Coexistence of orbital degeneracy lifting and superconductivity in iron-based superconductors

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Coexistence of orbital degeneracy lifting and superconductivity in iron-based superconductors

H. Miao, L.-M. Wang, P. Richard, S.-F. Wu, J. Ma, T. Qian, L.-Y. Xing, X.-C. Wang, C.-Q. Jin, C.-P. Chou, Z. Wang, W. Ku, and H. Ding

Phys. Rev. B 89, 220503(R) – Published 11 June 2014

Abstract

We report the angle-resolved photoemission spectroscopy observation of the lifting of symmetry-protected band degeneracy, and consequently the breakdown of local tetragonal symmetry in the superconducting state of Li( ${Fe}_{1 - x} {Co}_{x}$ )As. Supported by theoretical simulations, we analyze the doping and temperature dependences of this band splitting and demonstrate an intimate connection between ferro-orbital correlations and superconductivity.

Received 29 January 2014
Revised 29 May 2014

DOI:https://doi.org/10.1103/PhysRevB.89.220503

Authors & Affiliations

H. Miao¹, L.-M. Wang², P. Richard^1,3,*, S.-F. Wu¹, J. Ma¹, T. Qian¹, L.-Y. Xing¹, X.-C. Wang¹, C.-Q. Jin^1,3, C.-P. Chou^2,4, Z. Wang⁵, W. Ku², and H. Ding^1,3,†

¹Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA
³Collaborative Innovation Center of Quantum Matter, Beijing, China
⁴Beijing Computational Science Research Center, Beijing 100084, China
⁵Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA

^*p.richard@iphy.ac.cn
^†dingh@iphy.ac.cn

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Vol. 89, Iss. 22 — 1 June 2014

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Images

Figure 1
(a) ARPES experimental geometry. (b), (c) FS mapping at the Brillouin zone center measured under $σ$ and $π$ configurations. (d), (h) ARPES intensity plots of LiFeAs measured along the $Γ$ -M direction [the red line in (b) and (c)], and recorded with 51 eV incident light in the $σ$ and $π$ configurations to select odd and even orbital symmetries [20, 21, 22], respectively. (e), (i) Same as (d) and (h), but for ${LiFe}_{0.88} {Co}_{0.12}$ As. (f), (g) High-energy resolution ARPES cuts along the $Γ$ -M direction of LiFeAs and ${LiFe}_{0.88} {Co}_{0.12}$ As, respectively, recorded with the He i $α$ line of an helium discharge lamp. The red and blue curves in (d), (e), (h), and (i) are the original and fitted momentum distribution curves at $E_{F}$ , respectively. The blue, red, and green circles represent the peak positions associated with the $α$ ( $d_{odd}$ ), $α^{'}$ ( $d_{even}$ ), and $β$ ( $d_{x y}$ ) bands, respectively, where $d_{odd}$ ( $d_{even}$ ) is the odd (even) linear combination of the $d_{x z}$ and $d_{y z}$ orbitals. (j), (k) EDCs corresponding to the data shown in (f) and (g), respectively. The blue EDC in (j), also shown in inset, illustrates the splitting of the $α$ band.
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Figure 2
(a)–(c) Extracted band dispersion of the $d_{x z} / d_{y z}$ bands in LiFeAs, ${LiFe}_{0.94} {Co}_{0.06}$ As [22], and ${LiFe}_{0.88} {Co}_{0.12}$ As, respectively. (d), (e) Extracted band dispersion of ${NaFe}_{0.95} {Co}_{0.05}$ As [26] and ${FeTe}_{0.55} {Se}_{0.45}$ [27], respectively. Red dashed curves are parabolic fits. (f) Doping and $T_{c}$ dependence of $Δ_{band}$ . The open and solid symbols refer to the doping (bottom right) and $T_{c}$ (bottom left) axes. Error bars are determined by standard deviation of the fitting parameters [22].
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Figure 3
(a)–(e) High-energy resolution ARPES intensity plots at $T = 250$ , 200, 150, 100, and 50 K, respectively. (f)–(j) Same data but divided by the Fermi-Dirac function convoluted with the system resolution function to probe the electronic structure above $E_{F}$ . Band dispersions at different temperatures are extracted using momentum distribution curves (MDCs) and fitted to parabolic functions. (k) Energy distribution curves (EDCs) at the $Γ$ point at different temperatures. We used two Lorentzian peaks to extract the top of the $α$ and $α^{'}$ bands, and plot the fitted results on top of the original data using red dashed curves [22]. The top of the $α$ band is shifted towards high binding energy as temperature increases, and it almost merges with the top of the $α^{'}$ band at 250 K. (l) MDCs recorded 20 meV below $E_{F}$ , which corresponds to the red dashed lines shown in (a)–(e). At high temperature, the $α$ peak positions move towards $Γ$ , indicating that the band moves downward in energy. In contrast, the peak positions of the $α^{'}$ and $β$ bands are unchanged [22]. (m) Temperature evolution of $Δ_{band}$ . The values of $Δ_{band}$ are extracted from the electronic band dispersions, EDCs and MDCs. Error bars are determined by the standard deviation of the fitted parameters. (n) and (o) are ARPES intensity plots just above and well below $T_{c}$ , respectively. (p) EDCs at the $Γ$ point above and below $T_{c}$ .
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Figure 4
(a) An example of the configuration of a FO disordered system (represented by an Ising field) without long-range correlations. (b) The resulting average band structure that couples to the Ising field, showing no clear splitting of the band. (c), (d) The average spectral function at momentum $k = (0, 0)$ and $k = (0.25, 0.25)$ . (e)–(h) Similar to (a)–(d), however, the disordered system contains long-range, power-law decaying correlations of the local order parameter.
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