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Quasiparticle structure of Sr2RuO4
Physica B 259—261 (1999) 940—941
Quasiparticle structure of Sr RuO A. Pe´rez-Navarro*, J. Costa-Quintana, F. Lo´pez-Aguilar Grup d ’Electromagnetisme, Cn, Universitat Auto% noma de Barcelona, E-08193, Bellaterra, Barcelona, Spain
Abstract The non-copper layered perovskite, Sr RuO , is expected to be a very useful reference material for interpreting experiments on the high ¹ cuprate superconductors. A band structure calculation for Sr RuO is performed. Starting from the electronic structure determined in the local density formalism, the Dyson’s equation with self-energies arising from the Hubbard hamiltonian is solved by diagonalizing the Green’s function in k-space. The density of states is obtained by considering the renormalization factor and the life-times of the quasiparticle states in each pole of the interacting system. This leads to modification of the density of states calculated in the local density formalism, and the results fit experimental data not only in the position of peaks, but also in their intensity and in the number of states at Fermi level. 1999 Elsevier Science B.V. All rights reserved. Keywords: Sr RuO ; Hubbard’s self-energy; Electronic structure
Since their discovery in 1986 all high-¹ superconduc tors that have been characterized contain CuO planes. In 1994, a noncuprate perovskite, Sr RuO , was dis coverd which had a transition temperature of 0.93 K [1]. What makes this compound interesting is that it presents the same crystal structure as La CuO . The role played by CuO planes in cuprates is played by RuO in the ruthenate [2]. Experimentally, it seams clear that correlation effects are important for Sr RuO [1,3,4], but they have not still been included in any theoretical density of states (DOS) calculation [5,6]. These works fit recent X-ray fluorescence emission studies for p orbitals of oxygen, but not for d orbitals [7]. We calculate the band structure of Sr RuO by the symmetrized augmented plane wave method in the local density approximation (LDA). Our calculations fit experimental results [8] as well as Refs. [5,6]. In Fig. 1a the DOS is shown with a quite different structure from that obtained experimentally in Ref. [3] or Ref. [9]. In fact,
* Corresponding author. Tel.: 34-93-581-1353; fax: 34-93-5811350; e-mail: [email protected].
this last one is capable of differentiating a three peaks structure that Ref. [3] cannot. In our results we see a central peak a little above the Fermi level that is experimentally found below this level. We think that the origin of this problem is the non-inclusion of correlation effects in d orbitals. In order to take into account these correlations we diagonalize the Green’s function in k-space [10,11], with a self-energy obtained with the random phase approximation [12]:
ºf 1 n R(u)"! 2 X u#X #j!iK 1!n # u!X !m!iN 1 n # X u#X #j!iK 1!n # , (1) u!X !m!iN where º is the Coulomb correlation, f" 2gn(1!n), X"g!ºf and X"g#ºf are the plas mon frequencies, g"(j#m)!i(K#N), and j, m and
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 0 9 7 - 7
A. Pe& rez-Navarro et al. / Physica B 259—261 (1999) 940—941
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the structure shown by peaks B, C and D of Fig. 2 of Ref. [9]. We obtain N(E )"23 states/(Ry cell), which agrees $ with N(E )"19 states/(Ry cell) mentioned in Ref. [9]. $ Previous theoretical calculations have obtained values for N(E ) three times larger than our calculation. $ As a conclusion, we have introduced correlation effects into Sr RuO and were able to fit experimental results, not only the position of the peaks, but also their intensity. This work has been financed by the DGES (PB961143). One of us (APN) acknowledges the grant from CUR de la Generalitat de Catalunya.
References Fig. 1. (a) DOS of Sr RuO with LDA; (b) DOS of Sr RuO with self-energy.
K, N correspond, respectively, to positions and widths of double lorentzians that have been used as non-interacting DOS. As a first approximation we introduce the same selfenergy in all five d orbitals. We put º"0.22 Ry, j"0.07 Ry and K"0.0007 Ry, which are of the same order as that obtained experimentally [13]. The result obtained in this way is shown in Fig. 1b and fits very well the experimental results obtained in Ref. [9]. A small peak close to Fermi level and below it can be seen. The origin of this peak is an hybridization between orbitals d , d , d VW WX VX and p from oxygen 2, in agreement with this reference; also
[1] Y. Maeno et al., Nature 372 (1994) 532. [2] S. Nishizaki, Y. Maeno, T. Fujita, J. Phys. Soc. Japan 65 (1996) 1876. [3] T. Yokoya et al., Phys. Rev. B 53 (1996) 8151. [4] A.P. Mackenzie et al., Phys. Rev. Lett. 76 (1996) 3786. [5] T. Oguchi, Phys. Rev. B 51 (1995) 1385. [6] D.J. Singh, Phys. Rev. B 52 (1995) 1358. [7] E.Z. Kurmaev et al., Phys. Rev. B 57 (1998) 1558. [8] T. Yokoya et al., Phys. Rev. B 54 (1996) 13 311. [9] M. Schmidt et al., Phys. Rev. B 53 (1996) R14761. [10] J. Costa-Quintana, F. Lo´pez-Aguilar, L. Puig-Puig, Phys. Rev. B 48 (1993) 1139. [11] J. Costa-Quintana, M.M. Sa´nchez-Lo´pez, F. Lo´pez-Aguilar, Phys. Rev. B 54 (1996) 10 265. [12] J. Costa-Quintanta, F. Lo´pez-Aguilar, A. Pe´rez-Navarro, L. Puig-Puig, Physica B 230—232 (1997) 929. [13] Y. Maeno, Physica C 282—287 (1997) 206.
