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Electronic structure of iron pnictides
Physica C 470 (2010) S516–S517
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Electronic structure of iron pnictides Jingge Zhang a,*, Huaiming Guo b, Shiping Feng a a b
Department of Physics, Beijing Normal University, Beijing 100875, China Department of Physics, Capital Normal University, Beijing 100037, China
a r t i c l e
i n f o
a b s t r a c t Within the two-orbital t—t 0 —J model, the electronic structure of iron pnictides is studied. It is shown that the lowest energy peaks are well defined at all momenta, and the calculated electron dispersion along the high symmetry directions is in qualitative agreement with the angle-resolved photoemission spectroscopy experimental data for iron pnictides. Ó 2009 Elsevier B.V. All rights reserved.
Article history: Accepted 28 October 2009 Available online 31 October 2009 Keywords: Iron pnictides Electron dispersion Electronic structure
The recent discovery of superconductivity in iron pnictides [1] has generated great interests due to the role of magnetic fluctuations [2]. These iron-based superconductors are the first noncopper-oxide superconductors with the superconducting (SC) transition temperature exceeding 50 K, and also is hard to explain such a high SC transition temperature in terms of the conventional phonon-mediated SC mechanism [3]. In particular, these iron pnictides have a layered structure consisting of the FeAS layers separated by insulating layers, where the Fe ions are arranged on a square lattice. This structure is similar to cuprates superconductors in the sense that they also have a layered structure of the square lattice of the CuO plane separated by insulating layers [4]. Furthermore, a fundamental similarity between iron pnictide and cuprate superconductors has been seen in the phase diagram [5]. These facts suggest that the unusual physical properties of iron pnictides may have the same origin as in doped cuprates. It has been shown [5] that many of the unconventional physical properties of iron pnictides have often been attributed to particular characteristics of low energy excitations determined by the electronic structure. In this paper, we study the electronic structure of iron pnictides within the twoorbital t—t0 —J model [6],
H¼
X aig^ r
X
t ag^ C yair C aiþg^r þ
t0as^ C yair C aiþs^r
ais^r
X y 4t? C y1ir C 2ir þ C y2ir C 1ir þ l C air C air
ir
þJ
X
X aig^
Sai Saiþg^ þ J ?
X
air
S1i S2i
i
* Corresponding author. E-mail address: [email protected] (J. Zhang). 0921-4534/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2009.10.134
ð1Þ
^; s ^ ¼ ^ ^; a ¼ 1; 2 is energy band index. This ^ ¼ ^ where g x; y xy model is supplemented by the single occupancy local constraint P y r C air C air 6 1, which can be treated properly within the chargespin separation (CSS) fermion-spin theory [7], where the cony strained electron operators are decoupled as C ai" ¼ hai" S ai ; C ai# ¼ y þ iUair hai# Sai , with the spinful fermion operator hair ¼ e hai keeps track of the charge degree of freedom together with some effects of the spin configuration rearrangements due to the presence of the doped charge carrier itself, while the spin operator Sai keeps track of the spin degree of freedom. Within the CSS fermion-spin theory, the electronic structure of the doped bilayer cuprates has been discussed based on the bilayer t—J model [8]. For the present twobands t—t 0 —J model (1), we can follow the previous discussions for the bilayer cuprates [8], and then obtain explicitly the longitudinal and transverse parts of the electron spectral function of iron pnictides A1L ðk; xÞ; A2L ðk; xÞ, and AT ðk; xÞ [9]. Since there are two different orbitals in iron pnictides, A1L ðk; xÞ is not the same as A2L ðk; xÞ, this is different from the case in the bilayer cuprates [8]. In this case, the antibonding and bonding parts for the electron ðaÞ spectral function can be expressed as, A1 ¼ ðA1L AT Þ=2; ðbÞ ðaÞ ðbÞ A1 ¼ ðA1L þ AT Þ=2; A2 ¼ ðA2L AT Þ=2, and A2 ¼ ðA2L þ AT Þ=2. We have performed a calculation for the electron spectral function of iron pnictides. It is shown [9] that the hole-like (antibonding) quasiparticles are located around the [0, 0] point, while the electron-like (bonding) quasiparticles appear around the ½p; p point. To show this point clearly, we have made a series of calculations for the electron spectral functions at different momenta, and the results of the positions of the lowest energy quasiparticle peaks as a function of momentum along the high symmetry directions are plotted in Fig. 1. For comparison, the corresponding experimental data (circles) [5], the renormalized LDA result (solid line) and tight-binding fits (dashed line) are also shown in Fig. 1 (inset).
