[Paper Review] Kondo lattice model in magic-angle twisted bilayer graphene

Yang-Zhi Chou, S. Das Sarma|arXiv (Cornell University)|Nov 28, 2022

Graphene research and applications4 citations

TL;DR

This paper proposes a Kondo lattice model in magic-angle twisted bilayer graphene (MATBG) using the topological heavy fermion (THF) representation, where $SU(8)$ local moments on a triangular lattice hybridize with delocalized $c$ fermions. It identifies a fragile topological Dirac Kondo semimetal at $ =0$, resolving the transport-STM discrepancy, and maps a quantum phase diagram showing Kondo hybridization suppression near an $SU(8)$ Heisenberg model on a triangular lattice.

ABSTRACT

We systematically study emergent Kondo lattice models from magic-angle twisted bilayer graphene using the topological heavy fermion representation. At the commensurate fillings, we demonstrate a series of symmetric strongly correlated metallic states driven by the hybridization between a triangular lattice of $SU(8)$ local moments and delocalized fermions. In particular, a (fragile) topological Dirac Kondo semimetal can be realized, providing a potential explanation for the symmetry-preserving correlated state at $ν=0$. We further investigate the stability of the Dirac Kondo semimetal by constructing a quantum phase diagram showing the interplay between Kondo hybridization and magnetic correlation. The destruction of Kondo hybridization suggests that the magic-angle twisted bilayer graphene may be on the verge of a solid-state quantum simulator for novel magnetic orders on a triangular lattice. Experimental implications are also discussed.

Motivation & Objective

• To resolve the experimental contradiction between semimetallic transport and local correlation signals at $ =0$ in MATBG.
• To construct a Kondo lattice model using the topological heavy fermion (THF) representation for strongly correlated MATBG physics.
• To investigate the stability of the Dirac Kondo semimetal phase under magnetic correlations.
• To explore the emergence of exotic magnetic order, such as an $SU(8)$ Heisenberg model on a triangular lattice, in MATBG.

Proposed method

• Uses the topological heavy fermion (THF) representation to map MATBG flat bands onto a hybridization between localized $f$ fermions (forming $SU(8)$ moments) and delocalized $c$ fermions.
• Constructs a Kondo lattice Hamiltonian with Kondo hybridization $V^{( u)}_{\alpha a}(\bm{q})$ between $f$ orbitals at AA-stacking sites and $c$ fermions in continuous space.
• Solves self-consistent equations for the Kondo hybridization amplitude $B$, coherence factor $\chi$, and chemical potentials $\mu_f$, $\mu_c$ using a $30\times30$ momentum mesh.
• Performs finite-size analysis with $n=30$ and $n=37$ momentum mesh to assess convergence and identify a threshold $J_K \approx 0.01$ eV for Kondo hybridization.
• Constructs a quantum phase diagram by introducing Heisenberg exchange interactions among nearest-neighbor $f$ moments to probe magnetic order.
• Uses Hartree-Fock-like self-consistent mean-field theory to compute quasiparticle dispersions and analyze band reconstruction.

Experimental results

Research questions

• RQ1 Can a Kondo lattice model explain the coexistence of semimetallic transport and local correlations at $ =0$ in MATBG?
• RQ2 What is the nature of the correlated metallic state at $ =0$ when $SU(8)$ local moments hybridize with delocalized $c$ fermions?
• RQ3 How does Kondo hybridization compete with magnetic correlations in the presence of Heisenberg exchange?
• RQ4 Does the system host a fragile topological Dirac Kondo semimetal phase, and what are its stability conditions?
• RQ5 Can MATBG be viewed as a solid-state quantum simulator for exotic $SU(8)$ magnetic orders on a triangular lattice?

Key findings

• A fragile topological Dirac Kondo semimetal is realized at $ =0$ due to hybridization between $SU(8)$ local moments and delocalized $c$ fermions, providing a resolution to the $ =0$ transport-STM paradox.
• The Kondo hybridization amplitude $|B|$ is finite only for $J_K \gtrsim 0.01$ eV, indicating a threshold for Kondo screening in the thermodynamic limit.
• For $N_f=4$ ($\nu=0$), the quasiparticle dispersion shows a Dirac-like cone with a bandwidth of approximately $2M \approx 0.0074$ eV, consistent with fragile topology.
• The Kondo hybridization amplitude $|B|$ is maximized at $N_f=4$ and decreases for $|N_f - 4| > 0$, indicating strongest screening at half-filling of $f$ orbitals.
• Phase transitions occur at $J_K \approx 0.024$ eV ($N_f=1$) and $J_K \approx 0.036$ eV ($N_f=2$), marked by accidental band touching in the low-energy bands.
• The system is on the verge of realizing an $SU(8)$ Heisenberg model on a triangular lattice, suggesting MATBG as a quantum simulator for novel magnetic orders.