Fractional Quantum Hall effect
The Fractional Quantum Hall Effect (FQHE) is a phenomenon that occurs in two-dimensional electron systems subjected to a strong magnetic field at low temperatures. It was discovered by Daniel Tsui, Horst Störmer, and Robert Laughlin in the early 1980s, leading to their Nobel Prize in Physics in 1998. This groundbreaking discovery revolutionized our understanding of quantum mechanics and condensed matter physics.
In the presence of a strong magnetic field, electrons in a two-dimensional system form what are known as Landau levels, which are quantized energy levels. These Landau levels are characterized by discrete energy values that depend on the strength of the magnetic field. In the FQHE, when the electron density is sufficiently low, strange and fascinating phenomena arise.
The most striking feature of the FQHE is the appearance of fractionally charged quasiparticles. These quasiparticles are collective excitations of the electron system and have fractional charges, such as e/3, e/5, etc., where e is the elementary charge. This fractionalization of charge is a manifestation of the strong electron-electron interactions in the system. The fractional charges of the quasiparticles are a direct consequence of the topological properties of the electron wavefunctions in the FQHE.
Another important aspect of the FQHE is the emergence of a fractional quantum Hall state, which is a ground state of the system at certain filling fractions. The filling fraction is the ratio of the number of electrons to the number of available Landau levels. At specific fractions, such as 1/3, 2/5, or 3/7, the system undergoes a phase transition and forms a new state with unique properties. These states are characterized by a fractionalized Hall conductance, which is quantized in units of e2/h, where h is the Planck constant.
The FQHE has been studied extensively both theoretically and experimentally. Theoretical models, such as the Laughlin wavefunction, have been proposed to explain the origin of the FQHE and the properties of the fractional quantum Hall states. These models describe the electron system as a quantum fluid with exotic properties, such as fractional statistics and collective excitations that carry fractional charges.
Experimental investigations of the FQHE have been conducted using high-quality semiconductor devices. Researchers have measured the Hall conductance and observed plateaus at fractional values, confirming the existence of the fractional quantum Hall states. These experiments have provided crucial evidence for the validity of the theoretical models and have further deepened our understanding of the FQHE.
The FQHE has important implications for both fundamental physics and potential applications. It has opened up new avenues for studying exotic quantum phenomena and has provided insights into the nature of strongly correlated electron systems. Furthermore, the fractional quantum Hall states could potentially be harnessed for quantum computing and other technological advancements.
In conclusion, the Fractional Quantum Hall Effect is a remarkable phenomenon that occurs in two-dimensional electron systems subjected to a strong magnetic field. It is characterized by the emergence of fractionally charged quasiparticles and fractional quantum Hall states. The FQHE has been the subject of extensive theoretical and experimental investigations, leading to groundbreaking insights into the nature of quantum mechanics and condensed matter physics.