Quasiparticle structure of Sr RuO A. Pe´rez-Navarro*, J. Costa-Quintana, F. Lo´pez-Aguilar Grup d ’Electromagnetisme, Cn, Universitat Auto% noma de Barcelona, E-08193, Bellaterra, Barcelona, Spain
Abstract The non-copper layered perovskite, Sr RuO , is expected to be a very useful reference material for interpreting experiments on the high ¹ cuprate superconductors. A band structure calculation for Sr RuO is performed. Starting from the electronic structure determined in the local density formalism, the Dyson’s equation with self-energies arising from the Hubbard hamiltonian is solved by diagonalizing the Green’s function in k-space. The density of states is obtained by considering the renormalization factor and the life-times of the quasiparticle states in each pole of the interacting system. This leads to modification of the density of states calculated in the local density formalism, and the results fit experimental data not only in the position of peaks, but also in their intensity and in the number of states at Fermi level. 1999 Elsevier Science B.V. All rights reserved. Keywords: Sr RuO ; Hubbard’s self-energy; Electronic structure
Since their discovery in 1986 all high-¹ superconduc tors that have been characterized contain CuO planes. In 1994, a noncuprate perovskite, Sr RuO , was dis coverd which had a transition temperature of 0.93 K [1]. What makes this compound interesting is that it presents the same crystal structure as La CuO . The role played by CuO planes in cuprates is played by RuO in the ruthenate [2]. Experimentally, it seams clear that correlation effects are important for Sr RuO [1,3,4], but they have not still been included in any theoretical density of states (DOS) calculation [5,6]. These works fit recent X-ray fluorescence emission studies for p orbitals of oxygen, but not for d orbitals [7]. We calculate the band structure of Sr RuO by the symmetrized augmented plane wave method in the local density approximation (LDA). Our calculations fit experimental results [8] as well as Refs. [5,6]. In Fig. 1a the DOS is shown with a quite different structure from that obtained experimentally in Ref. [3] or Ref. [9]. In fact,
* Corresponding author. Tel.: 34-93-581-1353; fax: 34-93-5811350; e-mail: [email protected].
this last one is capable of differentiating a three peaks structure that Ref. [3] cannot. In our results we see a central peak a little above the Fermi level that is experimentally found below this level. We think that the origin of this problem is the non-inclusion of correlation effects in d orbitals. In order to take into account these correlations we diagonalize the Green’s function in k-space [10,11], with a self-energy obtained with the random phase approximation [12]:
ºf 1 n R(u)"! 2 X u#X #j!iK 1!n # u!X !m!iN 1 n # X u#X #j!iK 1!n # , (1) u!X !m!iN where º is the Coulomb correlation, f" 2gn(1!n), X"g!ºf and X"g#ºf are the plas mon frequencies, g"(j#m)!i(K#N), and j, m and
0921-4526/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 1 0 9 7 - 7
A. Pe& rez-Navarro et al. / Physica B 259—261 (1999) 940—941
941
the structure shown by peaks B, C and D of Fig. 2 of Ref. [9]. We obtain N(E )"23 states/(Ry cell), which agrees $ with N(E )"19 states/(Ry cell) mentioned in Ref. [9]. $ Previous theoretical calculations have obtained values for N(E ) three times larger than our calculation. $ As a conclusion, we have introduced correlation effects into Sr RuO and were able to fit experimental results, not only the position of the peaks, but also their intensity. This work has been financed by the DGES (PB961143). One of us (APN) acknowledges the grant from CUR de la Generalitat de Catalunya.
References Fig. 1. (a) DOS of Sr RuO with LDA; (b) DOS of Sr RuO with self-energy.
K, N correspond, respectively, to positions and widths of double lorentzians that have been used as non-interacting DOS. As a first approximation we introduce the same selfenergy in all five d orbitals. We put º"0.22 Ry, j"0.07 Ry and K"0.0007 Ry, which are of the same order as that obtained experimentally [13]. The result obtained in this way is shown in Fig. 1b and fits very well the experimental results obtained in Ref. [9]. A small peak close to Fermi level and below it can be seen. The origin of this peak is an hybridization between orbitals d , d , d VW WX VX and p from oxygen 2, in agreement with this reference; also
[1] Y. Maeno et al., Nature 372 (1994) 532. [2] S. Nishizaki, Y. Maeno, T. Fujita, J. Phys. Soc. Japan 65 (1996) 1876. [3] T. Yokoya et al., Phys. Rev. B 53 (1996) 8151. [4] A.P. Mackenzie et al., Phys. Rev. Lett. 76 (1996) 3786. [5] T. Oguchi, Phys. Rev. B 51 (1995) 1385. [6] D.J. Singh, Phys. Rev. B 52 (1995) 1358. [7] E.Z. Kurmaev et al., Phys. Rev. B 57 (1998) 1558. [8] T. Yokoya et al., Phys. Rev. B 54 (1996) 13 311. [9] M. Schmidt et al., Phys. Rev. B 53 (1996) R14761. [10] J. Costa-Quintana, F. Lo´pez-Aguilar, L. Puig-Puig, Phys. Rev. B 48 (1993) 1139. [11] J. Costa-Quintana, M.M. Sa´nchez-Lo´pez, F. Lo´pez-Aguilar, Phys. Rev. B 54 (1996) 10 265. [12] J. Costa-Quintanta, F. Lo´pez-Aguilar, A. Pe´rez-Navarro, L. Puig-Puig, Physica B 230—232 (1997) 929. [13] Y. Maeno, Physica C 282—287 (1997) 206.