Doped Mott insulators are insulators: hole localization in the cuprates

TL;DR

This paper shows that lightly doped Mott insulators like cuprates remain insulating at low temperatures due to hole localization caused by a pseudogap with vanishing density of states, independent of disorder.

Contribution

It reveals that the pseudogap in doped Mott insulators is tied to the non-commutativity of the limits of infinite Coulomb repulsion and system size, explaining hole localization.

Findings

Doped Mott insulators remain insulators at low temperature without disorder.

The pseudogap's energy scale is set by the singlet-triplet splitting.

Hole localization is linked to the vanishing density of states in the pseudogap.

Abstract

We demonstrate that a Mott insulator lightly doped with holes is still an insulator at low temperature even without disorder. Hole localization obtains because the chemical potential lies in a pseudogap which has a vanishing density of states at zero temperature. The energy scale for the pseudogap is set by the nearest-neighbour singlet-triplet splitting. As this energy scale vanishes if transitions, virtual or otherwise, to the upper Hubbard band are not permitted, the fundamental length scale in the pseudogap regime is the average distance between doubly occupied sites. Consequently, the pseudogap is tied to the non-commutativity of the two limits $U\to\infty$ ($U$ the on-site Coulomb repulsion) and $L\to\infty$ (the system size).