**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Concept# Fractional quantum Hall effect

Summary

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2-dimensional (2D) electrons shows precisely quantized plateaus at fractional values of . It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations have a fractional elementary charge and possibly also fractional statistics. The 1998 Nobel Prize in Physics was awarded to Robert Laughlin, Horst Störmer, and Daniel Tsui "for their discovery of a new form of quantum fluid with fractionally charged excitations"
The microscopic origin of the FQHE is a major research topic in condensed matter physics.
The fractional quantum Hall effect (FQHE) is a collective behavior in a 2D system of electrons. In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures. As in the integer quantum Hall effect, the Hall resistance undergoes certain quantum Hall transitions to form a series of plateaus. Each particular value of the magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta)
where p and q are integers with no common factors. Here q turns out to be an odd number with the exception of two filling factors 5/2 and 7/2. The principal series of such fractions are
and
Fractionally charged quasiparticles are neither bosons nor fermions and exhibit anyonic statistics. The fractional quantum Hall effect continues to be influential in theories about topological order. Certain fractional quantum Hall phases appear to have the right properties for building a topological quantum computer.
The FQHE was experimentally discovered in 1982 by Daniel Tsui and Horst Störmer, in experiments performed on gallium arsenide heterostructures developed by Arthur Gossard.
There were several major steps in the theory of the FQHE.
Laughlin states and fractionally-charged quasiparticles: this theory, proposed by Robert B.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Ontological neighbourhood

Related courses (10)

Related lectures (32)

Related publications (121)

Related people (32)

Related units (7)

Related concepts (12)

PHYS-756: Lectures on twisted bilayer graphene

Twisted Bilayer Graphene (TBG) is a change of paradigm in condensed matter: with flat topologic bands, it provides a platform for unconventional superconductivity, correlated insulation, Plankian meta

PHYS-462: Quantum transport in mesoscopic systems

This course will focus on the electron transport in semiconductors, with emphasis on the mesoscopic systems. The aim is to understand the transport of electrons in low dimensional systems, where even

PHYS-638: Some aspects of topology in condensed matter physics

Some topics covered in this class are: The Index theorem, solitons, topological band insulators/superconductors, bulk-edge correpondence, quantum anomalies, quantum pumping, symmetry protected topolog

Topological order

In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground state degeneracy and quantized non-Abelian geometric phases of degenerate ground states. Microscopically, topological orders correspond to patterns of long-range quantum entanglement. States with different topological orders (or different patterns of long range entanglements) cannot change into each other without a phase transition.

Quasiparticle

In physics, quasiparticles and collective excitations are closely related phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For example, as an electron travels through a semiconductor, its motion is disturbed in a complex way by its interactions with other electrons and with atomic nuclei. The electron behaves as though it has a different effective mass travelling unperturbed in vacuum.

Topological quantum computer

A topological quantum computer is a theoretical quantum computer proposed by Russian-American physicist Alexei Kitaev in 1997. It employs quasiparticles in two-dimensional systems, called anyons, whose world lines pass around one another to form braids in a three-dimensional spacetime (i.e., one temporal plus two spatial dimensions). These braids form the logic gates that make up the computer. The advantage of a quantum computer based on quantum braids over using trapped quantum particles is that the former is much more stable.

Graphene Properties and Applications

Explores graphene properties, band structure, electronics, and nanoscale phenomena like the Quantum Hall effect and the Casimir effect.

Itinerant Magnetism: Spin Density Wave

Explores itinerant magnetism, emphasizing the spin density wave phenomenon and related concepts such as Kohn anomaly and collective excitations.

Vibrations in Solids: Harmonic Oscillators and Phonons

Explores vibrations in solids, including harmonic oscillators, phonons, and the Einstein model of heat capacity.

Excitons play an essential role in the optical response of two-dimensional materials. These are bound states showing up in the band gaps of many-body systems and are conceived as quasiparticles formed by an electron and a hole. By performing real-time simu ...

Disorder at etched edges of graphene quantum dots (GQD) enables random all-to-all interactions between localized charges in partially filled Landau levels, providing a potential platform to realize the Sachdev-Ye-Kitaev (SYK) model. We use quantum Hall edg ...

2024Modern condensed matter physics relies on the concept of topology to classify matter, from quantum Hall systems to topological insulators. Engineered systems, benefiting from synthetic dimensions, can potentially give access to topological states predicted ...