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The Lieb lattice possesses three bands and with intrinsic spin orbit coupling$\lambda$, supports topologically non-trivial band insulating phases. At halffilling the lower band is fully filled, while the upper band is empty. Thechemical potential lies in the flat band (FB) located at the middle of thespectrum, thereby stabilizing a flat band insulator. At this filling, weintroduce on-site Hubbard interaction $U$ on all sites. Within a slave rotormean field theory we show that, in spite of the singular effect of interactionon the FB, the three bands remain stable up to a fairly large criticalcorrelation 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 theFB to the upper and lower bands. We show that all the correlation driveninsulating phases host edge modes with linearly dispersing bands along with aFB passing through the Dirac point, exhibiting that the topological nature ofthe bulk band structure remains intact in presence of strong correlation.Furthermore, in the limiting case of $U$ introduced only on one sublatticewhere $\lambda=0$, we show that the Lieb lattice can support mixed edge modescontaining contributions from both spinons and electrons, in contrast to purelyspinon edge modes arising in the topological Mott insulator.

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