Pis'ma v ZhETF, vol. 98, iss. 7, pp. 427-431
© 2013 October 10
Correlated band structure of superconducting NdFeAsO0.9F01:
dynamical mean-field study
S. L. Skornyakov, I. R. Shein+, A. L. Ivanovskii+, V. I. Anisimov Institute of Metal Physics UB of the RAS, 620990 Yekaterinburg, Russia Ural Federal University, 620002 Yekaterinburg, Russia +Institute of Solid State Chemistry UB of the RAS, 620990 Ekaterinburg, Russia
Submitted 1 July 2013 Resubmitted 18 August 2013
In this Letter we report the LDA+DMFT (method combining local density approximation with dynamical mean-field theory) results for spectral properties of the superconductor NdFeAsOo.gFo.i in the paramagnetic phase. The calculated momentum-resolved spectral functions are in good agreement with angle-resolved photoemission spectra (ARPES). The obtained effective quasiparticle mass enhancement (m*/m = 1.4) is smaller than the one in isostructural parent compound LaFeAsO which critical temperature under the same fluorine doping (LaFeAsO0.gF0.1) is two times lower. Our results demonstrate that in quaternary FeAs-based superconductors of the same class, changes of the crystal structure caused by substitution of one rare-earth atom, implicitly result in reduction of the electronic correlation strength.
DOI: 10.7868/S0370274X1319003X
The discovery of high-temperature superconductivity in iron-arsenic compounds [1] attracts considerable amount of attention to this class of systems from theoretical and experimental communities [2-17]. This interest is stimulated by the fact that the new superconductors are similar to well-studied cuprates. Both superconducting families adopt layered crystal structures where layers of atoms responsible for superconductivity alternate with non-conducting layers. As in the cuprates, superconductivity in the pnictides emerges under doping and parent compounds typically are not superconducting. The main difference between the two classes of superconductors is the nature of the ground state of their parent systems. In the case of cuprates it corresponds to a Mott insulator while for the pnictides it is a metal. It is well established that strong Coulomb correlations between copper electrons play a key role in formation of superconducting state in the cuprates. Thus, studying correlation phenomena in the pnictides is important for revealing the pairing mechanism in these systems.
Strength of electronic correlations in the pnictides was a central topic of numerous works [2-9]. These studies were done within the LDA+DMFT scheme [18] which is the most powerful first-principle approach that can be routinely applied to studying electronic structure of realistic strongly correlated systems. It combines the local density approximation (LDA) which describes band dispersion in real materials with the ability of
the dynamical mean-field theory (DMFT) [19] to treat the whole range of on-site Coulomb correlations. First LDA+DMFT results [3] on pnictides were interpreted in such a way that these systems should be considered as strongly correlated systems close to a Mott transition. However, analysis of band dispersion carried out in later studies [4-6] have shown that it is more correct to classify the new superconductors as moderately correlated compounds.
The highest Tc in the pnictides is detected for doped systems [20, 21], therefore studying the electronic properties in the doped cases and revealing differences with the stoichiometric cases can be useful for understanding the physics of superconductivity in these compounds.
Neodymium ferrooxyarsenide is a parent compound for high-temperature superconductors with common formula NdFeAsOi-^ (Tc = 51K for x = 0.1 [21]). This compound is the second synthesized pnictide-based material after PrFeAsO that under fluorine doping turns into superconducting state above 50 K [21, 11] and is isostructural to other famous pnictide superconductor LaFeAsO (Tc = 26K for LaFeAsOo.gFo.i [20]). Since substitution of La with isovalent and chemically equivalent Nd preserves the crystal lattice symmetry, electronic structures in these two cases are not expected to be qualitatively different. However, due to small difference in the ionic radii this change causes structural relaxation which results in small decrease
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of the lattice parameters and reduction of the Fe-As-Fe bond angle. These changes of the crystal structure seem to be very important since critical temperatures in these two cases are considerably different. Therefore the change La^Nd influence the superconducting properties and, probably, the Fermi surface, indirectly. Interplay between the structural changes and the electron pairing in so-called "1111" systems (quaternary compounds like LaFeAsO, NdFeAsO) was studied by Kuroki et al. [12] within density-functional theory and model approaches employing random-phase approximation.
