Anyon-trions in atomically thin semiconductor heterostructures

The study of anyons in topologically ordered quantum systems has mainly relied on edge-state interferometry. However, realizing controlled braiding of anyons necessitates the ability to detect and manipulate individual anyons within the bulk. Here, we propose and theoretically investigate a first step toward this goal by demonstrating that a long-lived, optically generated interlayer exciton can bind to a quasihole in a fractional quantum Hall state, forming a composite excitation we term an anyon-trion. Using exact diagonalization, we show that mobile anyon-trions possess a binding energy of approximately 0.5 meV, whereas static anyon-trions exhibit a binding energy of about 0.9 meV, that is linearly proportional to the quasiholes fractional charge. An experimental realization based on photoluminescence from localized interlayer excitons in a quantum twisting microscope setup should allow for a direct optical observation of anyon-trions.

💡 Research Summary

The authors present a theoretical proposal for creating and detecting a novel composite quasiparticle—dubbed an “anyon‑trion”—in atomically thin semiconductor heterostructures under strong magnetic fields. The system consists of a MoSe₂/WSe₂ van der Waals bilayer that supports long‑lived interlayer excitons (IXs) placed in close proximity (≈1 nm) to a graphene monolayer which, at high magnetic field, forms integer or fractional quantum Hall (IQH/FQH) states. Because IXs carry a permanent electric dipole, they interact repulsively with the electrons in graphene. In a uniform quantum Hall fluid this repulsion is spatially constant, but at the location of a quasihole the local electron density is reduced, weakening the repulsive potential. Consequently an IX experiences a local energy minimum and can bind to the quasihole, forming a bound state that the authors call an anyon‑trion.

Two regimes are explored. In the IQH case the bound state is a “magnetic trion”: a 1s interlayer exciton bound to a single hole (the absence of an electron) in the lowest Landau level (LLL). Exact diagonalization (ED) of the few‑body Hamiltonian shows that the binding energy grows with magnetic field B and with the inter‑layer spacing d, vanishing as B→0. The dominant contribution comes from the 1s exciton and the LLL hole; higher Landau levels are suppressed by a factor (a_X/l_B)^2≈10⁻² at B≈16 T.

The more striking result concerns the ν = 1/3 Laughlin FQH state. Here the authors treat up to eight electrons on a sphere threaded by a magnetic monopole (the standard spherical geometry for FQH calculations). To keep the Hilbert space tractable they apply a Lee‑Low‑Pines (LLP) unitary transformation that rotates the electronic subsystem into the exciton’s co‑moving frame, thereby fixing the exciton at the north pole while preserving total angular momentum. ED of the transformed Hamiltonian yields a low‑energy manifold whose ground state occurs at total angular momentum J = J_qh = N/2, exactly the angular momentum of an isolated quasihole. The dispersion E(J)∝(J−J_qh)² indicates a finite effective mass for the bound object, i.e., a mobile anyon‑trion.

Two robust gaps appear in the spectrum for all particle numbers. Finite‑size scaling (∝1/N) extrapolates these gaps to ≈0.5 meV for a mobile anyon‑trion and ≈0.9 meV for a static (localized) anyon‑trion. Importantly, the binding energy scales linearly with the quasihole’s fractional charge (e/3), providing a direct optical signature of anyonic charge.

Experimentally, the authors propose a device where the MoSe₂/WSe₂ bilayer is separated from graphene by a thin hBN spacer (d≈0.6 nm). A quantum‑twisting microscope (QTM) tip creates a localized defect that traps an IX, turning it into a nanoscale quantum emitter. When a quasihole passes beneath the trapped IX, the reduced repulsion leads to a red‑shift of the IX photoluminescence (PL) line by the binding energy. Because the PL linewidth in TMD heterostructures can be sub‑meV, this red‑shift should be directly observable. By scanning the tip or by using multiple trapped IXs, one could map the spatial distribution of quasiholes with nanometer resolution and verify the linear dependence of the shift on the fractional charge.

Methodologically, the work combines several sophisticated techniques: exact diagonalization of few‑body Hamiltonians in Landau‑quantized systems, the LLP transformation to exploit rotational symmetry, and realistic modeling of the exciton‑electron interaction V_Xe(r) that incorporates dielectric screening from hBN and the finite inter‑layer distance. The calculations are performed for realistic magnetic fields (B≈16 T) and material parameters (exciton mass, binding energy ≈100 meV), ensuring that the predicted binding energies are experimentally accessible.

In summary, this paper introduces anyon‑trions as a new class of quasiparticles that bind a photogenerated interlayer exciton to a fractional quasihole. The proposal offers a bulk, optical route to detect and manipulate individual anyons, overcoming the spatial limitations of edge‑state interferometry. If realized, it would constitute a major step toward bulk anyon braiding and could open pathways for topological quantum information processing using optically addressable quasiparticles in van der Waals heterostructures.