Fractional Quantum Hall Effect Unlocks Exotic Matter Phases
Quantum Hall Effect Fraction
When a two-dimensional electron system is exposed to extremely low temperatures and intense magnetic fields, fractional quantum hall (FQH) states form. A delicate and fascinating quantum liquid is created by highly interacting electrons, making this phenomena an essential condensed matter physics topic.
Discoveries and Core Features
In 1982, Daniel Tsui and Horst Störmer discovered the Fractional Quantum Hall Effect (FQHE) using Arthur Gossard's premium gallium arsenide materials. This discovery shocked the physics community since it showed that Hall conductance could be quantised at fractional values as well as integer multiples of e2h.
Noteworthy FQH observations:
The Hall resistance shows flat plateaus at specific fractional "filling factors" (h/e² values). Filling factor is the ratio of electrons to magnetic flux quanta.
At these plateaus, longitudinal resistance drops to zero, indicating an incompressible, gapped state without dissipation, resembling the integer quantum Hall effect.
Most FQH states occur in odd-denominator factors like 1/3, 2/5, and 3/7. Though rare, even-denominator situations are intriguing.
Electrons' strong Coulomb repulsion drives them into a highly correlated, collective state, which cannot be explained by non-interacting electrons.
Fractionalisation and Quasiparticles Robert Laughlin proposed a new quantum fluid to explain FQH states in a groundbreaking way. This fluid's fundamental excitations, or "quasiparticles," have a fraction of an electron's charge, its most remarkable property. When the filling factor is 1/3, quasiparticles have a charge of e/3. These fractionally charged quasiparticles are real, as proved by direct experiments.
None of these quasiparticles are fermions or bosons. Anyons, a third particle, stay in two dimensions. Exchange of two anyons causes a phase shift in the system's wavefunction that can be any fractional value, unlike the sign change for fermions or the absence of a change for bosons. Fractional statistics characterise FQH states' topological order.
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unified framework for composite fermions The fundamental 1/3 requirement was well-characterized by Laughlin's theory, but the large variety of other observable fractions was ignored. Jainendra K. Jain developed a more complete composite fermion model.
A composite fermion is formed when an electron binds with an even number of magnetic flux quanta, which are vortices in the quantum fluid, in the presence of a strong magnetic field and interactions. This conceptual transformation simplifies strongly interacting electrons to weakly interacting composite fermions moving in a reduced, “effective” magnetic field, making it powerful.
This approach holds that electrons' principal FQH states are integer quantum Hall states of composite fermions. Composite fermions' initial integer state is equivalent to electrons' 1/3 state. This model accurately predicts odd-denominator fraction sequences like 2/5, 3/7, 4/9, etc.
Non-Abelian Anyons and Even-Denominator States
Most FQH states have odd denominators, but few have even ones at filling factor 5/2. These states are intriguing because the composite fermion model cannot explain them. Composite fermions couple in this state, exactly how superconductor electrons form Cooper pairs, according to the prevalent hypothesis.
Even-denominator states are likely to have quasiparticles that are non-Abelian anyons. Unlike the 1/3 state's Abelian anyons, exchanging non-Abelian anyons can fundamentally change the system's quantum state and add a phase. They can store information non-locally in the braiding of these anyons, making them a promising candidate for error-resistant fault-tolerant topological quantum computing.
This study seeks experimental proof of non-Abelian statistics. The latest research shows that ultra-high-quality materials can develop FQH states at even 1/6 and 1/8 even-denominator fills.