In view of the fact that transition temperatures in NdFeAsO and LaFeAsO are almost two times different it is instructive to study and compare electronic structure of these compounds. Direct probe of band dispersion and Fermi surface in real materials is provided by photoemission spectroscopy with angular resolution which requires large high-quality single crystals. Comparison of an ARPES data with calculated spectral properties allows to judge on the role and strength of electronic correlations. However, it turned out that growth of such crystals is a non-trivial task for some representatives of the "1111" family.
Electronic structures of NdFeAsOi_KFK and LaFeAsO were intensively studied experimentally [13-17]. Authors of these works have shown that observed band structure of the investigated compounds in general can be interpreted as renormalized LDA bands but formation of some important features of the Fermi surface cannot be understood and within LDA. It was also noted that the surface states contribute significantly to the ARPES spectra and distinction between the bulk and the surface contributions requires separate analysis. Theoretical investigation of spectral properties of stoichiometric LaFeAsO in framework of LDA+DMFT was done by Aichhorn et al. [4] and Anisimov et al. [2]. These results are in good agreement with angle-resolved and angle-integrated spectra [13-15,22]. Thus, first high-resolution ARPES spectra of fluorine-doped NdFeAsO were measured more than four years ago [16] and so far only few DFT-based calculations of its electronic structure without any account of strong electronic correlations were reported [16, 23].
In this work, we present the LDA+DMFT results for spectral properties of NdO1_KFKFeAs and its parent system in the paramagnetic state. We demonstrate that local Coulomb correlations taken into account within single-site dynamical mean-field approach are essential for proper description of electronic structure of this compound. Our results are in good agreement with the
available ARPES data. We compare our results with LDA+DMFT data for LaFeAsO.
Implementation of the LDA+DMFT scheme employed in the present work consists of three steps. First, self-consistent LDA calculation is carried out and the effective on-site Coulomb parameter U and intraatomic exchange parameter J are computed by means of the constrained DFT method [24]. In our study we calculate the LDA band structure and spectral function with ELK full-potential code [25] using the experimentally determined atomic positions [26] and default parameters controlling the LAPW basis. On the second step basis of Wannier states describing band structure in vicinity of the Fermi energy is generated and the effective tight-binding Hamiltonian HWF in that basis is constructed by means of projection technique [27]. Then many-body Hamiltonian H(k),
#(k) = Hwf (k) + HHu - Hdc,
(1)
is iteratively solved by DMFT. On each iteration the effective DMFT impurity problem is solved by the hybridization function expansion continuous time quantum Monte-Carlo method (CTQMC) [28]. In Eq. (1) Hu describes the on-site Coulomb interaction energy and the term HDC is the correction for the Coulomb energy already accounted by LDA. In our work we used the Coulomb interaction term in the density-density form,
u —
2 ^
ijaa'
Uj
Ha ,vja'
(2)
where nia is the particle-number operator for the orbital i and spin projection a — t4-, Uij is the interaction matrix which is parametrized [29] by U and J. The double-counting HDC is represented by a diagonal matrix with nonzero elements in the block of partilly filled states (Fe 3d states in the present case). It was taken in the form U(na — 0.5) where n^ is the total number of electrons in partially filled shells, and U = — ij Uj /N(N — 1) is the average Coulomb energy for N spin-orbitals (N =10 in the case of a d element). This form of HDC can be successfully applied for modeling of spectral and magnetic properties of different FeAs superconductors [5, 6, 10].
Momentum-resolved spectral functions including effects of local electronic correlations were computed as imaginary part of the DMFT Green's function:
= ——Trlm[(w + /x)/ — flwF(k) + Hdc —
71
(3)
Here ¡j, is the self-consistently determined chemical potential, E(w) is the real-frequency self-energy obtained
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by means of analytical continuation of the DMFT self-energy E(iwn) (w„ is the Matsubara frequency) with the use of Pade approximants [30] and I is the identity operator.
Comparison of spectral functions of stoichiometric NdFeAsO and LaFeAsO obtained within LDA is shown in Fig. 1. As in other pnictides in both cases Fe 3d states
Fig. 1. Orbitally resolved spectral functions of stoichiomet-ric NdFeAsO (solid curves) and LaFeAsO (dashed curves) calculated within LDA. 0 eV corresponds to the Fermi energy
form a broad band in the energy region (—2.0, 2.0) eV relative to the Fermi level. Features in the energy window (—6.0, —2.0) eV are due to Fe d - As p hybridization.
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