Engineering Macroscopic Quantum Coherence in Disordered Moiré Metamaterials

In the paper's words

The study of moiré materials is defined by a central paradox: the experimental observation of robust, macroscopic quantum phases, such as superconductivity and topological insulation, in devices known to possess significant atomistic disorder. This work bridges this “disorder-topology gap” by establishing quantum percolation as the fundamental mechanism for the emergence of global coherence. We develop a Stochastic Time-Dependent Ginzburg-Landau (TDGL) model that incorporates a physically realistic, multi-modal disorder potential.

The abstract, verbatim, and its opening sentence is the claim. Every line below is quoted from the text.

Numbers it reports

1. The Largest_Cluster_Frac is 0.9855, indicating that over 98% of all the superconducting sites in the grid belong to a single, connected component.

   from 4.4 The

2. We identify a sharp, topological percolation threshold at a simulation time of t=1.25, where a sample-spanning network first forms at an average superfluid density of 0.31.

   from Engineering

3. (2024) have demonstrated the existence of photonic “Bound States in the Continuum” (BICs) in twisted silicon slabs.

   from 1.6 The

4. The efficiency of the Euler-Maruyama method allowed us to perform simulations on a large 128x128 grid for long durations (5000 steps), which is essential for properly resolving the mesoscopic structure of the percolating clusters.

   from 3.4 Numerical

5. A site is labeled as superconducting if its density exceeds a small but finite threshold (e.g., 0.1).

   from 3.5

6. Threshold Breach ($t = 1.25$) At the precisely identified simulation time of t=1.25, the system undergoes a sharp topological phase transition, crossing the percolation threshold.

   from 4.5 The Percolation

How it is done

1. The simulation, performed on a high-resolution 128x128 lattice, is analyzed using an objective Hoshen-Kopelman cluster-finding algorithm.

   from Engineering

2. This approach, while fruitful, treated the moiré phenomenon as a static property of a given sample, with the physics “locked in” during fabrication.

   from 1.1 The Moiré

3. This work provides definitive, quantitative proof that the real-space structure of a moiré material is far from the idealized picture used in many theoretical calculations.

   from 1.2 The Disorder-Topology Gap

4. The power of this approach is exemplified by the engineering of “bichromatic” potentials in asymmetric TMD trilayers, such as WSe$_2$/WS$_2$/WSe$_2$.

   from 1.4 Hierarchical

What would falsify it

1. A foundational conflict defines the current frontier of moiré physics: the gap between theoretical models that predict robust topological phases based on global symmetry and the stark experimental evidence of profound, symmetry-breaking atomistic disorder.

   from 1.2 The Disorder-Topology Gap

2. Within this pristine mathematical construct, powerful concepts from band theory can be used to calculate topological invariants, such as Chern numbers, which predict the existence of quantized Hall conductivity and protected edge states.

   from 1.2 The Disorder-Topology Gap

3. (2025) predict that twisting bilayers of 1T-SnSe$_2$ will produce flat bands with a six-fold degeneracy, arising from the combination of three M-valleys and the spin degree of freedom.

   from 1.3

Where the claim stops

1. However, the focus remained on a singular system and a singular control knob—the twist angle.

   from 1.1 The Moiré

2. The variability between devices was high, and the underlying principles governing the emergence of these correlated states in the presence of real-world disorder were not yet fully understood.

   from 1.1 The Moiré

3. The idealized continuum models that assume perfect, infinite lattices are insufficient for describing a reality where the essential physics may be governed by the statistics of disorder.

   from 1.1 The Moiré

Where to read

1. Engineering14,664 words · 64 min
2. INITIAL_SEEDING |8 words · 1 min
3. ISLAND_NUCLEATION |8 words · 1 min
4. CLUSTER_GROWTH |8 words · 1 min
5. CLUSTER_GROWTH |8 words · 1 min
6. PRE-PERCOLATION |8 words · 1 min
7. PERCOLATION_THRESHOLD_BREACH |8 words · 1 min
8. GLOBAL_COHERENCE_STRENGTHENING |8 words · 1 min
9. EQUILIBRIUM_APPROACH |8 words · 1 min
10. EQUILIBRIUM_REACHED |8 words · 1 min
11. EQUILIBRIUM_REACHED |8 words · 1 min
12. EQUILIBRIUM_REACHED |8 words · 1 min