IV of (23)]. Because both Embedded Image and Embedded Image evolve to finite wave vectors Embedded Image and Embedded Image, respectively, as E → 0 (Fig. 2, E and F), FeSe superconductivity is demonstrably in the Bardeen-Cooper-Schrieffer limit, and not near the Bose-Einstein condensation limit where BQPI wave vectors must evolve to 0 as E → 0. From the conventional N(E) Embedded Image dI/dV(E) density-of-states spectrum at T = 280 mK (Fig. 2, G and H), we find that the maximum gap on any band is Embedded Image, whereas another coherence peak occurs at the gap maximum of a second band at Embedded Image. The maximum gaps were assigned to each band on the basis of the energy evolution of BQPI to the energy limit E → 2.3 meV for the α-band and E → 1.5 meV for the ε-band. Lastly, because no conductance was detected in the energy region Embedded Image for all bands.

Fig. 2 Visualizing BQPI in FeSe.

To achieve sufficient Embedded Image resolution, we use a field of view that is about 90 by 90 nm in which we image Embedded Image with bias modulation of 100 μV at T = 280 mK [section IV of (23)]. (A) Typical Embedded Image measured using a low-resolution STM tip that is predominantly sensitive to α-band effects. (B) Typical Embedded Image measured with tips with very high spatial resolution, which emphasize very-short-wavelength BQPI and are predominantly sensitive to ε-band effects. (C) Measured Embedded Image derived from (A). The BQPI wave vector triplet Embedded Image is identified by black crosses at the points of maximum amplitude. The blue crosses indicate the (±2π/8aFe, ±2π/8bFe) points. (D) Measured Embedded Image derived from (B). The BQPI triplet Embedded Image is identified by black crosses at the points of maximum amplitude. The blue crosses indicate the (±2π/8aFe, ±2π/8bFe) points. (E) Measured evolution of Embedded Image, Embedded Image, and Embedded Image. The Embedded Image data are shown in movie S1. The black diamond is the first Embedded Image data point. (F) Measured evolution of Embedded Image, Embedded Image, and Embedded Image. The Embedded Image data are shown in movie S2. The black diamond corresponds to the last Embedded Image data point. Representative error bars in (E) and (F) show the uncertainty of extracted wave vectors. (G) Measured N(E) = dI/dV(E) density of states (DOS) spectrum. Black arrows indicate the maximum energy gap on any band, which we determine from BQPI to be on the α-band (Fig. 3). Red arrows indicate a smaller energy gap on a second band, which, from BQPI, is assigned to the ε-band (Fig. 3). (H) Calculated density of states N(E) from the band structure and gap structure model used herein [sections II and VIII of (23)].

The Fermi surfaces for the α- and ε-bands were next determined using the fact that the Embedded Image loci of CEC banana tips from both Embedded Image and Embedded Image follow the Fermi surface of each band (Fig. 1) (2022). The measured evolution of the BQPI wave vector triplets Embedded Image and Embedded Image is plotted in Fig. 2, E and F. The two Fermi surfaces of the α- and ε-bands of FeSe determined from BQPI imaging [section V of (23)] are shown in Fig. 3, A and B, using blue dots with errors bars for each measured point and blue curves for the Fermi surface. The area of the Fermi surfaces extracted by BQPI imaging is consistent with that at kz = 0 [section III of (23) and fig. S5]. We schematically plot the measured magnitude of the energy gap Embedded Image on the α-band in Fig. 3A and the measured magnitude Embedded Image on the ε-band in Fig. 3B; in both cases, we use the width of the gray shaded region to indicate Embedded Image and include values of extrema of any energy gap from N(E). Although exhibiting extraordinarily anisotropic Embedded Image C2-symmetric energy-gap structures, FeSe remains a fully gapped or nodeless (3438) superconductor with gap minima Embedded Image.

Fig. 3 BQPI determination of Fermi surfaces and energy gaps.

The BQPI data analysis steps yielding the results shown here are explained in detail in section V of (23). (A) The Fermi surface of the α-band is measured using the BQPI triplet Embedded Image, Embedded Image, and Embedded Image and shown as blue dots with representative error bars showing the uncertainty for each wave vector (red dots indicate superconducting gap magnitudes). The energy-gap magnitude for the α-band is measured using the energy dependence of the BQPI triplet Embedded Image(E), Embedded Image(E), and Embedded Image(E), plus the values of the maximum and minimum energy gap from N(E) in Fig. 2G. (B) Same as (A), but for the ε-band using Embedded Image, Embedded Image, and Embedded Image. (C) Embedded Image schematics of FeSe interband scattering wave vector Embedded Image between the α- and ε-bands, which connects gaps of opposite sign in the Δ+− scenario. (D) Measured Embedded Image topograph centered on a typical individual impurity site in a field of view ~6.5 by 6.5 nm. Red x’s, surface (upper) Se sites; yellow pluses, Fe sites. (E) Typical measured Embedded Image from BQPI Embedded Image at E = 1.05 meV in the energy range within both Δα and Δε. Complete Embedded Image data are shown in movie S3. G1 and G2 are the reciprocal lattice vectors identified in (C). (F) The predicted ρ(E) for ± pairing symmetry using the band-gap structure of FeSe [(A) and (B), and sections II, VI, and VIII of (23)] is shown as a solid black curve. The measured ρ(E) for FeSe (black dots) is calculated by integration over the Embedded Image region identified by the black circle in Fig. 4E. The predicted ρ(E) for no gap sign change in FeSe is shown as a solid red curve. The vertical dashed black line marks the energy of the maximum superconducting gap.

