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Doping and anion height are found to drastically affect the electronic structures of superconductors [1-2]. In this study, we investigated the composition-dependence of the electronic properties of the newly discovered intercalated TlFe$_{2}$Se$_{2}$ superconductor using density functional theory. We calculated the electronic structures of Tl$_{x}$Fe$_{2}$Se$_{2}$ with various Tl concentrations (x = 1.00, 0.75 and 0.50) using a 2 x 2 x 1 supercell. Fractional coordinate z$_{Se}$ of Se which essentially controls the anion height are taken from “relaxed” nonmagnetic and magnetic configurations of TlFe$_{2}$Se$_{2}$ which have values of z$_{Se}$ = 0.341 Å and 0.348 Å, respectively. We also used the experimental value of z$_{Se}$ = 0.357 Å taken from [3], which is higher than the simulated ones. We also added a hypothetical value of z$_{Se}$ = 0.364 Å which is the highest among the fractional coordinate values used. All calculations of the electronic structures are done using QUANTUM ESPRESSO [4]. Generalized gradient approximation of Perdew-Burke-Ernzerhof [5] is used for exchange-correlation potentials.
The density of states (DOS) for various Tl content has shown metallic properties where states near the Fermi energy (E$_{F}$) are mostly from Fe-d states. This is consistent with the typical features of iron-based superconductors. For various fractional coordinates, z$_{Se}$, the DOS have also shown similar characteristics. Band structure calculations on the other hand revealed different results. For x = 1.00, no pocket is found around the zone center (Γ point) of the First Brillouin zone. For x = 0.75 and 0.50 on the other hand, hole-like pockets are being observed around the Γ point which is typical of Fe-based superconductors. The appearance of the hole-like pockets might be due to the shifting of the E$_{F}$ towards lower energy when Tl content is reduced. This indicates a possible doping effect in this material (i.e. hole doping).
Furthermore, we also studied the possible three dimensionality of Tl$_{x}$Fe$_{2}$Se$_{2}$ with various Tl content by observing the Z point of the first Brillouin zone. As Tl content is reduced, a shift of bands is observed towards higher energies which resulted to an appearance of a shallow electron-like pocket around the Z point when x = 0.75. The electron-like pocket is mainly of Fe-d$_{xz}$+d$_{yz}$ character. This is not consistent though with the experiments where the observed electron-like pocket has Fe-d$_{xy}$+Se-p$_{z}$ character [6]. Looking at the band structure calculations for various z$_{Se}$, the electron-like band found around the Z-point above E$_{F}$ for z$_{Se}$ = 0.341 Å seems to shift towards lower energies as the z$_{Se}$ increases, which eventually crossed the E$_{F}$ for z$_{Se}$ = 0.357 Å. This electron-like pocket is now consistent with the experimental results where the orbital character is found to be of Fe-d$_{xy}$+Se-p$_{z}$. Increasing further the z$_{Se}$ to 0.364 Å, the bands split and a hole-like band is formed below E$_{F}$.
In conclusion, these results suggest that the Tl content plays a significant role in tuning the electronic properties of Tl$_{x}$Fe$_{2}$Se$_{2}$ where doping effect might occur with the appropriate value of Tl concentration. In addition, the anion height shows strong control of the band topology of this material.
References
[1] Shein I.R. and Ivanovskii A.L. Phys. Lett. A 375, 1028-1031 (2011).
[2] Shein I.R. and Ivanovskii A.L. Journal of Superconductivity and Novel Magnetism 24, 2215-2221 (2011).
[3] K. Klepp, H. Boller. Monatshefte fr Chemie/Chemical Monthly 109,1049-57 (1978).
[4] P. Giannozzi, et al. Journal of Phys.: Cond. Mat. 21, 395502 (2009).
[5] J.P.Perdew, K.Burke, and M. Ernzerhof. Phys. Rev. Lett. 77, 3865 (1996).
[6] Z.-H. Liu, et al. Phys. Rev. Lett. 109, 037003, (2012).