J. Zhang et al. / Physica C 470 (2010) S516–S517
S517
ðaÞ ðaÞ ðbÞ ðbÞ Fig. 1. The positions of the lowest energy peaks of the hole-like [solid A1 and dot–dashed A2 lines] and electron-like [dashed A2 and dotted A1 lines] electron spectra as a function of momentum with temperature T ¼ 0:05J at the doping d ¼ 0:10 for t 1x =J ¼ 4; t 1y =J ¼ 2; t2x =J ¼ 2; t 2y =J ¼ 4; t01 =J ¼ 1; t 02 =J ¼ 1; t? =J ¼ 1 and J? =J ¼ 0:3. Inset: the corresponding experimental data (circles), the renormalized LDA result (solid line) and tight-binding fits (dashed line) taken from Ref. [5].
Our result shows that the Fermi level is only slightly below the hole-like band around the [0, 0] point and above the electron-like band around the ½p; p point, in qualitative agreement with the angle-resolved photoemission spectroscopy (ARPES) measurements on iron pnictides [5]. Our result is also consistent with a fact that iron-based superconductors exhibit an anomalously strong pairing behavior on small Fermi surface which are connected by the antiferromagnetic wave vector [2] Q ¼ ½p; p. The essential physics of the hole-like and electron-like band structure in iron pnictides is dominated by the multiband interaction. The electron spectral function is divided into the hole-like and electron-like parts, respectively, due to the two-band interaction, and are obtained by considering the charge carrier fluctuation due to the spin pair bubble, therefore the nature of the electron structure in the normal state are closely related to the strong interaction between the electron quasiparticles and collective magnetic excitations. As a consequence, both hole-like and electron-like quasiparticle bandwidths are reduced to the order of (a few) J, and then the energy scales of both hole-like and electron-like bands are controlled by the magnetic interaction. Our present results also show that the unusual behavior of the electron structure of iron pnictides is intriguingly related to the strong coupling between the electron quasiparticles and collective magnetic excitations.
In conclusion we have shown within the two-orbital t—t0 —J model that the lowest energy quasiparticle peaks of iron pnictides are well defined at all momenta, and the calculated electron dispersion along the high symmetry directions is in qualitative agreement with the ARPES experimental data for iron pnictides. Acknowledgements This work was supported by the National Natural Science Foundation of China, and the funds from the Ministry of Science and Technology of China. References [1] [2] [3] [4] [5] [6] [7]
Y. Kamihara et al., J. Am. Chem. Soc. 130 (2008) 3296. W. Bao et al., Phys. Rev. Lett. 102 (2009) 247001. J. Bardeen et al., Phys. Rev. 108 (1957) 1175. M.A. Kastner et al., Rev. Mod. Phys. 70 (1998) 897. H. Ding et al., arXiv:0812.0534. Q. Si et al., Phys. Rev. Lett. 101 (2008) 076401. Shiping Feng et al., J. Phys. Condens. Matter 16 (2004) 343; Shiping Feng et al., Int. J. Mod. Phys. B 22 (2008) 3757. [8] Yu Lan et al., Phys. Rev. B 75 (2007) 134513. [9] Jingge Zhang et al., unpublished.
