Fractionalization
Encyclopedia
In physics
, fractionalization is the phenomenon whereby the quasiparticle
s of a system cannot be constructed as combinations of its elementary constituents. One of the earliest and most prominent examples is the fractional quantum Hall effect
, where the constituent particles are electrons but the quasiparticles carry fractions of the electron charge.
Other examples include spin–charge separation and emergent magnetic monopoles in spin ice
(which is well described by a classical statistical
model). They should be contrasted with quasiparticles such as magnon
s (constructed from an electron plus a hole
) and Cooper pair
s (two electrons), which have quantum numbers that are combinations of those of the constituents.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, fractionalization is the phenomenon whereby the quasiparticle
Quasiparticle
In physics, quasiparticles are emergent phenomena that occur when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in free space...
s of a system cannot be constructed as combinations of its elementary constituents. One of the earliest and most prominent examples is the fractional quantum Hall effect
Fractional quantum Hall effect
The fractional quantum Hall effect is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values of e^2/h. It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations...
, where the constituent particles are electrons but the quasiparticles carry fractions of the electron charge.
Other examples include spin–charge separation and emergent magnetic monopoles in spin ice
Spin ice
A spin ice is a substance that is similar to water ice in that it can never be completely frozen. This is because it does not have a single minimal-energy state. A spin ice has "spin" degrees of freedom , with frustrated interactions which prevent it freezing...
(which is well described by a classical statistical
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
model). They should be contrasted with quasiparticles such as magnon
Magnon
A magnon is a collective excitation of the electrons' spin structure in a crystal lattice. In contrast, a phonon is a collective excitation of the crystal lattice atoms or ions. In the equivalent wave picture of quantum mechanics, a magnon can be viewed as a quantized spin wave. As a...
s (constructed from an electron plus a hole
Electron hole
An electron hole is the conceptual and mathematical opposite of an electron, useful in the study of physics, chemistry, and electrical engineering. The concept describes the lack of an electron at a position where one could exist in an atom or atomic lattice...
) and Cooper pair
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair is two electrons that are bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Cooper...
s (two electrons), which have quantum numbers that are combinations of those of the constituents.