Exciton
It is an electrically neutral quasiparticle regarded as an elementary excitation primarily in condensed matter, such as insulators, semiconductors, some metals, and in some liquids.
Here 'hole' represents the unoccupied quantum mechanical electron state with a positive charge, an analogue in crystal of a positron.
Exciton binding energy and radius can be extracted from optical absorption measurements in applied magnetic fields.
[6] The exciton as a quasiparticle is characterized by the momentum (or wavevector K) describing free propagation of the electron-hole pair as a composite particle in the crystalline lattice in agreement with the Bloch theorem.
The exciton energy also depends on the respective orientation of the electron and hole spins, whether they are parallel or anti-parallel.
In metals and highly doped semiconductors a concept of the Gerald Mahan exciton is invoked where the hole in a valence band is correlated with the Fermi sea of conduction electrons.
The concept of excitons was first proposed by Yakov Frenkel in 1931,[7] when he described the excitation of an atomic lattice considering what is now called the tight-binding description of the band structure.
Another example of Frenkel exciton includes on-site d-d excitations in transition metal compounds with partially filled d-shells.
Absorption of a photon resonant with a d-d transition leads to the creation of an electron-hole pair on a single atomic site, which can be treated as a Frenkel exciton.
Small effective mass of electrons that is typical of semiconductors also favors large exciton radii.
Likewise, because of the lower masses and the screened Coulomb interaction, the binding energy is usually much less than that of a hydrogen atom, typically on the order of 0.01eV.
Often more than one band can be chosen as source for the electron and the hole, leading to different types of excitons in the same material.
For example, in GaAs, we have relative permittivity of 12.8 and effective electron and hole masses as 0.067m0 and 0.2m0 respectively; and that gives us
One must instead turn to numerical procedures, and it is precisely this potential that gives rise to the nonhydrogenic Rydberg series of the energies in 2D semiconductors.
[11] Monolayers of a transition metal dichalcogenide (TMD) are a good and cutting-edge example where excitons play a major role.
In particular, in these systems, they exhibit a bounding energy of the order of 0.5 eV[3] with a Coulomb attraction between the hole and the electrons stronger than in other traditional quantum wells.
In molecular physics, CT excitons form when the electron and the hole occupy adjacent molecules.
At surfaces it is possible for so called image states to occur, where the hole is inside the solid and the electron is in the vacuum.
Dark excitons are those where the electrons have a different momentum from the holes to which they are bound that is they are in an optically forbidden transition which prevents them from photon absorption and therefore to reach their state they need phonon scattering.
Molecular excitons typically have characteristic lifetimes on the order of nanoseconds, after which the ground electronic state is restored and the molecule undergoes photon or phonon emission.
In these crystals an elementary cell includes several molecules sitting in symmetrically identical positions, which results in the level degeneracy that is lifted by intermolecular interaction.
First, self-trapped exciton states are always of a small radius, of the order of lattice constant, due to their electric neutrality.
Transforming a free exciton state into a self-trapped one proceeds as a collective tunneling of coupled exciton-lattice system (an instanton).
Coexistence of free and self-trapped excitons was observed in rare-gas solids,[37][38] alkali-halides,[39] and in molecular crystal of pyrene.
If a large density of excitons is created in a material, they can interact with one another to form an electron-hole liquid, a state observed in k-space indirect semiconductors.
[42] In 2017 Kogar et al. found "compelling evidence" for observed excitons condensing in the three-dimensional semimetal 1T-TiSe2.
[43] Normally, excitons in a semiconductor have a very short lifetime due to the close proximity of the electron and hole.
However, by placing the electron and hole in spatially separated quantum wells with an insulating barrier layer in between so called 'spatially indirect' excitons can be created.
These excitons form when electrons and holes bind in a two-dimensional material separated by an insulating layer of hexagonal boron nitride.
When exposed to strong magnetic fields, these systems display fractionalized excitonic behavior with distinct quantum properties.