Contents lists available at ScienceDirect
Physica C journal homepage: www.elsevier.com/locate/physc
Electronic structure of iron pnictides Jingge Zhang a,*, Huaiming Guo b, Shiping Feng a a b
Department of Physics, Beijing Normal University, Beijing 100875, China Department of Physics, Capital Normal University, Beijing 100037, China
a r t i c l e
i n f o
a b s t r a c t Within the two-orbital t—t 0 —J model, the electronic structure of iron pnictides is studied. It is shown that the lowest energy peaks are well defined at all momenta, and the calculated electron dispersion along the high symmetry directions is in qualitative agreement with the angle-resolved photoemission spectroscopy experimental data for iron pnictides. Ó 2009 Elsevier B.V. All rights reserved.
Article history: Accepted 28 October 2009 Available online 31 October 2009 Keywords: Iron pnictides Electron dispersion Electronic structure
The recent discovery of superconductivity in iron pnictides [1] has generated great interests due to the role of magnetic fluctuations [2]. These iron-based superconductors are the first noncopper-oxide superconductors with the superconducting (SC) transition temperature exceeding 50 K, and also is hard to explain such a high SC transition temperature in terms of the conventional phonon-mediated SC mechanism [3]. In particular, these iron pnictides have a layered structure consisting of the FeAS layers separated by insulating layers, where the Fe ions are arranged on a square lattice. This structure is similar to cuprates superconductors in the sense that they also have a layered structure of the square lattice of the CuO plane separated by insulating layers [4]. Furthermore, a fundamental similarity between iron pnictide and cuprate superconductors has been seen in the phase diagram [5]. These facts suggest that the unusual physical properties of iron pnictides may have the same origin as in doped cuprates. It has been shown [5] that many of the unconventional physical properties of iron pnictides have often been attributed to particular characteristics of low energy excitations determined by the electronic structure. In this paper, we study the electronic structure of iron pnictides within the twoorbital t—t0 —J model [6],
H¼
X aig^ r
X
t ag^ C yair C aiþg^r þ
t0as^ C yair C aiþs^r
ais^r
X y 4t? C y1ir C 2ir þ C y2ir C 1ir þ l C air C air
ir
þJ
X
X aig^
Sai Saiþg^ þ J ?
X
air
S1i S2i
i
* Corresponding author. E-mail address: [email protected] (J. Zhang). 0921-4534/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2009.10.134
ð1Þ
^; s ^ ¼ ^ ^; a ¼ 1; 2 is energy band index. This ^ ¼ ^ where g x; y xy model is supplemented by the single occupancy local constraint P y r C air C air 6 1, which can be treated properly within the chargespin separation (CSS) fermion-spin theory [7], where the cony strained electron operators are decoupled as C ai" ¼ hai" S ai ; C ai# ¼ y þ iUair hai# Sai , with the spinful fermion operator hair ¼ e hai keeps track of the charge degree of freedom together with some effects of the spin configuration rearrangements due to the presence of the doped charge carrier itself, while the spin operator Sai keeps track of the spin degree of freedom. Within the CSS fermion-spin theory, the electronic structure of the doped bilayer cuprates has been discussed based on the bilayer t—J model [8]. For the present twobands t—t 0 —J model (1), we can follow the previous discussions for the bilayer cuprates [8], and then obtain explicitly the longitudinal and transverse parts of the electron spectral function of iron pnictides A1L ðk; xÞ; A2L ðk; xÞ, and AT ðk; xÞ [9]. Since there are two different orbitals in iron pnictides, A1L ðk; xÞ is not the same as A2L ðk; xÞ, this is different from the case in the bilayer cuprates [8]. In this case, the antibonding and bonding parts for the electron ðaÞ spectral function can be expressed as, A1 ¼ ðA1L AT Þ=2; ðbÞ ðaÞ ðbÞ A1 ¼ ðA1L þ AT Þ=2; A2 ¼ ðA2L AT Þ=2, and A2 ¼ ðA2L þ AT Þ=2. We have performed a calculation for the electron spectral function of iron pnictides. It is shown [9] that the hole-like (antibonding) quasiparticles are located around the [0, 0] point, while the electron-like (bonding) quasiparticles appear around the ½p; p point. To show this point clearly, we have made a series of calculations for the electron spectral functions at different momenta, and the results of the positions of the lowest energy quasiparticle peaks as a function of momentum along the high symmetry directions are plotted in Fig. 1. For comparison, the corresponding experimental data (circles) [5], the renormalized LDA result (solid line) and tight-binding fits (dashed line) are also shown in Fig. 1 (inset).
