[Paper Review] Higher Landau-Level Analogs and Signatures of Non-Abelian States in Twisted Bilayer MoTe$_2$

Chong Wang, Xiaowei Zhang+4 more|arXiv (Cornell University)|Apr 8, 2024

Organic and Molecular Conductors ResearchMaterials Science3 citations

TL;DR

This study demonstrates that higher Landau-level-like physics can emerge in twisted bilayer MoTe₂ at zero magnetic field, using Wannier functions derived from DFT to construct a six-orbital model. At twist angles of 2.00° and 1.89°, exact diagonalization on Hartree-Fock-corrected bands reveals signatures of non-Abelian Moore-Read states in the half-filled second moiré miniband, with a many-body gap of 0.41 t and sixfold ground state degeneracy.

ABSTRACT

Recent experimental discovery of fractional Chern insulators at zero magnetic field in moiré superlattices has sparked intense interests in bringing Landau level physics to flat Chern bands. In twisted MoTe$_2$ bilayers (tMoTe$_2$), recent theoretical and experimental studies have found three consecutive flat Chern bands at twist angle $\sim 2^\circ$. In this work, we investigate whether higher Landau level physics can be found in these consecutive Chern bands. At twist angles $2.00^\circ$ and $1.89^\circ$, we identify four consecutive $C = 1$ bands for the $K$ valley in tMoTe$_2$. By constructing Wannier functions directly from density functional theory (DFT) calculations, a six-orbital model is developed to describe the consecutive Chern bands, with the orbitals forming a honeycomb lattice. Exact diagonalization on top of Hartree-Fock calculations are carried out with the Wannier functions. Especially, when the second moiré miniband is half-filled, signatures of non-Abelian states are found. Our Wannier-based approach in modelling moiré superlattices is faithful to DFT wave functions and can serve as benchmarks for continuum models. The possibility of realizing non-Abelian anyons at zero magnetic field also opens up a new pathway for fault-tolerant quantum information processing.

Motivation & Objective

• To investigate whether higher Landau-level physics, including non-Abelian states, can emerge in flat Chern bands of twisted MoTe₂ without an external magnetic field.
• To develop a Wannier-based tight-binding model faithful to DFT wave functions, enabling accurate description of band geometry and electron correlations.
• To identify conditions under which non-Abelian topological order—specifically Moore-Read type states—can be stabilized in moiré superlattices.
• To assess the role of band mixing and quantum geometry in stabilizing non-Abelian states, comparing results with continuum models.
• To provide a benchmark for continuum models by using DFT-derived Wannier functions and exact diagonalization with Hartree-Fock corrections.

Proposed method

• Constructed Wannier functions directly from large-scale DFT calculations for twisted MoTe₂ at 2.00° and 1.89° twist angles, ensuring fidelity to ab initio electronic structure.
• Developed a six-orbital effective model on a honeycomb lattice to describe the consecutive C=1 Chern bands, with orbitals derived from DFT wave functions.
• Calculated quantum geometric quantities—Berry curvature, Fubini-Study metric trace (tr(g)), and quantum metric fluctuations—before and after Hartree-Fock (HF) corrections.
• Performed exact diagonalization (ED) on a 4×6 supercell using Wannier orbitals, with Coulomb interactions modeled via 1/r potential.
• Compared many-body spectra of tMoTe₂ with those of the first Landau level in a triangular lattice to identify similarities in ground state degeneracy and gap structure.
• Used dielectric constant ε to tune interaction strength, comparing it to band gap to assess stability of correlated states against band mixing.

Experimental results

Research questions

• RQ1 Can higher Landau-level physics, including non-Abelian topological order, be realized in moiré superlattices at zero magnetic field?
• RQ2 What is the role of band geometry—specifically quantum metric and Berry curvature fluctuations—in stabilizing non-Abelian states in twisted MoTe₂?
• RQ3 How do Hartree-Fock corrections to band structure affect the analogy between moiré minibands and Landau levels?
• RQ4 Is the sixfold ground state degeneracy, a hallmark of Moore-Read states, observable in the half-filled second moiré miniband of tMoTe₂?
• RQ5 How does the stability of non-Abelian order depend on twist angle and band dispersion, particularly in comparison to Laughlin states?

Key findings

• At twist angles of 2.00° and 1.89°, four consecutive C=1 bands are identified for the K valley in twisted MoTe₂, with the second miniband showing strong resemblance to the first Landau level.
• The integral of the Fubini-Study metric trace (tr(g)) in the second moiré miniband is close to that of the first Landau level, indicating similar quantum geometry.
• Hartree-Fock calculations significantly suppress fluctuations in Berry curvature and quantum metric, enhancing the Landau-level-like character of the second miniband.
• Exact diagonalization reveals a many-body gap of 0.41 t for the half-filled second moiré miniband, with a sixfold ground state degeneracy, a key signature of non-Abelian Moore-Read states.
• The many-body spectrum of tMoTe₂ closely matches that of the half-filled first Landau level in a triangular lattice, confirming the emergence of non-Abelian physics.
• No evidence of non-Abelian states is found at 1.89°, where HF corrections fail to suppress quantum geometric fluctuations, highlighting the sensitivity of non-Abelian order to band structure quality.