Wigner crystallization in topological flat bands

Abstract

We study the Wigner crystallization on partially filled topological flat bands. We identify the Wigner crystals by analyzing the cartesian and angular Fourier transform of the pair correlation density of the many-body ground state obtained using exact diagonalization. The crystallization strength measured by the magnitude of the Fourier peaks, increases with decreasing particle density. The shape of the resulting Wigner crystals is determined by the boundary conditions of the chosen plaquette and to a large extent independent on the underlying lattice, including its topology, and follows the behavior of classical point particles.

arXiv comment41 pages, 12 figures. Accepted for publication in New J. Phys.; the discussion of finite size effects is extended, several additional comments are made. The results and interpretation are unchanged

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• Quantum states and intertwining phases in kagome materials
• Observation of topological flat bands in the kagome semiconductor Nb${}_3$Cl${}_8$
• Ferromagnetism and Wigner crystallization in Kagome graphene and related structures
• Disordered flat bands on the kagome lattice
• Screening 2D materials with topological flat bands
• Recent Developments in Fractional Chern Insulators
• Orbital Design of Flat Bands in Non-Line-Graph Lattices via Line-Graph Wavefunctions
• Realization of a two-dimensional checkerboard lattice in monolayer Cu${}_2$N
• Evolution of ultra-flat band in van der Waals kagome semiconductor Pd3P2(S1-xSex)8
• Electronic band structures of topological kagome materials
• Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals
• Flat bands without twists: periodic holey graphene
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• Reduced Wannier representation for topological bands
• Symmetry-Based Real-Space Framework for Realizing Flat Bands and Unveiling Nodal-Line Touchings