One of the key characteristics of iron-based superconductors is whether the energy gaps on different bands have opposite signs (2, 3). For FeSe, this situation should be designated ± because the more conventional designation s± (2, 3) is rendered inappropriate by the orthorhombic crystal symmetry. One technique for measuring Embedded Imagepairing symmetry is to detect the enhancement in the amplitude of Embedded Image at specific BQPI wave vectors when a magnetic field is applied; this was proposed to occur because field-induced scattering results in amplified quasiparticle interference between regions of Embedded Image with same-sign energy gaps (39). In Fe(Se,Te), this approach has yielded field-induced QPI intensity reduction for wave vectors linking the electron and hole pockets, indicative of ± pairing symmetry (40). Yet there are reservations about this interpretation (41) because (i) the wave vectors where the Fe(Se,Te) field-induced alternations are reported occur at Bragg points of the reciprocal lattice, and (ii) a microscopic explanation for these field-induced reductions is absent. To address these issues, another BQPI technique designed to determine Embedded Imagepairing symmetry has been proposed (41). It is based on conventional (nonmagnetic) impurity scattering and the realization that the particle-hole symmetry of interband scattering interference patterns depends on the relative sign of the energy gaps on those bands (41). As a result, the energy-symmetrized Embedded Image and energy-antisymmetrized Embedded Image phase-resolved Bogoliubov scattering interference amplitudesEmbedded Image (4)have, at the Embedded Image for interband scattering, distinct properties depending on the relative sign of the two gaps. Importantly, this approach, although not requiring variable temperature measurements, requires phase-resolved imaging of BQPI in order to reliably discriminate Embedded Imagefrom Embedded Image (where Re is the real component and Im is the imaginary component). Moreover, the (anti)symmetrized functions Embedded Image must be integrated over a particular Embedded Image region. Specifically, we focus onEmbedded Image(5)with radius δq confining Embedded Image to interband scattering processes between two distinct energy gaps (Fig. 3C). Given our quantitative knowledge of the Fermi surface and energy gaps of FeSe (Fig. 3, A and B), the Embedded Image can be predicted specifically for this material, with the result shown as a solid black curve in Fig. 3F for the FeSe gaps Embedded Image and Embedded Image with ± pairing symmetry [section VI of (23)].

Experimentally, the challenge is then to achieve phase-resolved imaging of BQPI surrounding a single impurity atom in FeSe, such as an Fe site vacancy (42, 43). Therefore, we measured Embedded Image around individual impurity sites, each in a field of view ~6.5 by 6.5 nm (for example, Fig. 3D), and then mapped the Embedded Image data onto a perfectly periodic atomic lattice. The Embedded Image origin of this lattice was then set at the impurity site (Fig. 3D) and Embedded Image was measured. Figure 3E is a typical example of Embedded Image [section VII of (23)]. Lastly, the ρ(E) was determined from Eq. 5, with the integration radius δq chosen to capture only intensity related to scattering between Embedded Image and Embedded Image inside the black circle in Fig. 3E. The resulting ρ(E) is shown as black dots in Fig. 3F. Comparison of this measured ρ(E) with its predicted form for the FeSe gaps Embedded Image and Embedded Image with ± symmetry (solid black curve) shows them to be in good agreement, especially in that ρ(E) for ± pairing symmetry does not cross zero within the range of energy gaps. Thus, within the framework of (41), these data demonstrate that the sign of Embedded Image is opposite to that of Embedded Image.

The key results of our study are summarized in Fig. 4, A and B: The measured values of Embedded Image and Embedded Image are both extremely anisotropic but nodeless, each having C2 symmetry with deep minima that are aligned along orthogonal crystal axes. Recalling that our x axis is defined to always be the orthorhombic aFe axis, we have found these results to be equally true in both nematic domains. Such a gap structure is highly divergent from conventional spin fluctuation pairing theory (24), which yields a weak, almost isotropic gap on the α-band and a strong gap on the ε-band but with an anisotropy of opposite Embedded Image orientation to that of the experimental data [section VIII of (23)].

However, orbital-selective pairing concentrated in the dyz channel can provide an explanation for the observed Embedded Image and Embedded Image. Figure 4B shows our measured angular dependence of Embedded Image about Γ = (0, 0) and the equivalent for Embedded Image about X = (π/aFe, 0). For a dyz orbital-selective pairing interaction that peaks at wave vector Embedded Image, the predicted angular dependence of Embedded Image and Embedded Image is shown in Fig. 4C [section VIII of (23)], and its comparison with the measured Embedded Image and Embedded Image in Fig. 4B indicates the existence of orbital-selective Cooper pairing in FeSe.

