Fractional quantum Hall effect

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values of e 2 / h {displaystyle e^{2}/h} . 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' However, Laughlin's explanation was a phenomenological guess and only applies to fillings ν = 1 / m {displaystyle u =1/m} where m {displaystyle m} is an odd integer. The microscopic origin of the FQHE is a major research topic in condensed matter physics. The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values of e 2 / h {displaystyle e^{2}/h} . 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' However, Laughlin's explanation was a phenomenological guess and only applies to fillings ν = 1 / m {displaystyle u =1/m} where m {displaystyle m} is an odd integer. The microscopic origin of the FQHE is a major research topic in condensed matter physics. The fractional quantum Hall effect (FQHE) is a collective behaviour in a two-dimensional 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