Pis'ma v ZhETF, vol.93, iss.3, pp. 182-185

© 2011 February 10

Electronic structure, topological phase transitions and superconductivity in (K,Cs)a;Fe2Se2

I. A. Nekrasov1^, M. V. Sadovskii^ Institute for Electrophysics RAS, Ural Branch, 620016 Ekaterinburg, Russia Submitted 30 December 2010

We present LDA band structure of novel hole doped high temperature superconductors (Tc ~ 30 K) KyFeiSei and Csa,Fe2Se2 and compare it with previously studied electronic structure of isostructural FeAs superconductor BaFe-> As-> (Bal22). We show that stoichiometric KFoiSej and CsFoiSoi have rather different Fermi surfaces as compared with Bal22. However at about 60% of hole doping Fermi surfaces of novel materials closely resemble those of Bal22. In between these dopings we observe a number of topological Fermi surface transitions near the F point in the Brillouin zone. Superconducting transition temperature Tc of new systems is apparently governed by the value of the total density of states (DOS) at the Fermi level.

The FeAs based high-temperature superconductors [1] attracted a lot of attention and huge number of experimental and theoretical investigations have been done (for review see [2, 3]) and many are still going on. Pretty high values of superconducting transition temperature were discovered also in Fe chalcogenides FeSe^ and FeSei-zTe* [4].

Structurally FeSe systems are similar to FeAs compounds and consist of layers of FeSe4 tetrahedra. Recent discovery of intercalated K„Fe2Se2 and Csj.Fe2Se2 compounds produced much higher values of Tc=31 K [5] and 27 K [6] similar to those in FeAs 122 systems [2, 3]. This was followed by Tc = 31K in (Tl,K)PeBSe2 [7].

Electronic structure of Fe(S,Se,Te) materials was described in details in Ref. [8]. However K„Fe2Se2 and Cs,.Fe2Se2 have different crystal structure and are actually isostructural to BaF<>L>As2 (Bal22). Its electronic structure was reported in Refs. [9-11]. First calculations of electronic spectrum of K„Fe2Se2 were described in a recent preprint [12].

In this work we present comparative study of electronic structure, densities of states for Bal22 and K„Fe2Se2, Csj.Fe2Se2 systems, demonstrating changes of Fermi surface topology upon doping and making some simple estimates of superconducting Tc.

The K„Fe2Se2 and Csj.Fe2Se2 systems are isostructural to Bal22 (for the last one see Ref. [9]) with ideal body centered tetragonal space group I4/mmm. The K^FeaSea has a = 3.9136 A and c = 14.0367 A with K ions occupying 2a, Fe - 4d and Se - 4e positions with z5,;=0.3539 [5]. In case of Csj.Fe2Se2 lattice parameters are a=3.9601 A and c=15.2846A and zSe is 0.3439 [6]. For given crystal structures we performed band struc-

e-mail: nekrasov0iep.uran.ru, sadovski0iep.uran.ru

ture calculations within the linearized muffin-tin orbitals method (LMTO) [13] using default settings.

In Fig.l we compare Bal22 band structure and different densities of states of Ref. [9] (left) and those for K„Fe2Se2 (black lines) and Csj.Fe2Se2 (gray lines) (right) for stoichiometric case of x = 0. In a bird eye view K„Fe2Se2 and Csj.Fe2Se2 have nearly the same band dispersions which to some extent are similar to those in Bal22. However, there are some quantitative differences. First of all Fe-3d and Se-4p states in new systems are separated in energy in contrast to Fe-3d and As-4p Bal22. Also Se-4p states are of about 0.7 eV lower than As-4p states.

Similar to Bal22 the Fermi level Ep in K and Cs chalcogenides is crossed by Fe-3d states. Detailed band structure near the Fermi level, which is decisive for the formation of superconducting state, for the new systems is compared with that of Bal22 in Fig.2. To some extent Bal22 bands near Ep (upper part of Fig.2) would match those for (K,Cs)Fe2Se2 if we shift them down in energy by about 0.2 eV. Main difference between old and new systems is seen around F point. For (K,Cs)Fe2Se2 systems antibonding part S<>-4p; band in the Z-F direction forms electron-like pocket. In Bal22 corresponding band lies about 0.4 eV higher and goes much steeper, thus it is quite far away from F point. However, if we dope (K,Cs)Fe2Se2 systems (in a rigid band manner) with holes (as shown by horizontal lines in Fig.2 on lower panel) we obtain bands around F point (close to the Fermi level) very similar to those in case of Bal22. Namely at 60% hole doping we obtain three hole-like cylinders while stoichiometric KFe2Se2 has one small electron pocket and larger hole like one and CsFe2Se2 has just one electron pocket near F point. Thus, in fact under hole doping we observe several topological transi-


