#fractionalquantumhalleffect

[govindhtech]

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.

Read Nanophotonic Devices T Centres In Quantum Networking and

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.

[govindhtech]

Quantum Hall Effect Applications And Fundamental Principles

Exceptionally low temperatures and large magnetic fields perpendicular to the electron system's plane cause two-dimensional electron systems to display the Quantum Hall Effect. Throughout a wide range of charge carrier densities or magnetic field strengths, the Hall resistance computed by dividing the Hall voltage by the applied current is unique and consistent.

This blog covers the quantum hall effect's definition, fundamental principles (Landau levels and disorder), topological origin, applications, experimental realisations, and fresh findings.

Definition of quantum hall effect

Klaus von Klitzing's 1980 QHE observation earned him the 1985 Nobel Prize in Physics. He found that the Hall resistance quantised a fundamental quantity by integers to produce accurate, consistent values. This first finding is called the Integer Quantum Hall Effect (IQHE). The discovery of plateau values for fractional integers led to the 1982 discovery of the Fractional Quantum Hall Effect (FQHE). Despite its complexity, the FQHE remains an open study topic. Existence depends on electron interactions.

Fundamentals: Landau Levels and Disorder

Understanding the IQHE starts with Landau levels. A strong magnetic field quantises electrons' circular paths into discrete energy levels in a two-dimensional electron system. The Landau levels' significant degeneracy allows many electron states to coexist at the same energy. These energy levels further split when an electron's spin aligns with a high magnetic field due to the Zeeman effect. Hall resistance plateaus are caused by material disorder or contaminants.

Disorder broadens the crisp Landau levels into energy bands. Electron states can be localised or expanded in these bands. Extended states can travel, whereas localised states are limited and do not contribute to the flow. When the Fermi energy, the highest energy level occupied by electrons, falls within a “mobility gap” between Landau levels and the Hall conductivity stays constant, creating plateaus, the material acts as an insulator in the longitudinal direction. Importantly, the condition does not affect these plateaus' exact values.

Topological Origin

The IQHE's stability and resistance to microscopic disorder and macroscopic system deformations strongly suggest a topological origin. Hall effect integers are topological quantum numbers. Berry's phase, a quantum system's geometric phase, is intimately related to Chern numbers. Due to this link, the material's fundamental features, which are dictated by its topological structure, influence its electrical properties.

Metrology the discipline of measuring has various QHE applications.

Electrical Resistance Standard: Due to its precision of more than one part in a billion, quantised Hall conductance has become the new practical standard for electrical resistance. This standard is based on the von Klitzing constant, named for its discoverer. In 1990, this constant was standardised for global resistance calibrations. The 2019 revision of the International System of Units (SI) specified the von Klitzing constant and other fundamental constants like Planck's constant and the elementary charge exactly.

The IQHE accurately and independently determines the fine-structure constant. The basic constant describes the strength of elementary particle electromagnetic interaction.

Experimental Results and Discoveries

When a two-dimensional electron system forms in a thin silicon-based MOSFET surface layer, the QHE was first observed. It has been widely studied in semiconductor materials like gallium arsenide heterostructures.

QHE has been observed in graphene and other materials recently. Graphene exhibits a half-integer quantum Hall effect. This half-integer behaviour is caused by graphene's relativistic-like energy dispersion and electron-hole degeneracy at Dirac locations. In contrast to semiconductor devices, graphene's QHE can occur at temperatures near to ambient temperature.

QHE in Bi2O2Se thin films is a novel and intriguing discovery. In thicker Bi2O2Se films, researchers detected only even-integer quantum Hall states at extremely high magnetic fields. Strange conduct is attributed to a “hidden Rashba effect”. Local violation of inversion symmetry in [Bi2O2]$^{2+}$ layers causes opposite spin polarisations to cancel each other out.

When the Bi2O2Se film is formed on a SrTiO3 substrate and thinned to a single unit cell, the intrinsic asymmetry of the top surface and bottom interface creates a “net polar field”. The “global Rashba effect,” which lifts band degeneracies in thicker films, produces odd- and even-integer quantum Hall states. This study emphasises the complex link between spin-orbit coupling, material structure, and quantum Hall phenomena.