Quantum Hall Quasiparticle Exciton

• Quantum Hall quasiparticle exciton is a neutral bound state formed by a fractionally charged quasiparticle and its quasihole, exhibiting anyonic statistics.
• Theoretical models using Laughlin and composite-fermion formalisms, along with inelastic scattering and interferometry, reveal its nontrivial dispersion and roton minimum.
• Its unique topological order and electrically tunable quantum coherence enable potential applications in quantum simulation and topological device engineering.

A quantum Hall quasiparticle exciton is a neutral bound state formed from a fractionally charged quasiparticle and its corresponding quasihole within the topological many-body environment of a quantum Hall fluid. Unlike conventional excitons, which are composed of integer-charged electrons and holes, quantum Hall quasiparticle excitons inherit their properties from the correlated quantum Hall ground state, resulting in unique statistical, energetic, and transport phenomena. Their formation, dynamics, and experimental manifestations serve as a window into the collective excitations and topological order characteristic of quantum Hall systems.

1. Fundamental Nature and Definition

In the framework of the fractional quantum Hall (FQH) effect, the lowest-lying charged excitations are fractionally charged quasiparticles—either quasiparticles or quasiholes—that obey anyonic exchange statistics distinct from the fermionic (electron) or bosonic (hole) paradigms. A quantum Hall quasiparticle exciton is defined as the neutral complex formed when a quasiparticle and corresponding quasihole bind, typically through their mutual Coulomb interaction. Both constituents carry fractional charge and, crucially, anyonic quantum statistics. This binding fundamentally differs from the electron–hole exciton in semiconductors, as the exciton's quantum numbers and statistics are inherited from the highly entangled quantum Hall background (Zhang et al., 25 Jul 2024, Zhang et al., 2023).

The energy dispersion of the quasiparticle exciton is nontrivial, and often exhibits a pronounced roton minimum, as originally described by Girvin, MacDonald, and Platzman for neutral collective modes of the Laughlin fluid. The statistical properties of the constituents imprint themselves on the composite exciton's exchange phase and optical selection rules (Zhang et al., 25 Jul 2024).

2. Theoretical Modeling and Many-Body Structure

Quantum Hall quasiparticle excitons are embedded in the many-body Hilbert space of the FQH state, whose ground state is described by, for example, the Laughlin wave function, the Moore–Read Pfaffian, or composite-fermion (CF) theory constructions (Rodriguez et al., 2011, Bentalha, 2019). The excitation spectrum is modeled by combining a localized quasiparticle with a localized quasihole, yielding neutral collective modes whose energetic and spatial structure are computed using exact diagonalization, CF-diagonalization, or variational approaches.

The binding energy, spatial extent, and dispersion of these excitons depend on the interaction parameters and details of screening. Screening by “composite fermion excitons” (neutral CF particle–hole pairs) leads to significant renormalization, especially at higher Landau levels as seen in the ν=7/3 state, where quasiparticle and quasihole excitations become “dressed” by an extensive exciton cloud, strongly modifying both their energy and density profile (Balram et al., 2013). In bilayer quantum Hall systems or systems with additional degrees of freedom, modeling incorporates layer pseudospin or spin, enabling pseudospin, spin-triplet, or interlayer excitonic modes (Giudici et al., 2010, Zhang et al., 2023).

K-matrix formalism and wavefunction constructions (e.g., Halperin (mmn) states, composite-fermion flux-attachment schemes) allow calculation of the charge and statistical phase of constituent quasiparticles. The resulting exciton may possess bosonic, fermionic, or anyonic statistics according to

$\theta_s = \pi l^T K^{-1} l \pmod{2\pi}$

where $l$ is the quasiparticle vector and $K$ the topological K-matrix (Zhang et al., 25 Jul 2024).

3. Experimental Signatures and Probing Techniques

Quantum Hall quasiparticle excitons are electrically neutral and primarily contribute to the neutral excitation spectrum rather than charge transport. Key experimental signatures include:

