Topological Flat Minibands and Fractional Chern Insulators in Rashba Systems with Tunable Superlattice Potentials

Abstract

We propose a programmable platform for engineering topological flat minibands by imposing a tunable electrostatic superlattice potential on a Rashba spin-orbit-coupled thin film subject to a Zeeman field. The interplay between the superlattice potential and Zeeman coupling produces an isolated flat miniband with Chern number $\mathcal{C}=1$. Using many-body exact diagonalization, we show that this miniband supports fractional Chern insulators at filling factors $n = 1/3$ and $2/3$, both of which remain robust over broad parameter ranges. We further identify realistic material candidates and the corresponding device conditions that enable experimental realization. These results establish a versatile and experimentally accessible platform for engineering topological flat minibands and exploring correlated topological phases.

Figures (5)

• Figure 1: (a) Schematic of the proposed setup, consisting of a Rashba material sandwiched between a ferromagnetic (FM) insulator and a patterned dielectric layer. (b) Representative miniband structure for a superlattice potential with period $L=15$ nm. (c) Berry curvature $\Omega$ of the 1st miniband shown in (b), with the dashed hexagon denoting the MBZ. (d) Trace of the Fubini-Study metric $\text{Tr}(g)$ of the 1st miniband. The units for both $\Omega$ and $\text{Tr}(g)$ are $2\pi/A_{\text{MBZ}}$, with $A_{\text{MBZ}}$ denoting the area of MBZ. These results are obtained with $\tilde{\lambda}=0.4$, $\tilde{V}_z=0.12$, and $\tilde{U}_0=0.03$ (corresponding to $U_0\approx6$ meV).
• Figure 2: (a)-(d) Evolution of the miniband structure upon sequentially adding $\tilde{U}_0$ and $\tilde{V}_z$ to the model described by Eq. (\ref{['eq:dimensionlessH']}). Dashed circles and squares in (b) highlight band degeneracies at high-symmetry points of the MBZ. These results are obtained with $\tilde{\lambda} = 0.4$.
• Figure 3: (a) Bandwidth $W$ of the 1st miniband and direct band gap $\Delta$ as functions of $\tilde{V}_z$. (b) $W$ and $\Delta$ as functions of $\tilde{U}_0$. These results are obtained using $\tilde{U}_0=0.03$ for (a), $\tilde{V}_z=0.12$ for (b), and $\tilde{\lambda}=0.4$ for both panels.
• Figure 4: (a)-(c) Phase diagrams of (a) direct band gap $\Delta$, (b) bandwidth $W$, and (c) their ratio $\Delta/W$ as functions of $\tilde{\lambda}$ and $\tilde{V}_z$. White dashed lines indicate gap-closing boundaries, separating the parameter sapce into several regions with corresponding Chern number $\mathcal{C}$ marked. The region labeled $s$ in (a) denotes $\mathcal{C}=-2$. Results in (a)-(c) are obtained with $\tilde{U}_0=0.03$. (d)-(f) Phase diagrams of (d) $\Delta$, (e) $W$, and (f) $\Delta/W$ as functions of $\tilde{U}_0$ and $\tilde{V}_z$, calculated with $\tilde{\lambda} = 0.4$.
• Figure 5: (a),(b) Many-body spectra for filling factors (a) $n=1/3$ and (b) $n=2/3$. (c),(d) Spectral flow of the ground states under magnetic flux insertion, with the three nearly degenerate states distinguished by colors. Results in (a)-(d) are obtained with $\tilde{\lambda}=0.6$, $\tilde{V}_z=0.28$, and $\tilde{U}_0=0.03$. (e),(f) Excitation gaps $E_{gap} = E_{4}-E_3$ as functions of $\tilde{V}_z$ for (e) $\tilde{\lambda}=0.6$ and (f) $\tilde{\lambda}=0.4$, where $E_{i}$ denotes the $i$-th lowest energy state. All these results are obtained on a $5\times 6$ cluster with dielectric constant $\epsilon=5$.