Progress on artificial flat band systems: classifying, perturbing, applying

Abstract

We highlight recent progress in the study of artificial flat band systems with a threefold focus. First, we discuss single-particle flat band physics, which has advanced through the design of various flat band generators. These generators rely on the classification of flat bands in terms of compact localized states - their fundamental building blocks. A related development is the complete real-space description of flat band projectors. Next, we review studies on perturbations of flat bands, which provide new insights into the effects of disorder and, more importantly, the intricate interplay between many-body interactions and flat band physics. Finally, we survey the growing number of experimental realizations of flat bands across diverse physical platforms.

Figures (3)

• Figure 1: (a) Generalized checkerboard lattice. The hopping strengths are equal to $1$ (red lines), $A$ (black lines) and $A^2$ (blue lines). The CLS amplitudes are colored in black. (b) Orthogonal flat bands at $E=\pm1$ achieved for $A=0$. (c) Linearly independent flat band at $E=-5/4$ (red) gapped from the dispersive band (blue), achieved for $A=0.5$. (d) Linearly dependent flat band at $E=-2$ (red) touching the dispersive band (blue), achieved for $A=1$. This figure is inspired from some of the results presented in kim2025real.
• Figure 2: (a) Eight bands comb structure with flat bands $E=\pm t_2$. Projection of the eigenstates onto the Néel state, with the scars highlighted with crosses at $E=0,\pm2t_2,\pm4t_2$. Return probability $\mathcal{R}$ of a Néel state excitation. Reprinted with permission from Ref. hart2020compact. (b) Two examples of many-body flat band lattices supporting Hilbert space fragmentation for interacting bosons (top) and hardcore bosons (bottom). Reprinted with permission from Refs. danieli2020manylee2024trapping. (c) Top: Dice lattice with pseudomagnetic field (red color); potential landscape and pseudomagnetic field for a possible implementation. Bottom: Berry connection; Berry curvature; trace of the quantum metric tensor of the singular flat band. Reprinted with permission from Ref. yang2025fractional.
• Figure 3: (a) Acoustic platform. Top: configurations of the acoustic waveguide arrays driven via a pumping loop. Bottom: simulated sound wave propagation (left) and measured pressure at discrete locations along the waveguides. Reprinted with permission from Ref. you2022observation. (b) Superconducting transmon qubit platform. Left top: zero-flux plaquette, with zoomed qubit orientations that yield zero (left) and $\pi$-flux (right) plaquette. Left bottom: detailed hopping profile of the $\pi$-flux plaquette (left) and single particle eigenbasis (right). Right: average qubit populations in the different qubits of the plaquette as function of time for single photon particle (top) and two interacting photon particles (bottom). Reprinted with permission from Ref. martinez2023interaction.