Orbital Origin of Extremely Anisotropic Superconducting Gap in Nematic Phase of FeSe Superconductor

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Orbital Origin of Extremely Anisotropic Superconducting Gap in Nematic Phase of FeSe Superconductor

Defa Liu et al.

Phys. Rev. X 8, 031033 – Published 2 August 2018

Abstract

The iron-based superconductors are characterized by multiple-orbital physics where all the five Fe $3 d$ orbitals get involved. The multiple-orbital nature gives rise to various novel phenomena like orbital-selective Mott transition, nematicity, and orbital fluctuation that provide a new route for realizing superconductivity. The complexity of multiple-orbital physics also requires us to disentangle the relationship between orbital, spin, and nematicity, and to identify dominant orbital ingredients that dictate superconductivity. The bulk FeSe superconductor provides an ideal platform to address these issues because of its simple crystal structure and unique coexistence of superconductivity and nematicity. However, the orbital nature of the low-energy electronic excitations and its relation to the superconducting gap remain controversial. Here, we report direct observation of the highly anisotropic Fermi surface and extremely anisotropic superconducting gap in the nematic state of the FeSe superconductor by high-resolution laser-based angle-resolved photoemission measurements. We find that the low-energy excitations of the entire hole pocket at the Brillouin zone center are dominated by the single $d_{x z}$ orbital. The superconducting gap exhibits an anticorrelation relation with the $d_{x z}$ spectral weight near the Fermi level; i.e., the gap size minimum (maximum) corresponds to the maximum (minimum) of the $d_{x z}$ spectral weight along the Fermi surface. These observations provide new insights in understanding the orbital origin of the extremely anisotropic superconducting gap in the FeSe superconductor and the relation between nematicity and superconductivity in the iron-based superconductors.

Received 3 May 2018

DOI:https://doi.org/10.1103/PhysRevX.8.031033

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Iron-based superconductors

Condensed Matter, Materials & Applied Physics

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Popular Summary

Superconductors, which exhibit zero electrical resistance below a certain critical temperature, are in demand because they can carry currents without any loss in energy. Iron selenium (FeSe) superconductors, in particular, have attracted attention because of their simple crystalline structure and unique ground state in which superconductivity and nematicity (i.e., the in-plane dichotomy between two perpendicular directions) coexist. Here, we report direct observations of the extremely anisotropic superconducting gap in FeSe generated predominantly on the $d_{x z}$ orbital. Our findings provide important insights into the pairing interaction that gives rise to superconductivity in FeSe superconductors.

All five Fe $3 d$ orbitals in FeSe are believed to participate in its superconductivity, which appears at $T_{c} = 8.0 K$ . However, the orbital nature of the low-energy excitations and the superconducting gap symmetry have remained highly controversial. Using high-resolution, laser-based, angle-resolved photoemission measurements, we study the highly anisotropic Fermi surface of FeSe and its superconducting gap. We find that the $d_{x z}$ orbital is the primary component of the Fermi surface. This discovery sheds light on the mechanism of superconductivity in FeSe superconductors. Moreover, we show that the superconducting gap exhibits an anticorrelation relation with the $d_{x z}$ spectral weight near the Fermi level.

Our results related to the Fermi surface, the superconducting gap, and the orbital nature of an FeSe superconductor pave the way for future studies of the relationship between superconductivity and nematicity in iron-based superconductors.

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Vol. 8, Iss. 3 — July - September 2018

