Understanding Mott transitions in a two-band model

By Tom Sharp on September 30, 2016

A recent theoretical work in Journal of Physics: Condensed Matter by David Logan, Martin Galpin and Jonathan Mannouch uncovers new results for the Mott transition in the periodic Anderson model. We find out more from the authors below:

Strong Coulomb repulsion between electrons in solids can lead to behaviour inexplicable in terms of independent electrons filling energy bands. A classic example is the Mott metal-insulator transition, occurring when a metal – a partially-filled band – is driven to an insulator as electron-electron interactions increase through a critical strength. Roughly speaking, the electrons collectively localise around individual nuclei, rather than delocalising across the solid, because it reduces their overall mutual repulsion.

The basic ingredients for the Mott transition are found in the well-known Hubbard model. Each atom provides a single orbital, between which electrons may tunnel, but electrons in the same orbital repel each other. Much work has of course been devoted to the study of this deceptively simple model, and its Mott transitions have been studied in detail.

In our paper, we examine Mott transitions in the periodic Anderson model (PAM). Like the Hubbard model, the PAM involves a core orbital around each nucleus, where electrons interact. But instead of tunnelling directly between the core orbitals, the electrons go via an additional set of extended orbitals. Such a ‘two-band’ picture shows richer behaviour, relevant to the physics of transition metal oxides and lanthanide-based heavy-fermion compounds.

We show that, close to the Mott transition, the PAM in the ‘DMFT- limit’ of large spatial dimensions maps precisely onto an effective, long-ranged Hubbard model. Using some exact results and physically-motivated approximations, we can then predict when Mott transitions will occur in the PAM. Remarkably, we find for example that a Mott transition may still arise in the PAM when the Coulomb interaction is arbitrarily weak relative to the interorbital tunnelling strength, since it must only be strong compared to a renormalised tunnelling energy that can be very much smaller. We also derive several exact results for the PAM Mott insulator phase itself, using our recently-developed approach that generalises diagrammatic many-body perturbation theory to systems with degenerate ground states.

We complement the analysis by detailed numerical calculations. These confirm the mapping and our exact results, and provide tangible examples of the famous Zaanen-Sawatzky-Allen diagram used for classifying transition metal oxides.

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