Quantum Phase Transition And Topological Flat Bands In2D Tight-binding Electrons Under The Modulation Of Staggered Magnetic Field

Recently, several models with nearly flat bands and nontrivial topology in absence ofLandau levels have been proposed. Systematic numeric works exhibited convincingevidences of the existence of fractional quantum Hall (FQH) phases of interacting fermionsand hard-core bosons in topological flat bands (TFB) models. TFB with C=2was alsoconstrcuted on the dice lattice, which may lead to the edge theory be SU(3) level-2.Thisfractional quantum states which carries non-Abelian statistics have important applicationsfor performing tolerant topological quantum computation.A peculiar staggered–flux driven topological quantum phase transition ontwo-dimensional triangular lattice filled with tight-binding electrons is studied in detail.The total magnetic fields have a uniform flux with strength φ and a staggered flux withstrength φ. When the uniform flux strength is fixed, the variation of staggered fluxstrength leads to the quantized Hall conductance exhibiting a direct transition and theredistribution of Chern number between neighboring Landau subbands. The phasetransition is robust against weak disorder. The calculation of the total free energy of thesystem shows the phase transition is a3rd order phase transition. The ground state fidelitysusceptibility is studied under the modulation of staggered flux. Moreover, the evolution ofBerry curvature in Brillouin zone shows convincing evidence for exchange of Chernnumber between neighboring bands at the transition point.Nearly flat band model with Chern number C=1paved a new path to obtain theFQH states in lattice systems. We study nearly flat band with higher Chern number in triangular lattice under staggered-modulated flux. Numeric calculation of Hall conductanceand edge states show the flat band carries non-trivial topological property. Calculation ofBerry curvature distribution in the momentum space exhibits the strong similarity betweenTFB and Landau level. Interestingly, nearly flat band with different Chern numbers can beobtained only through the tuning of staggered flux strength. It provides a new platform forthe study of phase transition between different FQH phases.