Fig. 2: Landau level spreading of a generic system with an IFB.
From: Geometric characterization of anomalous Landau levels of isolated flat bands
a Lattice structure for the spin–orbit-coupled (SOC) Lieb model composed of three sublattices, A, B and C. The double-headed green arrows denote the nearest neighbor hoppings, and the single-headed green arrows indicate the spin–orbit coupling between A and C sublattices. The next-nearest hoppings t between A and C is set to be zero (t = 0.0) in the SOC Lieb model. b The band structure of HsocL(k) with λsoc = 0.2. c Distribution of \({{{{{{{\rm{Im}}}}}}}}\ {\chi }_{{{{{{{{\rm{socL}}}}}}}},xy}^{{{{{{{{\rm{fb}}}}}}}},-}({{{{{{{\bf{k}}}}}}}})\). Note that \({{{{{{{\rm{Im}}}}}}}}\ {\chi }_{{{{{{{{\rm{socL}}}}}}}},xy}^{{{{{{{{\rm{fb}}}}}}}},-}({{{{{{{\bf{k}}}}}}}})=-{{{{{{{\rm{Im}}}}}}}}\ {\chi }_{{{{{{{{\rm{socL}}}}}}}},xy}^{{{{{{{{\rm{fb}}}}}}}},+}({{{{{{{\bf{k}}}}}}}})\). d The modified band dispersion \({E}_{{{{{{{{\rm{fb}}}}}}}},B}^{{{{{{{{\rm{socL}}}}}}}}}({{{{{{{\bf{k}}}}}}}})\) of the flat band in the presence of magnetic flux. e Landau level spectra of the flat band (black dots) as a function of λsoc for magnetic flux ϕ/ϕ0 = 1/500. f Landau level spectra of the flat band (black dots) as a function of magnetic flux ϕ/ϕ0 for λsoc = 0.2.
