# Self-doping effect arising from electron correlations in multi-layer cuprates

## TL;DR

This paper investigates the self-doping effect in multi-layer cuprate superconductors, showing that electron correlations lead to electron distribution patterns consistent with experimental observations, which differ from simple band-structure predictions.

## Contribution

The study introduces a three-layer Hubbard model with a two-particle self-consistent approach to explain electron distribution due to correlations, revealing a self-doping mechanism.

## Key findings

- Electron correlations cause more electrons to enter inner planes than outer planes.
- Double occupancy decreases more in inner planes, indicating stronger correlations.
- Results align with experimental observations of electron distribution.

## Abstract

A self-doping effect between outer and inner CuO$_2$ planes (OPs and IPs) in multi-layer cuprate superconductors is studied. When one considers a three-layer tight-binding model of the Hg-based three-layer cuprate derived from the first principle calculations, the electron concentration gets to be large in the OP compared to IP. This is inconsistent with the experimental fact that more hole carriers tend to be introduced into the OP than IP.We investigate a three-layer Hubbard model with the two-particle self-consistent approach for multi-layer systems to incorporate electron correlations. We observe that the double occupancy (antiferromagnetic instability) in the IP decreases (increases) more than the OP, and also reveal that more electrons tend to be introduced into the IP than OP to obtain the energy gain from the on-site Hubbard interaction. These results are consistent with the experimental facts, and this electron distribution between the OP and IP can be interpreted as a self-doping effect arising from strong electron correlations.