Emergence and transition of incompressible phases in decorated Landau levels

TL;DR

The paper shows that dressing a single Landau level with a periodic electrostatic potential creates a decorated Landau level (dLL) consisting of exact zero-energy Chern subbands separated from dispersive bands, enabling diverse incompressible topological phases where σ_xy can differ from the LL filling. By analyzing magnetic translations, Berry curvature, and one-body potential effects, the authors establish a minimal, tunable framework in which Laughlin and non-Abelian (Moore–Read) states can emerge within the dLL under realistic interactions, including screened Coulomb and short-range models. They provide a concrete method to compute conductivities via twisted boundary phases, demonstrate the equivalence of dLL projections to LLL physics, and explore the role of dLL graviton modes, concluding that graviton lifetimes are typically short in the lattice-dominated regime. The results illuminate how lattice-scale geometry and interparticle interactions conspire to realize rich 2D quantum fluids in both lattice/moiré and engineered LL platforms, with tunable experimental pathways. Overall, the work introduces dLL as a versatile, controllable arena for exploring quenched, interacting topological phases and their collective excitations.

Abstract

We show a single Landau level (LL) dressed with periodic electrostatic potentials can realize a plethora of interacting topological phases where the Hall conductivity generally does not equal to the LL filling factor. Their physics can be captured by a minimal model of a delta potential lattice within a single LL, realizing exact zero energy Chern bands (denoted as decorated Landau levels or dLL) gapped from dispersive bands with rich geometric properties. With $p/q$ magnetic fluxes per unit cell, there are $q$ dispersive bands and $p-q$ zero energy bands forming the dLL. When the one-body potential strength dominates the electron-electron interaction, band mixing is suppressed and the dispersion bands consist of ``localized states" with vanishing total Chern number. Nevertheless these dispersive bands can have highly nontrivial Berry curvature distribution, and even non-zero Chern numbers when $q>1$. Interestingly even in the limit of large short range interaction, band mixing between dLL and dispersion bands can be strongly suppressed at low filling factor, leading to robust topological phases within the dLL stabilized by the one-body potential. The dLL and the associated dispersive bands can serve as minimal theoretical models for correlated physics in lattice or moire systems; they are also highly tunable experimental platforms for realizing rich phase diagrams of exotic 2D quantum fluids.

Figures (12)

• Figure 1: (a) Schematic illustration of LLL splitting into dispersive bands and the dLL due to the local potential lattice. BC: Berry Curvature. The color scale gives the Berry Curvature. (b) Electron density in real space with a fully filled dLL, leading to an integer quantum Hall (IQHE) phase.
• Figure 2: Schematics of occupation on the dLL and the trivial band in the presence of $V_{int}$ and delta potential lattice. Panels (a)–(d) correspond to the regime of interaction as a perturbation, whereas panels (e) and (f) correspond to the regime of dominating interaction. In particular for (f) band mixing is suppressed if the dLL is partially filled with short range interaction.
• Figure 3: (a) Schematic of the spectrum evolution with $\lambda$ (left) and the graviton mode (GM) behavior (right). The calculation uses the $V_1$ pseudopotential at $\nu_l = 1/6$ with $N_\delta = N_o/2$. In the small–$\lambda$ regime of the spectrum, the purple region denotes states outside the $V_1$ nullspace $\mathcal{H}_1$, while the red and blue regions represent Laughlin quasihole states inside and outside the dLL Hilbert space $\mathcal{H}_\delta$, and there is a single GM peak $G_0$. As $\lambda$ increases, mixing between these sectors causes $G_0$ to split into two components: $G_1$ that gains strength within $\mathcal{H}_\delta$, and $G_2$ that remains outside the dLL. For $\lambda > \lambda_2$, $G_1$ saturates as the dominant peak within dLL, while $G_2$ is pushed to higher energies. (b) Finite size scaling of the GM energy for $\lambda > \lambda_2$. The variational energy with respect to $V_{\delta} = \lambda V_{local}$ is normalized by $\lambda$ to allow comparison across different values of $\lambda$. The finite size trend indicates that the GM asymptotically resides within the dLL. (c) Spectral function of the dLL GM at large $\lambda$. In the regime dominated by the lattice potential, as illustrated in Fig. \ref{['fig2']}g, the GM peak decays rapidly with increasing system size, indicating that GMs in the dLL acquire a short lifetime.
• Figure 4: Phase diagram of the Hamiltonian in Eq. (\ref{['vint']}). The blue, grey, red and black area indicate Fermi liquid, correlated metal, topological phases, and insulating phase, respectively. The values on the topological phases indicate the conductivity of the phase in the unit of $e^2/ h$. (a) Phase diagram for interaction $V_1$. (b) Phase diagram for Yukawa interaction, $V(\bm{r})=\frac{e^{-|\bm{r}|/d}}{|\bm{r}|}$. (c) Phase diagram for Yukawa interaction when $\lambda>0$, $\nu_{dl}=1/3$ and dispersive bands are empty. The scale of the color shows the scale of the FQH gap. (d) Same as (c) but for $\lambda<0$, so $\nu_{dl}=1/3$ and dispersive bands are fulled filled footnote3.
• Figure S1: The energy dispersion and Berry Curvature distribution of $p=6$ and $q=5$ case. BC: Berry Curvature. (a) Berry Curvature of the highest dispersive band. (b) Energy dispersion of the highest band. (c) Berry Curvature of the lowest band (dLL). (d) Spectra of $p=6$ and $q=5$, in which the highest dispersive band has Chern number 1.