# Impact of strong correlations on a band topological insulator on the Lieb lattice

## TL;DR

This paper investigates how strong electron correlations affect the topological and insulating properties of a Lieb lattice with spin-orbit coupling, revealing a transition from a correlated flat band insulator to a Mott insulator while preserving topological edge states.

## Contribution

It introduces a slave rotor mean field approach to study correlation effects on a topological Lieb lattice, showing the stability of topological phases up to a critical interaction and the emergence of mixed edge modes.

## Key findings

- Stable topological flat band insulator up to critical U
- Transition to Mott insulator with spectral weight transfer
- Presence of edge modes with contributions from spinons and electrons

## Abstract

The Lieb lattice possesses three bands and with intrinsic spin orbit coupling $\lambda$, supports topologically non-trivial band insulating phases. At half filling the lower band is fully filled, while the upper band is empty. The chemical potential lies in the flat band (FB) located at the middle of the spectrum, thereby stabilizing a flat band insulator. At this filling, we introduce on-site Hubbard interaction $U$ on all sites. Within a slave rotor mean field theory we show that, in spite of the singular effect of interaction on the FB, the three bands remain stable up to a fairly large critical correlation strength ($U_{crit}$), creating a correlated flat band insulator. Beyond $U_{crit}$, there is a sudden transition to a Mott insulating state, where the FB is destroyed due to complete transfer of spectral weight from the FB to the upper and lower bands. We show that all the correlation driven insulating phases host edge modes with linearly dispersing bands along with a FB passing through the Dirac point, exhibiting that the topological nature of the bulk band structure remains intact in presence of strong correlation. Furthermore, in the limiting case of $U$ introduced only on one sublattice where $\lambda=0$, we show that the Lieb lattice can support mixed edge modes containing contributions from both spinons and electrons, in contrast to purely spinon edge modes arising in the topological Mott insulator.