Abstract
We derive an effective low-energy Hamiltonian for potassium loaded zeolite A, a unique ferromagnet from non-magnetic elements. We perform ab initio density functional calculations and construct maximally localized Wannier functions for low-energy states made from potassium s electrons. The resulting Wannier orbitals, spreading widely in the alminosilicate cage, are found to be the superatomic s and p orbitals in the confining potential formed by the host cage. We then make a tight-binding model for these superatomic orbitals and introduce interaction parameters such as the Hubbard U . After mean-field calculations for the effective model, we find that ab initio spin density functional results are well reproduced by choosing appropriate sets of the interaction parameters. The interaction parameters turn out to be as large as the band width, ∼0.5 eV, indicating the importance of electron correlation, and that the present system is an interesting analog of correlated multi-orbital transition metal oxides.
Highlights
Electron correlation in materials, which often causes various non-trivial phenomena, has been one of the central issues in condensed matter physics
Recent ab initio calculations have elucidated that the band dispersion around the Fermi level is well represented by a very simple tightbinding model,3–8) suggesting that correlation effects in lowenergy physics of zeolites can be systematically described by the many-body superatom model
From the six bands around the Fermi level, we constructed the maximally localized Wannier functions for the geometry I and II (III and IV), which are employed as bases of the effective Hamiltonian in eq (3)
Summary
Electron correlation in materials, which often causes various non-trivial phenomena, has been one of the central issues in condensed matter physics. The host alminosilicate cage makes a gap of several eV, in which the guest alkali s-electrons form a few narrow bands around the Fermi level This situation is described by the so-called superatom picture,1–3) where each zeolite cage is regarded as a huge atom. The term H0 describes the kinetic-energy part of the effective model, where im and timjm[0] are the ionization potential and transfer, respectively In this model, we take into account of the superatom p states in the cage and the superatom s states in the cage, which lie just above the Fermi level as explained . We can estimate the interaction and selfinteraction parameters, U , U , U0 , J , S , and S , by fitting the model band dispersion to the ab initio spin density functional results
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