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.
