Fractional quantum Hall effect of Bose-Fermi mixtures

Abstract

Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. Here, we report the theoretical discovery of fractional quantum hall effect of strongly correlated Bose-Fermi mixtures classified by the $\mathbf{K}=\left(\begin{array}{cc}m& 1\\ 1& n\end{array}\right)$ matrix (even $m$ for boson and odd $n$ for fermion), using topological flat band models. Utilizing the state-of-the-art exact diagonalization and density-matrix renormalization group methods, we build up the topological characterization based on three inherent aspects: (i) topological $(mn-1)$-fold ground-state degeneracy equivalent to the determinant of the $\mathbf{K}$ matrix, (ii) fractionally quantized topological Chern number matrix equivalent to the inverse of the $\mathbf{K}$ matrix, and (iii) two parallel-propagating chiral edge branches with level counting $1,2,5,10$ consistent with the conformal field theory description.

arXiv comment6 pages, 5 figures; revised version

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• Recent Developments in Fractional Chern Insulators
• Halperin $(m^{\prime },m,n)$ fractional quantum Hall effect in topological flat bands
• Integer quantum Hall effect of two-component hardcore bosons in a topological triangular lattice
• Three-component fractional quantum Hall effect in topological flat bands