Core-level photoemission measurements of the chemical potential shift as a probe of correlated electron systems

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Abstract

The shift of the chemical potential as a function of band filling provides useful insight into the electronic structure of solids. In this article, we describe how the chemical potential shift can be measured using core-level photoemission spectroscopy and what information can be obtained from the measured chemical potential shift, in particular on strongly correlated systems. We present results on various transition-metal oxides, which include materials showing typical Fermi-liquid behavior, pseudogap behavior, charge–density wave formation, ‘stripe’ formation, etc.

Introduction

Since strongly correlated electron systems are characterized by their unusual magnetic and charge responses [1], the measurements of these responses are of utmost importance to understand their complex behaviors. While the energy- and momentum-dependent magnetic susceptibility χ(q, ω) has been extensively studied by inelastic neutron scattering, and its static limit by nuclear magnetic resonance and magnetic susceptibility measurements, the corresponding information about the charge susceptibility χc(q, ω) has been rather limited. The dynamical susceptibility χc(q, ω) can in principle be measured by electron-energy-loss spectroscopy or inelastic X-ray scattering. The static (ω=0), uniform (q=0) limit of χc(q, ω) is the charge susceptibility χc∂n/∂μ, where n is the electron density and μ is the electron chemical potential or the Fermi level (EF), but few experimental studies have been reported so far on χc. The corresponding quantity in the magnetic response channel is the uniform magnetic susceptibility χ∂M/∂H, where M is the magnetization and H is the magnetic field. Because charge responses certainly play roles equally important to magnetic responses in strongly correlated systems, it is highly desired to develop a practical method to study the charge susceptibility.

In compounds where the band filling can be changed by chemically doping charge carriers, i.e. in filling-control systems, the uniform charge susceptibility can be determined by the rate of the chemical potential shift ∂μ/∂n through χc=(∂μ/∂n)−1. Because binding energies in photoemission spectra are measured referenced to the chemical potential μ, characteristic features in photoemission spectra should be shifted when the chemical potential is shifted. If there is no electron–electron interaction, the rate of the chemical potential shift ∂μ/∂n is simply given by the inverse of the bare electronic density of states Nb(μ) at the chemical potential:∂μ∂n=1Nb(μ).In an insulator, ∂n/∂μ vanishes unless states at μ are localized due to disorder. As one moves from p-type (hole) doping to n-type (electron) doping across the undoped insulator, μ should show a jump of the magnitude of the band gap.

The chemical potential shift in interacting electron systems, on the other hand, is not trivial, especially near a metal–insulator transition or when the system has peculiar charge responses such as charge–density wave formation and charge ‘stripe’ formation, as described below. In such cases, studies of the chemical potential shift gives particularly useful information about the electronic structures of interacting electron systems. In this article, we describe how one can deduce the chemical potential shift largely from measured core-level photoemission data and what one can learn from the chemical potential shift about the physics of strongly correlated systems.

Section snippets

Chemical potential shift in filling-control systems

The chemical potential of a many-electron system is defined as the increase of the Gibbs free energy density g per unit increase of the electron density: μ=∂g/∂n. Here, the neutralizing positive background charges, namely, the positive charges of ion cores, should increase by the same amount as the increase of the electronic charges to maintain the charge neutrality. If the charge neutrality is violated, a strong electrostatic field has to be applied from outside of the sample in order to

Applications to correlated electron systems

In the remainder of this article, we describe how the chemical potential shift measurements have been applied to filling-control systems, mostly transition-metal oxides, and how useful information can be obtained to understand strong correlation phenomena.

Conclusion

We have shown that the chemical potential shift as a function of band filling provides useful information about the electronic structure of filling-control systems. We have described how the chemical potential shift can be deduced from the measured shifts of core-level photoemission spectra and what information can be obtained from the chemical potential shift. Results are presented and discussed for cases where a rigid-band behavior, conventional CDW or charge ordering and charge stripe

Acknowledgements

This work was supported by a Grant-in-Aid for Scientific Research for a Priority Area ‘Novel Quantum Phenomena in Transition Metal Oxides’, a Grant-in-Aid for Scientific Research A12304018 and a Special Coordination Fund for the Promotion of Science and Technology from the Ministry of Education, Culture, Sports, Science and Technology.

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