• Inelastic Light Scattering: Neutral collective modes, including the magneto-roton exciton, are probed via Raman or resonant inelastic X-ray scattering (Zhang et al., 25 Jul 2024). The exciton's gap and dispersion can be extracted from energy- and momentum-resolved spectra.
• Transport in Bilayers and Corbino Devices: In bilayer systems and Corbino geometries, drag and counterflow measurements provide sensitive probes. Transport signatures such as dissipationless counterflow, perfect drag (where the drag current equals the drive current), and a robust charge gap coexist with a gapless neutral mode, directly reflecting the formation and transport of charge-neutral excitons (Liu et al., 2016, Eisenstein et al., 2012, Zhang et al., 25 Jul 2024).
• Interferometry: An interferometer can examine anyonic statistics of individual fractional excitations, with entry or exit of an anyon from the interferometer loop causing phase slips of magnitude $\Delta\theta \approx 2\pi/3$ (for ν=1/3), confirming that fractional (anyonic) excitations participate in the process (Samuelson et al., 28 Mar 2024).
• Antidot and Quantum Dot Spectroscopy: Localization, tuning, and quantum-coherent dynamics of a single exciton can be realized through engineered antidot devices, which allow precise electrical control and observation of quantum superpositions between vacuum and electron–hole (exciton) states. Conductance peaks' anti-crossing and gate dependence are direct evidence for such quantum-coherent excitonic states (Pu et al., 14 Sep 2025).

4. Emergent Quantum Phases and Topological Order

Fractional excitonic pairing leads to novel many-body phases:

• Fractional Exciton Condensate: The bilayer at total filling ν=1 hosts an excitonic Bose condensate, whose integer counterpart is the Halperin (111) state. At fractional filling (e.g., ν_total=1/3), the analogous Halperin (333) state is realized as a fractional exciton condensate, in which charge-neutral, fractionally charged quasiparticles bind into collective neutral modes that condense (Zeng et al., 2020, Zhang et al., 25 Jul 2024).
• Non-Bosonic (Fermionic or Anyonic) Excitons: Under certain composite-fermion constructions and K-matrix parameters, the exciton may possess fermionic or general anyonic quantum statistics (e.g., an exchange phase of π or 4π/3), challenging the paradigm of only bosonic excitons. These phases are characterized by robust charge gaps (insulating parallel flow conductance), perfect drag and counterflow transport (gapless neutral exciton channel), and are stabilized at specific layer fillings and parameters (Zhang et al., 25 Jul 2024).
• XY* Criticality and Fractionalization: Transitions driven by fractional exciton condensation (e.g., in (1/3,2/3) bilayers) are described by an "XY*" universality class in which the observable exciton order parameter is a composite of fractionalized fields (e.g., $\Phi=\phi^3$), resulting in anomalously large scaling dimensions and fractional universal counterflow conductances. Edge and bulk criticalities are distinct; for example, the edge remains superfluid-like with logarithmically slow decay, while the bulk exhibits conventional gapped behavior (Zhang et al., 2023).

5. Quantum Coherence, Superposition, and Electrical Control

Quantum Hall quasiparticle excitons, especially as realized and localized in antidot geometries, exhibit quantum-coherent dynamics and superposition between different occupation states. The observed anti-crossing in the tunneling conductance as a function of gate voltage or magnetic field is direct evidence for coherent mixing of vacuum and electron–hole pair states. The phenomenology is quantitatively modeled by a two-level system with Hamiltonian parameters directly extracted from experimental knob settings. The realization of such single-exciton devices opens the door for complex "molecules" of excitons and potential quantum information applications (Pu et al., 14 Sep 2025).

Electrical tuning is enabled via dual-gate control (creating local variations in carrier density and confinement) and via patterned gates defining antidots, allowing control of the edge–edge tunneling strength and electron–hole detuning, thus offering full control over the excitonic degree of freedom.

6. Theoretical and Experimental Outlook

The comprehensive theoretical treatment of quantum Hall quasiparticle excitons employs CF theory, K-matrix formalism, trial wavefunction construction, and field-theoretic approaches. Calculation of quasiparticle–exciton binding energies, statistics, and dispersion relations requires exact diagonalization and variational methods (Rodriguez et al., 2011, Bentalha, 2019).

Ongoing experimental advances are making it possible to probe not only the formation and energetics but also the nontrivial statistical properties and quantum-coherent dynamics of quantum Hall excitons. Promising directions include:

• Direct spectroscopic probing of neutral exciton modes and their statistics.
• Engineering arrays or “molecules” of interacting quantum Hall excitons for quantum simulation.
• Studying excitonic orders in new topological materials (e.g., transition metal dichalcogenides, moiré superlattices) and in the absence of magnetic field (quantum anomalous Hall systems).
• Exploring the interplay with superconductivity and magnetism in hybrid structures.
• Harnessing the long lifetime and robustness of quantum Hall excitons for tunable quantum devices.

These research themes affirm that quantum Hall quasiparticle excitons are a central concept, connecting topological order, fractionalization, unconventional statistics, and electrically controlled quantum coherence (Zhang et al., 25 Jul 2024, Pu et al., 14 Sep 2025, Zhang et al., 2023).