Stabilizing Fractional Chern States in Twisted MoTe2: DSRG Reveals Reduced Gaps at Ν = 1/3 and 2/3

The pursuit of fractional Chern states in twisted materials has gained considerable momentum, and recent observations in twisted molybdenum ditelluride, or MoTe2, present a fascinating puzzle for physicists. Run Hou and Andriy H. Nevidomskyy, from Rice University, along with their colleagues, now demonstrate that accurately describing these states requires considering the influence of multiple electron bands, a factor often overlooked in previous theoretical work. The team developed a novel computational method, a driven similarity renormalization group, to account for the strong interactions between these bands, and applied it to MoTe2 at specific electron densities. Their results reveal that these interband interactions significantly alter the energy landscape, reducing excitation gaps and, crucially, stabilising the sought-after fractional Chern insulating phases at larger twist angles, aligning with experimental evidence and offering a deeper understanding of the underlying mechanisms at play.

Twisted MoTe2 Stabilized by Multi-band Correlations

This research investigates the stabilization of fractional Chern states in twisted MoTe2, highlighting the crucial role of interactions between electrons in multiple energy bands. The team employed a sophisticated computational approach, a non-perturbative renormalization group method, to explore the complex behaviour of electrons in this material. This method examines how interactions between electrons in different bands influence the emergence and stability of fractional Chern insulators, which exhibit unusual fractionalized excitations and hold promise for future quantum computing technologies. The technique systematically removes high-energy effects to reveal the essential interactions governing the system’s behaviour.

The study demonstrates that including these multi-band interactions significantly alters predicted behaviour compared to simpler calculations, leading to enhanced stability of fractional Chern states at conditions relevant to experiments. The results show that these interactions induce new forces that protect the fractional Chern insulator from imperfections and thermal disturbances, preventing its breakdown. Furthermore, the team identified specific conditions where the system exhibits robust topological order, characterized by a precisely quantized Hall conductance and the presence of conducting edge states. This understanding is crucial for designing materials that can reliably host and manipulate these exotic states for potential technological applications. The research advances our theoretical understanding of correlated topological insulators and provides insights into the interplay between electron interactions and topological order, bridging the gap between theoretical models and experimental observations.

Interband Interactions Stabilize Fractional Chern Insulators

This research demonstrates the importance of considering interactions between electronic bands when studying correlated electron phenomena in twisted molybdenum ditelluride. The team developed a novel computational method, driven similarity renormalization group, to accurately model the complex interplay between bands, going beyond the limitations of simpler approaches. Results reveal that these interband interactions significantly reduce energy gaps at certain electron fillings and, crucially, stabilize fractional Chern insulating phases at larger twist angles, aligning with experimental observations. Specifically, the study found that dynamic correlations arising from interband interactions, rather than geometric conditions within the material, are responsible for this stabilization at higher twist angles. The newly developed method proves particularly effective because it accurately captures dynamic correlations while remaining computationally manageable, even in systems where traditional methods struggle.

DFT Calculations of Twisted Bilayer MoTe2 Properties

This document provides detailed methodological information and supporting calculations for a study investigating the electronic and geometric properties of twisted bilayer MoTe2. It serves as a companion to the main publication, allowing other researchers to understand how the results were obtained and potentially reproduce them. The document covers the theoretical methods used, including Density Functional Theory calculations and a band-projected model, as well as the DSRG(2) method used to treat electron interactions. It also details how key quantities like the structure factor, Berry curvature, and quantum geometric tensor were calculated, and provides information about the numerical parameters used and how the results were validated.

The DSRG(2) calculation is central to the study, going beyond standard calculations to include electron-electron interactions accurately. The researchers focused on a few low-energy bands to simplify the calculations and concentrate on the relevant physics. The document details the calculation of the structure factor, which describes how electrons are spatially correlated, and the Berry curvature and quantum geometric tensor, which are related to the topological properties of the electronic bands. Convergence tests were performed to ensure the results were not sensitive to the numerical parameters used.

The structure factor provides information about the spatial correlations of electrons, while the Berry curvature and quantum geometric tensor are related to the topological properties of the electronic bands. The Chern number characterizes the band structure, and the Berry curvature standard deviation measures fluctuations in the Berry curvature. This detailed explanation of the methods and the inclusion of convergence tests will allow other researchers to reproduce the results and build upon them.