Optical conductivity and the correlation strength of high-temperature copper-oxide superconductors

Abstract

Since their discovery in 1986, the high-temperature copper-oxide superconductors have been a central object of study in condensed-matter physics. Their highly unusual properties are widely (although not universally) believed to be a consequence of electron-electron interactions that are so strong that the traditional paradigms of condensed-matter physics do not apply: instead, entirely new concepts and techniques are required to describe the physics. In particular, the superconductivity is obtained by adding carriers to insulating 'parent compounds'. These parent compounds have been identified 1 as 'Mott' insulators, in which the lack of conduction arises from anomalously strong electron-electron repulsion. The unusual properties of Mott insulators are widely 2 believed to be responsible for the high-temperature superconductivity. Here, we present a comparison of new theoretical calculations and published 3-8 optical conductivity measurements, which challenges this belief. The analysis indicates that the correlation strength in the cuprates is not as strong as previously believed, in particular that the materials are not properly regarded as Mott insulators. Rather, antiferromagnetism seems to be necessary to obtain the insulating state. By implication, antiferromagnetism is essential to the properties of the doped metallic and superconducting state as well.The prototypical 'parent compound' is La 2 CuO 4 , in which the lattice structure and electron counting is such that there is an odd number of electrons per formula unit. Thus, in the absence of further symmetry breaking, conventional band theory would predict that the material is a good metal. La 2 CuO 4 is however not metallic; it is an insulator with a gap determined by optical spectroscopy to be approximately 1.8 eV (refs 3,4). From one perspective, the insulating behaviour is not surprising. At temperature T = 0, La 2 CuO 4 has two-sublattice Néel order, so that the magnetic unit cell contains two formula units and thus an even number of electrons, compatible with the observed insulating behaviour. However, the consensus has been that the antiferromagnetic order is irrelevant. Instead, the materials have been identified 1,2 as 'Mott insulators' . (Although the cuprates are properly regarded as 'charge-transfer' and not 'Mott' insulators in the sense of ref. 9, we believe this issue is not relevant here: the high-energy-scale physics and chemistry of transition metal (Cu) and ligand (O) ions produces one band of electrons, with an effective interaction strength U which we aim to determine. In particular, optical data show that the nearest bands (arising mainly from the non-bonding oxygen orbitals) are 5-6 eV removed in energy, with only a weak absorption tail extending down to the energies of relevance here. The issue is discussed in more detail in the Supplementary Information.) In a Mott or charge-transfer insulator, the electron-electron interactions are so strong that a density of one electron per unit cell implies a 'jammed' situation: no electron ca...

Failure oft−Jmodels in describing doping evolution of spectral weight in x-ray scattering, optical, and photoemission spectra of cuprates

“…Some screening is present within the one band Hubbard model, and it is important to see whether the full doping dependence of U could be understood on the basis of a more exact treatment of the Hubbard model -i.e., whether the physics of cuprates can be fully understood within a single-band Hubbard model. Clearly, as more correlations are added the doping dependence of the effective U systematically decreases from Hartree-Fock calculations 31 to the present QP-GW model, to recent DMFT calculations that can successfully describe the doping evolution of the cuprates with fixed-U models 27,40,41 . However, neither exact diagonalization nor QMC with fixed U = 8t capture the ASWT, Fig.…”

“…At high energies, we subtract off a background from the experimental spectra associated with interband transitions to higher-lying bands not included in the present one band calculations. 16,[25][26][27][28] . We use a doping-independent background contribution shown as black dashed lines in Figs.…”

Doping evolution of Zhang-Rice singlet spectral weight: A comprehensive examination by x-ray absorption spectroscopy

“…4 A noticeable case from the x-ray absorption spectroscopy (XAS) was proposed by Peets et al 5 By compiling available XAS data for different cuprates, the spectral weight of ZRS was claimed to be saturated for the hole doping level p ≥ 0.21. (Also, see an earlier statement of saturated ZRS weight with p > 0.16 in Ref.…”

Signatures of Electronic Correlations in Optical Properties ofLaFeAsO1−xFx

“…Recent theoretical and experimental advances have demonstrated that electronic correlations profoundly influence the optical response at energies up to several eV. [6,15,16,17,18,19]. Spectroscopic ellipsometry allows one to accurately detect such modifications and is hence a highly distinctive probe of electronic correlations in transition metal oxides [18,19].…”

“…Spectroscopic ellipsometry allows one to accurately detect such modifications and is hence a highly distinctive probe of electronic correlations in transition metal oxides [18,19]. Dynamical mean-field theory (DMFT) calculations explain many aspects of strong temperature and doping dependent modifications of the optical spectral weight (SW) in the normal state of the superconducting cuprates [15,16,17]. Very recent DMFT studies indicate that LaFeAsO is slightly below the critical value of the Hubbard U required to obtain an insulating state [6,7].…”