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Fig.l. LDA calculated band dispersions and densities of states of Bal22 (upper panel) and KFe2Se2 (black lines) and CsFe2Se2 (gray lines)(lower panel). The Fermi level Ep is at zero energy

tions of the Fermi surfaces which we shall briefly discuss t29 states (xy, xz and yz) contribute to the density of

below. states at the Fermi level. The e9 states (3z2 — r2 and

To trace orbital composition of bands if Fig.3 we x2-y2) are almost absent in the density of states at EP.

show orbital resolved densities of states for KFe2Se2- In Fig.4 we present LDA calculated Fermi sur-

Again as for Bal22 [9] and other iron pnictides mainly faces (FS) for both K (upper row) and Cs (lower row)

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I. A. Nekrasov, M. V. Sadovskii

Fig.2. Top panel - LDA calculated band dispersions in the vicinity of the Fermi level for Bal22; Bottom panel -K;cFe2Se2 (black lines) and CsccFe2Se2 (gray lines). The Fermi level is at zero energy. Additional horizontal lines correspond to Fermi level position for the case of 20% and 60% hole doping

E (eV)

Fig.3. LDA calculated orbital resolved densities of states of KFe2 Se2. The Fermi level is at zero energy

(K,Cs)Fe2Se2 compounds for different hole doping levels of x = 0 (left), x = 0.2 (middle) and x = 0.6 (right). All Fermi surfaces have two almost two dimensional electron-like sheets in the corners of the Brillouin zone with topology independent of doping level. Compared

to Bal22 FeAs system the sharp difference in the Fermi surface topology around the center of the Brillouin zone (F-point) is observed at x = 0 and x = 0.2. In fact, KFe2Se2 compound has one electron and one hole toruslike FS sheets while CsFe2Se2 has just one electron-like hourglass FS sheet. With hole doping КРегБег torus transforms to electron-like hourglass and hole cylinder. For 20% hole doped Cs compound we get similar picture with smaller volume FS sheets of the same topology. For x = 0.6 both К and Cs new FeSe materials have Fermi surfaces quite similar to those in Bal22 iron pnictide (see Ref. [9]), with rather typical hole-Ike FS cylinders in the center of the Brillouin zone.

In the Ref. [6] it was shown that К and Cs compounds follow the tendency of Tc dependence on anion height in FeSe plane observed in Ref. [14], which was plausibly explained in Ref. [15] in terms of total density of states change at the Fermi level. Similar observation was made for related compounds SrPt2As2, BaNi2As2 and SrNi2As2 in Ref. [16].

Now we also can make some simple BCS-like estimates of Tc. Taking the LDA calculated value of total DOS at the Fermi level N(EF) 3.94 states/eV/cell for K3.=0Fe2Se2 and 3.6 states/eV/cell for Csj,=oFe2Se2, wd = 350 К and coupling constant g = 0.21 eV estimated for Bal22 (as described in Ref. [15]), then using the BCS expression for Tc = we immediately obtain Tc = 34 К and 28.6 К for К and Cs systems respectively (Tc ratio 1.18). That is very close to experimental Tc values 31К[5] and 27 К (Tc ratio 1.15) [6]. If we take into account the fact that upon hole doping N(Ep) grows for both compounds up to 4.9 states/eV/cell in К and 4.7 states/eV/cell in Cs at 60% doping level superconducting transition temperatures can be estimated in a similar way to give Tc = 57 К for К system and Tc = 52 К for Cs system, showing the potential role of doping. Thus, in accordance with our previous work on pnictides [15], the values of Tc apparently well correlate with the total DOS value at the Fermi level N (Ер). It should be stressed that these estimates do not necessarily imply electron-phonon pairing, as wd may just denote the average frequency of any other possible Boson responsible for pairing interaction (e.g. spin fluctuations). At the same time the lower values of Tc in Cs compound in comparison to К system can be probably attributed to the usual isotope effect.

To conclude, we investigated the band structure and Fermi surface topology of recently discovered chal-gogenide iron superconductors K„Fe2Se2 and Cs,,Fe2Se2 isostructural to Bal22 iron pnictide system at different hole doping levels. We show that at about 60% hole doping level both K„Fe2Se2 and Cs,,Fe2Se2 energy bands

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Fig.4. LDA calculated Fermi surfaces of K;cFe2Se2 (upper row) and CsccFe2Se2 (lower row) for different doping levels: x ■■ left column, x = 0.2 - middle and x = 0.6 - right

and Fermi surface topologies resemble very much those of Bal22 FeAs system. However, at intermediate dopings there are several topological transitions of the Fermi surfaces with changing of number of (electron-like and hole-like) sheets. Also we demonstrated that Tc values in new superconductors are well correlated with total DOS value at the Fermi level N(Ep), which is related to anion height relative to Fe square lattice, similar to that in other FeAs and Fe(Se,Te) systems.

This work is partly supported by RFBR grant 1102-00147 and was performed within the framework of programs of fundamental research of the Russian Academy of Sciences (RAS) "Quantum physics of condensed matter" (09-H-2-1009) and of the Physics Divi

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