Quantum Hall Phenomena in Two-Dimensional Electron Systems

Quantum Hall phenomena arise when electrons confined to a two-dimensional plane are subjected to a strong perpendicular magnetic field at low temperatures. Under such conditions, the kinetic energy of electrons is quenched into highly degenerate Landau levels, giving rise to quantised Hall conductance plateaux as the magnetic field or carrier density is varied. In the integer quantum Hall effect, these plateaux correspond to the complete filling of successive Landau levels and are understood in terms of non-interacting electrons and topological invariants known as Chern numbers. In contrast, the fractional quantum Hall effect emerges from strong electron–electron interactions, producing incompressible quantum fluids with ground states that carry fractional charge and anyonic excitations. These correlated states exhibit rich topological order, support gapless edge modes and can host non-Abelian quasiparticles of interest for fault-tolerant quantum computation. Advances in material engineering—such as high-mobility GaAs heterostructures, graphene and double quantum wells—have extended the range of accessible filling factors and enabled fine control of edge-state structures. Precision measurements of Hall resistance now serve as a primary standard for resistance metrology, while ongoing research explores novel states of matter, edge reconstruction, non-equilibrium dynamics and engineered platforms for anyonic braiding.

Research from Nature Portfolio

Recent studies have uncovered a mechanism analogous to Andreev reflection at a normal–superconductor interface in the ν=1/3 fractional quantum Hall regime. By injecting e/3 quasiparticles through a quantum point contact and analysing their scattering across a secondary constriction, researchers observed the conversion of an e/3 quasiparticle into a −2e/3 hole accompanied by transmission of an e quasielectron. Shot-noise and cross-correlation measurements confirmed the charge and coincidence of the reflected hole and transmitted particle, shedding light on unconventional quasiparticle dynamics and offering a route to engineer entangled anyonic excitations.

Efforts to reconstruct counter-propagating edge modes in the hole-conjugate ν=2/3 state have yielded a synthetic edge comprising independently tunable ν=1 and ν=1/3 channels. A double-quantum-well device with gated sub-regions created a controlled equilibration region where the two charged modes mix. By adjusting gate voltages and magnetic field, the downstream ν=2/3 charge mode and its upstream neutral companion could be dialled in, enabling systematic studies of charge equilibration, neutral modes and edge reconstruction phenomena.

Unexpected electron pairing has been demonstrated in the integer quantum Hall regime within an electronic Fabry–Pérot interferometer. At bulk filling factors between 2 and 5, high-visibility Aharonov–Bohm oscillations with half-flux-quantum periodicity were observed alongside shot-noise signatures of charge 2e. Controlled dephasing of an adjacent edge channel fully suppresses the paired interference, signalling strong inter-channel entanglement. This emergent pairing within a single edge channel challenges conventional understanding of electron–electron interactions in chiral one-dimensional systems.

Research from all publishers

A comprehensive review of fractional statistics has crystallised the theoretical framework and experimental milestones towards observing anyonic exchange phases. It outlines advances in interferometric and scattering experiments at ν=1/3, where fractional phase shifts have been detected, and discusses prospects for non-Abelian statistics in more elaborate engineered systems such as superconducting circuits and designer lattices.

Electronic Fabry–Pérot interferometry has been extended to the ν=2/5 fractional quantum Hall state, which supports two co-propagating edge modes. Interference of the outer mode reproduces patterns akin to ν=1/3, confirming its Laughlin-like character, while the inner mode exhibits discrete phase jumps indicative of distinct anyonic braiding statistics. Analysis accounting for bulk–edge coupling yielded precise values for the fractional charge and anyonic phase, providing direct experimental validation of theoretical predictions for hierarchical states.

A numerical exploration of the phase diagram at filling factor 5/2 has elucidated the competition between the Moore-Read Pfaffian and its particle-hole conjugate, the anti-Pfaffian. By including realistic effects such as Landau-level mixing and finite quantum-well width, the study identifies regimes in which the non-Abelian Pfaffian state is favoured, guiding the interpretation of spectroscopic and transport data in pursuit of topological quantum computation platforms.

Quantum Hall Phenomena in Two-Dimensional Electron Systems publication trend

The graph below shows the total number of articles in quantum hall phenomena in two-dimensional electron systems across all publications each year (not limited to Nature Index journals).

Technical terms

Landau level: A quantised energy level of two-dimensional electrons in a perpendicular magnetic field.

Filling factor: The ratio of electron density to the degeneracy of a Landau level, indicating how many levels are occupied.

Edge state: A one-dimensional conducting channel at the boundary of a quantum Hall system, arising from the bulk–boundary correspondence.

Anyons: Quasiparticles in two dimensions that acquire a fractional phase upon exchange, interpolating between bosons and fermions.

Chern–Simons theory: A topological quantum field theory that captures the long-wavelength dynamics and statistics of fractional quantum Hall states.

Composite fermion: An electron bound to an even number of flux quanta, forming a quasiparticle that experiences a reduced effective magnetic field.

References

1. Fractional Statistics. Annual Review of Condensed Matter Physics (2024).
2. Quasiparticle Andreev scattering in the ν = 1/3 fractional quantum Hall regime. Nature Communications (2023).
3. Fabry-Pérot Interferometry at the ν=2/5 Fractional Quantum Hall State. Physical Review X (2023).
4. Phase Diagram of the ν=5/2 Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width. Physical Review X (2015).
5. Synthesizing a ν=2/3 fractional quantum Hall effect edge state from counter-propagating ν=1 and ν=1/3 states. Nature Communications (2019).
6. Robust electron pairing in the integer quantum hall effect regime. Nature Communications (2015).