Two Energy Scales in the Magnetic Resonance Spectrum of Electron and Hole Doped Pnictide Superconductors

Tanmoy Das and A. V. Balatsky

Phys. Rev. Lett. 106, 157004 – Published 15 April 2011

Abstract

We argue that a multiband superconductor with sign-changing gaps may have multiple spin resonances. We calculate the RPA-based spin resonance spectra of a pnictide superconductor by using the five-band tight-binding model or angle-resolved photoemission spectroscopy Fermi surface (FS) and experimental values of superconducting gaps. The resonance spectra split in both energy and momenta due to the effects of multiband and multiple gaps in $s^{\pm}$ pairing; the higher energy peak appears around the commensurate momenta due to scattering between $α$ -FS to $γ / δ$ -FS pockets. The second resonance is incommensurate, coming from $β$ -FS to $γ / δ$ -FS scatterings, and its $q$ vector is doping-dependent and, hence, on the FS topology. Energies of both resonances $ω_{res}^{1, 2}$ are strongly doping-dependent and are proportional to the gap amplitudes at the contributing FSs.

Received 22 December 2010

DOI:https://doi.org/10.1103/PhysRevLett.106.157004

Authors & Affiliations

Tanmoy Das¹ and A. V. Balatsky^1,2

¹Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
²Center for Integrated Nanotechnology, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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Vol. 106, Iss. 15 — 15 April 2011

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Images

Figure 1
(a),(b) RPA-BCS $χ^{''} (ω)$ , plotted for calculation including the ME effect $M$ from Eq. (1) in (a) and without including the ME effect ( $M = 1$ ) in (b). (d)–(g) The corresponding lower panel figures clarify the mechanism of double resonances at two representative momenta cuts. $χ^{''}$ ’s are shifted by a constant value to ease comparison with others, while they all go to zero at $ω = 0$ . In (f)–(g), when $1 / U_{eff}$ intersects with $χ_{0}^{'}$ (without ME), a true resonance occurs within the RPA. In (d)–(e), the $1 / U$ in the $U_{s}$ vertex does not directly intersect to total $χ_{0}^{'}$ but to its intraorbital components only and thus is not shown [13]. (c) The corresponding LDA FS in the folded zone is plotted at the same doping. The white to black background color gives the $s^{\pm}$ symmetry. The two arrows point to the nesting channels which are responsible for the two modes in (a). The calculation is done with SC gap $Δ_{α} = Δ_{γ / δ} = 2 Δ_{β} = 7 meV$ .Reuse & Permissions
Figure 2
(a)–(c) Computed spectra of $χ^{''} (q, ω)$ are plotted in color for underdoping in (a), optimal doping in (b), and overdoping in (c) of the hole-doped sample. The magenta and yellow lines are the $q$ and $ω$ integrated value of $χ^{''}$ , respectively. The two energy scales in (b) match well with the available data at the same doping in Ref. 10. (d)–(f) The ARPES FSs corresponding to the INS spectra given in their upper panel at the same dopings [5].Reuse & Permissions
Figure 3
Computed INS spectra plotted for two underdopings in (a),(b) and optimal doping in (c) of the electron-doped case. (d)–(f) The corresponding FSs are given at their lower panels at the same dopings obtained from the LDA band in (d) and (e) and from ARPES data [20] in (f). The gap values in (d) and (e) are available from penetration depth measurement [21] and optics [22], respectively, at the same dopings where the same values for (c) are obtained from ARPES [20]. In the LDA, FS pockets are known to be slightly larger than the experimental value due to the neglect of the spin-density wave order [17].Reuse & Permissions
Figure 4
Doping dependence of two resonance energies and the SC gap amplitudes. The open symbols of various colors gives the SC gap values [red circles, $Δ_{α}$ ; blue squares, $Δ_{β}$ ; green stars, $Δ_{γ / δ}$ ] as taken from experiments (see the text). The filled symbols are the two resonance energies [magenta lower (cyan upper) triangles, $ω_{res}^{1}$ ( $ω_{res}^{2}$ )], shown in Figs. 1, 2. The shadings of same colors are a guide to the eyes.Reuse & Permissions

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