The ideal limit of rhombohedral graphene: Interaction-induced layer-skyrmion lattices and their collective excitations

TL;DR

The paper identifies an analytically tractable ideal limit of rhombohedral graphene on hBN where short-range interactions stabilize a layer-pseudospin skyrmion lattice, generating an emergent magnetic field and a $C=1$ Chern band. It develops a real-space formalism showing exact zero-energy ground states in the ideal limit, introduces a dispersion-aware ansatz that remains near-optimal as dispersion is turned on, and demonstrates a continuous connection to realistic $\text{R}^5\text{G}/\text{hBN}$ via adiabatic interpolation. The authors map the ground-state texture to magnetic Bloch states and reveal a rich spectrum of collective excitations—gapless phonons and higher-order chiral shape modes—organized by skyrmion-lattice dynamics, with clear experimental signatures in layer-resolved densities and spectroscopic probes. They further connect this real-space physics to broader frameworks such as parton constructions and potential fractional Chern insulating states, offering a unified lens on topology induced by interactions in moiré graphene, and suggesting concrete routes to observe skyrmion-related dynamics in STM, Raman, and THz measurements.

Abstract

We introduce an ideal limit of rhombohedral graphene multilayers. In this limit, we show analytically how short-range repulsion stabilizes a layer-pseudospin skyrmion lattice, which generates an effective magnetic field and gives rise to a Chern band. This establishes the real-space origin of interaction-driven topology in moiré rhombohedral graphene. The resulting interaction-induced skyrmion lattice is physically analogous to magnetic skyrmion crystals and hosts a hierarchy of collective excitations naturally described within the framework of skyrmion-lattice dynamics.

Figures (15)

• Figure 1: The single particle bands of realistic and ideal R$N$G. Band structures of the (A) realistic ($h_{\text{real}}$) and (B) ideal ($h_{\text{flat}}$) single-particle models for R$5$G. The first conduction band is highlighted in blue. Insets illustrate the layer- and sublattice-resolved densities of a representative state. Berry curvature $\Omega({\bm{k}})$ of the first conduction band of (C) $h_{\text{real}}$ and (D) $h_{\text{flat}}$.
• Figure 2: Visualizing the layer pseudospin skyrmion lattice in ideal R$2$G. The amplitude of (A) $|\chi_0({\bm{r}})|$ and (B) $|\chi_1({\bm{r}})|$, for the example $\chi_0=w_0$ defined in the main text. As discussed in the main text, $\chi_0({\bm{r}})$ can be viewed an Abrikosov antivortex lattice with a node at each skyrmion core. (C) The direction of the normalized pseudospinor $\hat{\bm{\chi}}({\bm{r}})\equiv\bm{\chi}({\bm{r}})/|\bm{\chi}({\bm{r}})|$ on the Bloch sphere, with the color indicating the $z$-component. Because $\hat{\bm{\chi}}({\bm{r}})$ wraps the Bloch sphere once per unit cell, this texture realizes a skyrmion lattice with winding number $N_\phi=1$.
• Figure 3: Hartree-Fock (HF) phase diagram of dispersive ideal R$5$G with parabolic dispersion $\mathcal{E}({\bm{k}})=\alpha|{\bm{k}}|^2$. (A) The phase diagram as a function of $\alpha/V_0$ and density $\rho/\rho_\gamma$. Here, $\rho_{\gamma}=1/(4\pi\gamma^2)$ is the density of a circular Fermi surface with radius $k_F=\gamma^{-1}$. (B) The momentum distribution function $n({\bm{k}})$ at several points in the phase diagram along $\rho=0.833\rho_\gamma$ [indicated by the colored points in (A)]. The shaded blue region shows $n({\bm{k}})$ of the ansatz, Eq \ref{['eq:nk']}, with the shading width indicating the angular variation. As $\alpha\rightarrow 0$, the HF state approaches the ansatz wavefunction Eq \ref{['eq:final_psi_nu1']}, with a near-unity per-particle overlap $(|\langle\Psi^{\text{HF}}|\Psi^{\text{ansatz}}\rangle|^2)^{\frac{1}{N_e}}\approx 0.997$.
• Figure 4: Connecting the real and ideal limits of $\theta=0.6^\circ$ R$5$G/hBN at $\nu=1$, corresponding to $\rho=0.3\rho_\gamma$. (A) The momentum distribution function $n({\bm{k}})$ at several parameter values interpolating from real ($\lambda=0,V_0=0$) to ideal ($\lambda=1, V_0$ large) showing a smooth evolution. Inset shows the trace condition violation $T$ along this interpolation. For real R$5$G/hBN, (B) top-layer charge density and (C) the total charge density. The top-layer charge density exhibits a pronounced near-zero at the skyrmion cores, relative to the total charge which exhibits a fairly shallow minimum. In the ideal limit, (D) the top-layer charge density has an exact zero, and (E) is the corresponding effective magnetic field. For details of model parameters, see SM supp.
• Figure 5: Collective excitations of dispersive ideal R$5$G at $\rho=0.3\rho_\gamma$ in the limit $\alpha\rightarrow 0$. (A) The TDHF spectrum shows two gapless phonon branches and a ladder of weakly dispersing excitations, labeled by $n$, which we identify as $n$-fold shape distortions of the layer skyrmion texture. Also shown are spectra calculated from $\chi$-TDVP and the single-mode approximation (SMA) as described in the main text. The top-layer charge density $\rho_{\ell=0}({\bm{r}},t)$ at two time instances for a coherent excitation of the (B,C) quadrupolar ($n=2$) and (D,E) sextupolar ($n=3$) shape modes. For technical details, see SM supp.