The spelling of "fractional quantum hall effect" can be a bit tricky to understand at first glance. The IPA phonetic transcription can help clarify the pronunciation: [ˈfræk.ʃən.əl ˈkwɑn.təm hɔl iːˈfɛkt]. The first part of the word, "fractional," is pronounced with a short "a" sound and a "sh" sound in the middle. "Quantum" is pronounced with a long "a" sound in the first syllable, and a "kw" sound. "Hall" is pronounced with a long "o" sound, and "effect" with a short "e" sound and a hard "k" sound.
The fractional quantum Hall effect is a fascinating phenomenon that occurs in a two-dimensional electron gas (2DEG) system at extremely low temperatures and high magnetic fields. It is characterized by the presence of fractions in the Hall resistance, which are rational numbers in the form of fractions instead of the expected integers.
In the fractional quantum Hall effect, when the 2DEG is subjected to a magnetic field perpendicular to its plane, quantum mechanical interactions between the electrons become significant. At certain specific filling factors, which represent the ratio of the number of electrons to the number of available quantum states in the system, the fractional quantum Hall effect manifests.
These filling factors correspond to fractions, such as 1/3, 2/5, or 3/7, indicating that the electrons are collectively forming quasi-particles with fractions of the elementary charge. These quasi-particles are called fractionally charged anyons, and they have fractional quantum numbers, which are peculiar characteristics of these quantum particles.
The fractional quantum Hall effect is a highly intricate and delicate phenomenon that has captured the attention of physicists for its deep relevance to condensed matter physics and the study of novel quantum states of matter. It has important implications in fields like quantum computing and topological physics, and its theoretical understanding has resulted in Nobel Prize-winning research.