Anomalous Quantum Hall Bilayer Effect

Quantum Hall bilayers (QHB) are two-component fractional quantum Hall (FQH) systems that provide a unique platform to realize exotic Abelian/non-Abelian FQH and excitonic condensate states, but in the presence of a high magnetic field. Here, we show that these states can be realized in an analog of bilayer Kagome lattice with flat bands (FBs) in each layer, leading to anomalous quantum Hall bilayer effect, without magnetic field. Using exact diagonalization of finite size bilayer Kagome lattices, we demonstrate the stabilization of excitonic condensate Halperin's (1,1,1) and (3,3,3) state at the total filling and of the two FBs, respectively. We further show that by tuning the interlayer tunneling at , one can expect a phase transition from Halperin's (3,3,0) state to particle-hole conjugate of Laughlin's 1/3 state, as previously observed in QHB systems. Our work significantly enriches the field of FB physics by demonstrating bilayer FB systems as an attractive avenue for realizing exotic QHB states without magnetic field.