SU(4) Kondo Lattice in Semiconductor Moiré Materials

TL;DR

This work proposes SU(4) Kondo lattices in semiconductor moiré multilayers as a route to rich correlated and topological phases. It derives an effective SU(4) Kondo lattice Hamiltonian via a Schrieffer-Wolff transformation, incorporating a three-site exchange $J_3$ in addition to the two-site exchange $J_2$ and Kondo coupling $J_K$, and analyzes the phase diagram using a parton mean-field approach. In the Kondo-unscreened regime, the $f$-sector forms Mott insulators such as plaquette order, a chiral spin liquid with quantized flavor Hall response, and a decoupled-chain state; with doping, a heavy Fermi liquid emerges that can exhibit lattice symmetry breaking and anomalous Hall signals. The study outlines experimental realizations in MoTe$_2$/WSe$_2$ heterobilayers and twisted TMD multilayers, offering a versatile platform to explore SU(4) spin physics and topological metal phases in moiré systems.

Abstract

Motivated by recent advances in transition metal dichalcogenide (TMD) moiré materials, we propose TMD moiré multilayers as a platform for realizing an approximately SU(4)-symmetric triangular Kondo lattice, generalizing the concept of the double quantum dot model. Our model extends the conventional Kondo lattice by incorporating a three-site exchange of SU(4) local moments, which drives spontaneous time-reversal and lattice symmetry breaking. Using a parton mean-field approach, we map out the phase diagram as a function of three-site exchange and hole doping. In the Kondo-unscreened regime, we identify Mott insulating phases, including bond-ordered states and a chiral spin liquid. With increasing doping, Kondo hybridization gives rise to a heavy Fermi liquid that exhibits distinct patterns of lattice symmetry breaking, with or without topological responses. We conclude with directions for future study.

Figures (5)

• Figure 1: Schematics of SU(4) Kondo lattices and phase diagram. (a) Schematic phase diagram at $\nu_f=1$ as a function of three-site exchange $J_3$ and $c$-hole filling $\nu_c$, with two-site exchange $J_2$ set to unity. Below the critical filling, the $f$-fermions are decoupled from the $c$-holes and form Mott insulators that host various bond-ordered phases---plaquette order, decoupled chain (DC)---as well as a chiral spin liquid (CSL). Above the critical filling, a Kondo transition to a heavy Fermi liquid occurs (red $\rightarrow$ purple). The heavy Fermi liquid (HFL) typically features various lattice symmetry breakings, with or without an anomalous Hall response. (b) TMD pentalayer Kondo lattice consisting of four identical layers and one distinct layer. The two layers adjacent to the middle layer are more correlated (red, $f$-layers) than the two outer layers (blue, $c$-layers). (c) Twisted AABB-stacked TMD tetralayer. A small twist angle $\theta$ is applied between the second (A) and third (B) layers. As in (b), the middle layers are more correlated than the outer layers.
• Figure 2: Self-consistent mean-field phase diagram at $\nu_f=1$ as a function of $J_3/J_2$ and $\nu_c$. The phase diagram is obtained for a $12\times12$ system with $(t_c/J_2,J_K/J_2)=(-3,2)$. (a) Density-tuned Kondo transition. Color coding represents the Kondo hybridization order parameter $\Phi$. In the Kondo-unscreened regime, the $f$-fermions form various Mott insulating phases: DC, CSL, and plaquette order. (b) Topological phase transition. Color coding represents the flavor Hall conductivity $\sigma_{\alpha,H}$. In the Kondo-unscreened regime, $\sigma_{\alpha,H}$ is quantized to unity in the CSL, reflecting the Chern number of the occupied spinon band. Other Mott insulators are topologically trivial. In the Kondo-screened regime, the heavy Fermi liquid can exhibit an anomalous Hall response $(0<\sigma_{\alpha,H}<1)$, which is mostly concentrated near the CSL, as indicated by the dashed line. (c) Lattice translation symmetry breaking. Color coding quantifies the strength of translation-symmetry breaking in bond orders. Blue corresponds to the $1\times1$ pattern, while red indicates either $2\times1$ or $2\times2$ patterns. $\Psi^{\mathrm{bdw}}$ is capped at 1 for clarity. (d) $C_3$ rotational symmetry breaking. Color coding quantifies the strength of $C_3$ symmetry breaking in bond strengths. See main text for the definition of $\Psi^{\mathrm{bdw}}$ and $\Psi^{C_3}$.
• Figure 3: Real space configuration of bond strengths $|\chi_{ij}|$ in the Kondo-unscreened regime
• Figure 4: HFLs with different symmetry breaking patterns. Bond strengths $(|\chi_{ij}|)$ and fermiology at representative parameter sets are shown. (a) $2\times 2$ CDW metal at $(J_3,\nu_c)=(0,1.47)$. (b) Chern metal at $(J_3,\nu_c)=(-0.2,0.38)$. (c) Quasi-1D metal at $(J_3,\nu_c)=(-0.4,0.33)$. Black hexagons represent the original and reduced Brillouin zones.
• Figure S1: Fermi surface (blue) of the triangular lattice tight-binding model at quarter filling, for (a) electron doping and (b) hole doping. (c) Largest eigenvalue of the polarization tensor across the first Brillouin zone, indicating an instability toward a bond order at the three M points.