Microscopically, such orbital-selective Cooper pairing may arise from differences in correlation strength for electrons with different orbital character. For example, correlations sufficient to generate incoherence for states with predominantly dxy orbital character (11, 12) would suppress their pairing within an itinerant picture. Moreover, superconducting FeSe must exhibit distinct quasiparticle weights at the Fermi surface for states with dxz and dyz orbital character because of the nematic state (15, 16). Under such circumstances, a Cooper pairing interaction focused at wave vector Embedded Image, and forming spin-singlets from electrons predominantly with dyz orbital character, can be modeled by enhancing the strength of the spin-fluctuation pairing interaction for electrons with dyz orbital character relative to that for those with dxzorbital character, while fully suppressing it for those with dxy orbital character [(24) and section VIII of (23) for details]. In this case, the orbital selectivity of pairing arises from quasiparticle weights in the various channels of itinerant spin-fluctuation pairing theory, which are hypothesized to be very different owing to orbital-selective correlations [section VIII of (23)]. Such a model could explain why the δ-band, predominantly associated with the dxy orbital, has weak visibility in ARPES (11, 12) and BQPI (Figs. 2 and 3) observations and could also account for a low-energy spin susceptibility that is dominant at Embedded Image, consistent with inelastic neutron scattering data (44). By projecting this form of orbital-selective pairing interaction onto the Fermi surfaces of FeSe (Fig. 3), the gap functions can be predicted by solving the linearized gap equation [(24) and section VIII of (23)]. The resulting predicted Embedded Image and Embedded Image (solid curves in Fig. 4C) are quantitatively consistent with the extremely anisotropic structure and sign reversal of the measured gap functions (Fig. 4, A and B). Moreover, because the magnitudes of Embedded Image and Embedded Image (solid curves in Figs. 4B) track the strength of dyz orbital character on both bands (dashed curves in Fig. 4C) [(2426) and section II of (23)], the influence of orbital selectivity on the Cooper pairing is directly manifest. Overall, these data reveal a distinctive and previously unknown form of correlated superconductivity based on orbital-selective Cooper pairing of electrons that, for FeSe, are predominantly from the dyz orbitals of Fe atoms. Such orbital selectivity may be pivotal to understanding the microscopic interplay of quantum paramagnetism, nematicity, and high-temperature superconductivity in iron-based superconductors.

Fig. 4 Orbital-selective Cooper pairing in FeSe.

(A) Measured Embedded Image structure of anisotropic energy gaps of FeSe (Fig. 3). The red and blue colors indicate the different signs of the two gap functions. (B) Measured angular dependence of FeSe superconducting energy gaps Embedded Image about Γ = (0,0) and Embedded Image about X = (π/aFe,0) from Fig. 3, A and B. Error bars show the energy uncertainty of extracted superconducting gap values. (C) Predicted angular dependence of Embedded Image and Embedded Image for an interband pairing interaction that peaks at Embedded Image and for which pairing is orbital-selective, occurring predominantly for electrons with dyz orbital character [section VIII of (23)]. The dashed gray curves show the dyz orbital character of states at the α-band and ε-band Fermi surfaces. These energy gap predictions are robust against variations in the quasiparticle orbital weights used in the theoretical calculations [section VIII of (23)], provided that the dyz orbital is kept considerably more coherent than the dxz orbital.

Supplementary Materials

www.sciencemag.org/content/357/6346/75/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S18

References (4563)

Movies S1 to S3

Data S1

References and Notes

  1. Materials and methods are available as supplementary materials.
Acknowledgments: We are grateful to A. Chubukov, S. D. Edkins, M. H. Hamidian, J. E. Hoffman, E.-A. Kim, S. A. Kivelson, M. Lawler, D.-H. Lee, J.-H. She, and H.-H. Wen for helpful discussions and communications. J.C.S.D. and P.C.C. gratefully acknowledge support from the Moore Foundation’s EPiQS (Emergent Phenomena in Quantum Physics) Initiative through grants GBMF4544 and GBMF4411, respectively. J.C.S.D. gratefully acknowledges the hospitality and support of the Tyndall National Institute, University College Cork, Cork, Ireland. P.J.H. acknowledges support from U.S. Department of Energy (DOE) grant DE-FG02-05ER46236. A.Kr. and B.M.A. acknowledge support from a Lundbeckfond Fellowship (grant A9318). Material synthesis and detailed characterization at Ames National Laboratory was supported by the U.S. DOE, Office of Basic Energy Science, Division of Materials Sciences and Engineering; Ames Laboratory is operated for the U.S. DOE by Iowa State University under contract DE-AC02-07CH11358. Experimental studies carried out by the Center for Emergent Superconductivity, an Energy Frontier Research Center, headquartered at Brookhaven National Laboratory, were funded by the U.S. DOE under grant DE-2009-BNL-PM015. The data described in the paper are archived by the Davis research group at Cornell University.
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