Prabhakar P. Singh Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai , India

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1 EPAPS Material showing (a) the comparison of FeTe electronic structure and (b) the application of rigid-band approximation to Fe Te and Fe Te Prabhakar P. Singh Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai , India 1

2 We first note that we use the same structural parameters for FeTe (taken from Ref. [1]), including z(te), as Han and Savrasov [2], and the same computer program (made available by one of the authors of the paper) to carry out the full-potential linear muffin-tin orbital (FP-LMTO) calculations. Our FP-LMTO electronic structure of FeTe is in total agreement with that of Han and Savrasov as stated in the Comment and shown below in detail. In the rigid-band approximation, one uses the electronic structure of the ordered FeTe to accommodate the excess electron resulting from the extra Fe in disordered Fe Te or Fe Te by rigidly shifting the Fermi energy. Thus, if the two calculations for FeTe give identical electronic structure then the shift in Fermi energy needed to go from FeTe to Fe Te (or Fe Te) should be identical. As stated in our Comment as well as shown below in detail, our full-potential linear muffin-tin orbital (FP-LMTO) results for ordered FeTe are in total agreement with the results of Han and Savrasov [2]. Therefore, the rigidband energy shift obtained for Fe Te (or Fe Te) by us should be the same as that of Han and Savrasov. However, they get a much larger rigid-band energy shift of 0.76 ev for going from FeTe to Fe Te (or Fe Te) as compared to our shift of 0.39 ev. Given the near-perfect agreement between the two calculations for FeTe, as shown below, it is not possible to have such a large difference in the rigid-band energy shift for Fe Te. We contend that the energy shift obtained by Han and Savrasov is in error, resulting in erroneous conclusion about the nesting in Fe Te. A correct application of the rigid-band approximation, as shown in our Comment, does not show a transition from a (π, π) to (π, 0) nesting with Fe doping in FeTe. In order to demonstrate that our FP-LMTO results for FeTe are in total agreement with that of Han and Savrasov, we compare our band structure and Fermi surface with their results as shown in Figs. 2(b) and 3(a) of Ref. [2] and reproduced here for convenience. Our calculated band structure (blue curves) for FeTe, superposed on the band structure as shown in Fig. 2(b) of Ref. [2] is shown in Fig. 1. The overlap of our calculated bands with that of Ref. [2] unambiguously demonstrates the total agreement between the two calculations for FeTe. As shown in Fig. 1, from 0 to 2 ev, our bands are in perfect agreement with that of Fig. 2(b) of Ref. [2], implying that for accommodating the same number of excess electrons the rigid-band energy shift should be the same in the two calculations. Our calculated Fermi surface for FeTe, shown in Fig. 2(b), is compared with the Fermi surface of Ref. [2], reproduced in Fig. 2(a). The two Fermi surfaces look identical, confirming 2

3 Energy (ev) Γ X M Γ Z R A Z Figure 1: Our FP-LMTO band structure of FeTe, denoted by blue lines is superposed over the band structure of FeTe as shown in Fig. 2(b) of Ref. [2]. The horizontal blue line indicates the Fermi energy. (a) (b) Figure 2: (a) The Fermi surface of FeTe as shown in Fig. 3(a) of Ref. [2] compared with (b) our FP-LMTO Fermi surface of FeTe. 3

4 DOS (st/ev atom) E (ev) NOS (unit cell) Figure 3: The DOS (black, solid) and the NOS (red, solid) of FeTe obtained using the FP-LMTO (black, solid) method. The NOS starts with 4 because of the four s-electrons contributed by the Se-derived s-bands situated around 12 ev. The Fermi energy for FeTe (0 ev) is shown by the vertical, dashed line in orange. Within the rigid-band approximation, the vertical dashed lines in green and blue represent the Fermi energies of Fe Te (0.39 ev) and Fe Te (0.68 ev) as obtained by us. The Han and Savrasov [2] result for the Fermi energy of Fe Te (0.76 ev) is shown by the vertical, dashed line in magenta. Note that the DOS is given in units of (st/ev atom) and the total number of states is given for the unit cell. the equivalence of the two calculations for FeTe. The Fermi surface for FeTe, shown in Fig. 2(b) is the same as that of Fig. 1 in our Comment but replotted for comparison. We also noticed that Fig. 3(b) of Ref. [2] is slightly tilted towards top-right instead of giving a top view. Finally, in Fig. 3 we show the density of states (DOS) and the total number of states (NOS) for FeTe obtained with our FP-LMTO calculations. The DOS is in good agreement with the DOS of Ref. [1], and it must also be in good agreement with the results of Ref. [2]. For describing Fe Te within the rigid-band approximation, we find the excess number of valence electrons to be times the number of valence electrons in Fe to be electrons per atom or electrons per unit cell. Adding to the number of valence electrons 4

5 in FeTe, we get a total of electrons per unit cell. To accommodate electrons per unit cell, we need to shift the Fermi energy by 0.39 ev, as shown by the dashed green line in Fig. 3. Similarly, for Fe Te, we need to accommodate electrons per unit cell, requiring a shift in the Fermi energy by 0.68 ev, as shown by the dashed blue line in Fig. 3. However, Han and Savrasov find a shift in Fermi energy of 0.76 ev for Fe Te, shown by dashed magenta line in our Fig. 3. Since we have shown that our calculations for FeTe are in total agreement with that of Han and Savrasov, such a large difference in the rigid-band energy shift is not possible. Our FP-LMTO results are consistent with the results of KKR-ASA calculations as described in our Comment. Based on the above, we contend that the energy shift obtained by Han and Savrasov is in error, and consequently Figs. 3(b) and 4(b) of Ref. [2] and their main conclusion that with Fe doping a transition from a (π, π) to (π, 0) nesting takes place in FeTe are based on erroneous data. [1] A. Subedi, L. Zhang, D. J. Singh, and M. H. Du, Phys. Rev. B 78, (2008). [2] M. J. Han and S. Y. Savrasov, Phys. Rev. Lett. 103, (2009). 5