What is the concept of fractional quantum Hall effect?
1 Answer
The fractional quantum Hall effect (FQHE) is a fascinating quantum phenomenon that occurs in two-dimensional electron systems subjected to a strong magnetic field at very low temperatures. It is a more complex and intriguing version of the quantum Hall effect (QHE).
The quantum Hall effect itself is the quantization of the Hall resistance in a two-dimensional electron gas when subjected to a magnetic field perpendicular to its plane. It was discovered by Klaus von Klitzing in 1980, for which he was awarded the Nobel Prize in Physics in 1985.
The fractional quantum Hall effect arises when the filling factor (the ratio of the number of electrons to the number of available quantum states) of the electron system takes on fractional values, typically of the form 1/3, 2/5, 3/7, etc. These fractions are not simple multiples of one another, which makes the FQHE distinct from the regular QHE, where the filling factor is typically an integer.
The FQHE is a manifestation of the strong correlations between electrons in a two-dimensional system. These correlations lead to the emergence of new types of particles called "quasiparticles," which have fractional charges and obey fractional statistics. These quasiparticles are not actual particles in the traditional sense but are collective excitations of the electron system.
The theoretical framework to understand the FQHE involves the concept of composite fermions. In this framework, it is proposed that electrons bind with an even number of quantized vortices in the electron gas, transforming them into composite particles that behave like non-interacting fermions in an effective magnetic field. This effective field cancels out the effects of the original magnetic field, allowing for the formation of quantized Hall states at fractional filling factors.
The fractional quantum Hall effect has been observed in various experiments involving high-mobility semiconductor devices. Its discovery has opened up a new realm of research in condensed matter physics, leading to a deeper understanding of topological states of matter, many-body interactions, and exotic quantum phenomena.
In summary, the fractional quantum Hall effect is a remarkable quantum phenomenon that occurs in two-dimensional electron systems under strong magnetic fields and low temperatures, leading to the emergence of fractionalized quasiparticles and novel states of matter.
The quantum Hall effect itself is the quantization of the Hall resistance in a two-dimensional electron gas when subjected to a magnetic field perpendicular to its plane. It was discovered by Klaus von Klitzing in 1980, for which he was awarded the Nobel Prize in Physics in 1985.
The fractional quantum Hall effect arises when the filling factor (the ratio of the number of electrons to the number of available quantum states) of the electron system takes on fractional values, typically of the form 1/3, 2/5, 3/7, etc. These fractions are not simple multiples of one another, which makes the FQHE distinct from the regular QHE, where the filling factor is typically an integer.
The FQHE is a manifestation of the strong correlations between electrons in a two-dimensional system. These correlations lead to the emergence of new types of particles called "quasiparticles," which have fractional charges and obey fractional statistics. These quasiparticles are not actual particles in the traditional sense but are collective excitations of the electron system.
The theoretical framework to understand the FQHE involves the concept of composite fermions. In this framework, it is proposed that electrons bind with an even number of quantized vortices in the electron gas, transforming them into composite particles that behave like non-interacting fermions in an effective magnetic field. This effective field cancels out the effects of the original magnetic field, allowing for the formation of quantized Hall states at fractional filling factors.
The fractional quantum Hall effect has been observed in various experiments involving high-mobility semiconductor devices. Its discovery has opened up a new realm of research in condensed matter physics, leading to a deeper understanding of topological states of matter, many-body interactions, and exotic quantum phenomena.
In summary, the fractional quantum Hall effect is a remarkable quantum phenomenon that occurs in two-dimensional electron systems under strong magnetic fields and low temperatures, leading to the emergence of fractionalized quasiparticles and novel states of matter.