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Figure 1
Fermi surface of the single domain FeSe measured at 1.6 K around the $Γ$ point and its superconducting gap. (a) Top view of FeSe crystal structure. The red, yellow, and gray circles represent Fe atom, Se atom above the Fe plane (Se top), and Se atom below the plane (Se bottom), respectively. The dashed line represents the 1-Fe unit cell while the solid line represents the 2-Fe unit cell. We define $x$ axis parallel to $a_{Fe}$ axis and $y$ axis parallel to $b_{Fe}$ axis. In the normal state, FeSe has $C_{4}$ symmetry with $a_{Fe} = b_{Fe}$ , but it breaks into $C_{2}$ symmetry in the nematic state with $a_{Fe} > b_{Fe}$ . (b) The Brillouin zone of FeSe. The dashed line and the solid line correspond to BZs of the 1-Fe unit cell and 2-Fe unit cell, respectively. The red circle represents the momentum area that can be measured simultaneously by our laser ARPES system with 6.994 eV photon energy. The whole Fermi surface of FeSe around the $Γ$ point can be covered by one time measurement which occupies a very small portion of the BZ. (c) Constant energy contours around the $Γ$ point at different binding energies measured at 1.6 K in $L V$ polarization geometry. The measured Fermi surface (leftmost panel) shows an elliptical shape with its long axis along $k_{y}$ axis and short axis along $k_{x}$ axis. The spectral weight concentrates to the vertex areas and gets depleted around the central area with increasing binding energy. (d) Photoemission spectra (EDCs) measured at different temperatures for two typical Fermi momenta. The locations of the two momenta, A and B, are marked in (c) as black dots. (e) Corresponding symmetrized EDCs from (d). The curves are fitted with a phenomenological gap formula [41] (solid red curves). For point A (left-hand panel), no gap opening is detected below $T_{c}$ within our experimental resolution. Apparent gap opening occurs for point B (right-hand panel). (f) Temperature dependence of the superconducting gap at B point. It follows the BCS gap form (red curve).
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Figure 2
Momentum dependence of the superconducting gap for FeSe measured at 1.6 K. (a) Symmetrized EDCs at different Fermi momenta along the Fermi surface measured at 1.6 K. These curves are fitted with a phenomenological gap formula (red curves). The same data are plotted in (b) as a false-color image where the variation of the superconducting peak position can be directly visualized. The location of the Femi momentum is defined by the Fermi surface (FS) angle $θ$ as shown in (c). (d) Momentum dependence of the superconducting gap derived from fitting the symmetrized EDCs in (a). To enhance the data statistics and keep the twofold symmetry, the gap value is obtained by averaging over the four quadrants. The measured gap (empty circles) is fitted by $s + d$ (blue curve), extended $s + d$ (red curve), and $p$ -wave (green curve) pairing gap forms.
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Figure 3
Band structure of FeSe along different momentum cuts and their orbital nature. (a) Definition of the momentum cuts across the $Γ$ point by the Fermi surface angle $θ$ . (b) Measured band structure along different momentum cuts varying from $θ = 90 °$ (vertical cut, leftmost panel) to $θ = 0 °$ (horizontal cut, rightmost panel). Three bands are observed, marked as $α$ , $β$ , and $γ$ in the $θ = 90 °$ and $θ = 0 °$ panels. The $α$ band is well fitted by a parabolic curve (red line) which gives a Fermi energy $ϵ_{F}$ of $\sim 6.7 meV$ above the Fermi level. The effective mass for different momentum cuts can be obtained from such a parabolic fitting. The dashed green and blue lines are guides to the eye for the $β$ and $γ$ bands, respectively. (c) The calculated Fermi surface of FeSe around $Γ$ point in the nematic state. (d) The calculated band structure along different momentum cuts defined by the Fermi surface angle $θ$ in (c). In panels (c) and (d), the $d_{x z}$ , $d_{y z}$ , and $d_{x y}$ orbital components are represented by red, green, and blue colors, respectively.
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Figure 4
Correlation between the superconducting gap, the spectral weight, and the effective mass of bands along the Fermi surface of FeSe. (a) Momentum distribution curves (MDCs) along different momentum cuts at the Fermi level measured at 9.8 K. The momentum cut is defined by the Fermi surface angle $θ$ as shown in the inset. For a given Fermi momentum on the Fermi surface, the angle between the momentum cut and the Fermi surface normal direction is defined as an angle $γ$ . The area of the MDCs marked in red is defined as the spectral weight $A_{MDC}$ in (d). (b) Photoemission spectra (EDCs) of FeSe along the Fermi surface measured at 9.8 K. After subtracting the Shirley background (dashed line), the area of the EDCs marked in red is defined as the spectral weight $A_{EDC}$ in (e). For the convenience of comparison, the superconducting gap measured at 1.6 K is replotted in (c). (d) MDC spectral weight along the Fermi surface obtained from (a) after considering the correction of the $γ$ angle as defined in inset of (a). (e) EDC spectral weight along the Fermi surface obtained from (b). (f) Effective mass of the $d_{x z}$ band along different momentum cuts as obtained by a parabolic fitting of the $α$ band in Fig. 3. (g) Superconducting gap plotted in the polar graph, overlaid with the measured Fermi surface in order to have a direct comparison of their relative orientations. (h) A schematic picture of the $d_{x z}$ orbitals in the Fe plane in the nematic state of FeSe. For the $d_{x z}$ orbitals, the dominant intraorbital coupling is the exchange interactions along the $x$ axis ( $J_{1 x}$ ). Both $J_{1 y}$ and $J_{2}$ are antiferromagneticlike while the $J_{1 x}$ coupling is ferromagnetic in iron chalcogenides [44, 45, 46, 47].
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