Exotic fractional topological states in a two-dimensional organometallic material

Abstract

Fractional Chern insulators (FCIs), having properties similar to those of the fractional quantum Hall effect, have been established numerically in various toy models. To fully explore their fundamental physics and to develop practical applications, material realization is indispensable. Here we theoretically predict a realization of FCI in a two-dimensional organometallic material, which is known to have the prerequisite topological flat bands. Using numerical exact diagonalization we demonstrate that the presence of strong electronic correlations and fractional filling of such a system could lead to a rich phase diagram, including Abelian fractional quantum Hall (FQH), Fermi-liquid, and Wigner crystal states. In particular, the FQH state has been confirmed systematically by calculating the topological ground-state degeneracies, topological Chern number, and the quasihole excitation spectrum as well as the particle entanglement spectrum. Future experimental realization of the FQH state in such material may provide a route for developing practical applications of FCI with no need of the extreme conditions.

Exotic electronic states in the world of flat bands: From theory to material

“…To see this competition quantitatively, let us calculate an example [52]. We will consider the XYH lattice.…”

Fractional quantum spin Hall effect in flat-band checkerboard lattice model

“…Here, we first calculate the static structure factor with charge and spin degrees of freedom 21 : Ψ|n(Ŝ) j |Ψ Ψ|n(Ŝ) l |Ψ ) , whereŜ i = 1 2 (n i↑ −n i↓ ) is a spin operator, and the wave function |Ψ is incoherent summation over the degenerate ground states, shown in Fig. 3(c).…”

“…Recently, a series of flat-band lattice models with nonzero Chern number, which belong to the same topological class as the Haldane lattice model, have been proposed [10][11][12] and demonstrated to host the fractional Chern insulating phases [12][13][14][15][16][17][18][19][20][21] when interacting particles partially fill up these topological flat bands. Such topological nontrivial states are examples of the fractional quantum Hall (FQH) effect without an external magnetic field.…”

Wigner crystallization in topological flat bands

“…Moreover, it was found that the charge ordering can coexist with topological ordering [73,75]. However, contrary to the Landau levels in which the Wigner crystallization occurs at arbitrarily low fillings, the short-range nature of interaction considered in [69][70][71][72][73][74][75] limits this effect to a certain filling factor.…”

“…Several authors investigated the charge ordering induced by short-range interaction at high filling factors [69][70][71][72][73][74][75]. Phase diagrams of various flat band models were obtained, showing the competition between the FCI and chargeordered ground state [71][72][73][74]. Moreover, it was found that the charge ordering can coexist with topological ordering [73,75].…”