J. Zhang et al. / Physica C 470 (2010) S516–S517
S517
ðaÞ ðaÞ ðbÞ ðbÞ Fig. 1. The positions of the lowest energy peaks of the hole-like [solid A1 and dot–dashed A2 lines] and electron-like [dashed A2 and dotted A1 lines] electron spectra as a function of momentum with temperature T ¼ 0:05J at the doping d ¼ 0:10 for t 1x =J ¼ 4; t 1y =J ¼ 2; t2x =J ¼ 2; t 2y =J ¼ 4; t01 =J ¼ 1; t 02 =J ¼ 1; t? =J ¼ 1 and J? =J ¼ 0:3. Inset: the corresponding experimental data (circles), the renormalized LDA result (solid line) and tight-binding fits (dashed line) taken from Ref. [5].
Our result shows that the Fermi level is only slightly below the hole-like band around the [0, 0] point and above the electron-like band around the ½p; p point, in qualitative agreement with the angle-resolved photoemission spectroscopy (ARPES) measurements on iron pnictides [5]. Our result is also consistent with a fact that iron-based superconductors exhibit an anomalously strong pairing behavior on small Fermi surface which are connected by the antiferromagnetic wave vector [2] Q ¼ ½p; p. The essential physics of the hole-like and electron-like band structure in iron pnictides is dominated by the multiband interaction. The electron spectral function is divided into the hole-like and electron-like parts, respectively, due to the two-band interaction, and are obtained by considering the charge carrier fluctuation due to the spin pair bubble, therefore the nature of the electron structure in the normal state are closely related to the strong interaction between the electron quasiparticles and collective magnetic excitations. As a consequence, both hole-like and electron-like quasiparticle bandwidths are reduced to the order of (a few) J, and then the energy scales of both hole-like and electron-like bands are controlled by the magnetic interaction. Our present results also show that the unusual behavior of the electron structure of iron pnictides is intriguingly related to the strong coupling between the electron quasiparticles and collective magnetic excitations.
In conclusion we have shown within the two-orbital t—t0 —J model that the lowest energy quasiparticle peaks of iron pnictides are well defined at all momenta, and the calculated electron dispersion along the high symmetry directions is in qualitative agreement with the ARPES experimental data for iron pnictides. Acknowledgements This work was supported by the National Natural Science Foundation of China, and the funds from the Ministry of Science and Technology of China. References [1] [2] [3] [4] [5] [6] [7]
Y. Kamihara et al., J. Am. Chem. Soc. 130 (2008) 3296. W. Bao et al., Phys. Rev. Lett. 102 (2009) 247001. J. Bardeen et al., Phys. Rev. 108 (1957) 1175. M.A. Kastner et al., Rev. Mod. Phys. 70 (1998) 897. H. Ding et al., arXiv:0812.0534. Q. Si et al., Phys. Rev. Lett. 101 (2008) 076401. Shiping Feng et al., J. Phys. Condens. Matter 16 (2004) 343; Shiping Feng et al., Int. J. Mod. Phys. B 22 (2008) 3757. [8] Yu Lan et al., Phys. Rev. B 75 (2007) 134513. [9] Jingge Zhang et al., unpublished.