Real-Time Evolution of the Electron Clouds of Transition Metal Ions: Possible Electron-Pairing Medium in Unconventional High-Temperature Superconductors
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The electron-pairing mechanism in unconventional high-temperature superconductors (HTS) has not been resolved. We proposed that the electron-pairing medium of unconventional HTS is the change of the electron clouds of transition metal ions, which is analogous to the lattice vibration in conventional superconductors. Real-time evolution of the electron clouds of transition metal ions under excitations in La2Fe2As2O2, FeSe sheet, and HgBa2Ca2Cu3O8 was calculated by the time-dependent density functional theory (TDDFT). The characteristic frequencies are 160 meV, 190 meV, and 250 meV, respectively. The frequencies are close to that of the lattice vibration in conventional HTS at high pressures, showing that the change of the electron clouds of the transition metal ions can be the electron-pairing medium.
KeywordsUnconventional high-temperature superconductor Time-dependent density functional theory Electron-pairing medium
The discovery of copper oxide [1, 2] and iron-based [3, 4] superconductors indicates that the electron-lattice interaction cannot explain the electron-pairing mechanism in unconventional HTS. According to the BCS theory [5, 6], the superconducting transition temperature (Tc) caused by the electron-lattice interaction (at normal pressures) cannot be higher than 40 K. In 1987, P. W. Anderson  has put forward the famous RVB model for copper-based superconductors. Other theories [8, 9, 10] have also been proposed. But P. W. Anderson  stated in 2007 that many theories about high-temperature superconducting electron-pairing mechanism might be in the wrong direction. Recently, orbital fluctuation has been extensively studied [12, 13, 14, 15], but the characteristic frequency of the fluctuation has been not obtained. The pairing mechanism for unconventional HTS is still under debate. There are two main viewpoints on the electron pairing. One is that there is a lattice-like medium. The other is that there is no lattice-like medium.
Based on the above consideration, T. G. Zhou had studied eight typical unconventional superconductors (Fe2KSe2, La2Fe2As2O2, Nd2Fe2As2O2, Ba2Fe4As4, YBa2Cu3O7, HgBa2Ca2Cu3O9, Tl2Ba2CaCu2O8, and Bi2Sr2Ca2Cu3O10) . Under a static electric field, the electron clouds of transition metal ions change significantly. A pairing mechanism was proposed. When a free electron comes to a new place, the electron clouds of the neighboring transition metal ions will change. In this way, the charge densities around the free electron will decrease. When the free electron leaves, the electron clouds of the transition metal ions will not relax immediately, so that there will be a region lack of charge. Another free electron will be attracted. An attraction appears. This mechanism is essentially the same as the electron-lattice interaction, except that the medium is the change of the electron clouds, not the displacement of the ions.
Based on the previous studies, we have made a further investigation, investigating the frequencies of the change of the electron clouds of transition metal ions. The real-time evolution of charge densities under some excitation of La2Fe2As2O2, FeSe sheet, and HgBa2Ca2Cu3O8 has been calculated by TDDFT [19, 20] method. This paper will report the methods and results.
Calculations were conducted within the Octopus package [21, 22]. The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) was used to describe the exchange-correlation energy. The GGA+U method [23, 24] was considered to deal with the strong correlation of the 3d electrons. HSCV pseudopotentials  were adopted. Approximated enforced time-reversal symmetry (AETRS) algorithm was used to approximate the evolution operator and the time step is 0.002 ћ/eV.
3 Results and Discussions
3.2 FeSe Sheet 
The characteristic frequencies are 160 meV, 190 meV, and 250 meV, respectively, for La2Fe2As2O2, FeSe sheet, and HgBa2Ca2Cu3O8. The results are unexpected, because the general view is that the change of the electron density is very quick and the frequency is much higher than the lattice vibration. The frequencies the author obtained are close to that of the lattice vibration, indicating it can be excited by free electrons. So, the change of the electron clouds of transition metal ions can be the electron-pairing medium. W. A. Little et al.  gave similar results, but the frequencies are too high. Whether it can be excited by free electrons should be justified.
We also studied other systems, such as Fe2KSe2  and CaCuO2 . Similar results were obtained. It is worth noting that the change of the electron clouds of transition metal ions is very complicated. For the same superconductor, there may be different modes, corresponding to different frequencies. For the same mode, the frequency is the same. Changing the parameters of the applied electric field may lead to different modes or may not affect the results. Why do the electron clouds of transition metal ions change this way? The main reason is that the 3d shell of transition metal ions is not fully filled. The electron clouds possess no spherical symmetry, and easy to change under electric fields.
Real-time evolution of the electron clouds of transition metal ions in unconventional HTS was calculated by the TDDFT method. The frequencies of evolution of electron clouds match well with the frequencies of the lattice vibrations in conventional HTS at high pressures. Though the frequencies obtained by this method are not accurate, it can give a significant evidence that the change of electron clouds can be the electron-pairing medium in HTS.
The author sincerely thanks Xu Zuo, Xinjie Zhao, Feng Lu, Hong Dong, Jian Zhou and Yu Bai for useful discussions.
This work was supported by project funded by the China Postdoctoral Science Foundation (2018M640245), project funded by the Hebei Province Postdoctoral Science Foundation (B2018003013), the Natural Science Foundation of Hebei, China (Grant No. F2017208031), the Natural Science Foundation of Nation, China (Grant No. 51674096), and the Fundamental Research Funds for the Central Universities, Nankai University (Grant No. 63191740).
- 21.Andrade, X., Strubbe, D.A., De Giovannini, U., Larsen, A.H., Oliveira, M.J.T., Alberdi-Rodriguez, J., Varas, A., Theophilou, I., Helbig, N., Verstraete, M., Stella, L., Nogueira, F., Aspuru-Guzik, A., Castro, A., Marques, M.A.L., Rubio, A.: Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems. Phys. Chem. Chem. Phys. 17, 31371–31396 (2015)CrossRefGoogle Scholar
- 23.Agapito, L.A., Curtarolo, S., Nardelli, M.B.: Reformulation of DFT + U as a pseudohybrid Hubbard density functional for accelerated materials discovery. Phys. Rev. X. 5(1), 011006 (2015)Google Scholar
- 29.Ricci, A., Poccia, N., Joseph, B., Arrighetti, G., Barba, L., Plaisier, J., Campi, G., Mizuguchi, Y., Takeya, H., Takano, Y., Saini, N.L., Bianconi, A.: Intrinsic phase separation in superconducting K0.8Fe1.6Se2 (T c = 31.8 K) single crystals. Supercond. Sci. Technol. 24, 082002 (2011)ADSCrossRefGoogle Scholar
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