Excitons

Condensed matter describes the state in which a large number of particles assemble to form a macroscopic system. Complex interactions can arise from collective phenomena within such an ensemble. In a crystalline solid, energy and momentum are transferred via exotic processes that can be accurately modelled as the propagation of subatomic particles with altered properties. Such particles are known as quasiparticles. In this article, excitons, a particular type of quasiparticle are discussed.

Electrons in Solids

Electrons in a solid experience a periodic potential due to the presence of atomic nuclei at lattice sites throughout the substances ordered structure. Solving for the electronic energies leads to the emergence of two bands of allowed states, as shown in Figure 1.

Figure 1: The electrons within a solid can occupy one of two bands. Electrons in the conduction band contribute to the conductivity of the material. Electrons can be promoted from the valence band if given enough energy from an external source.

The lower band is known as the valence band whilst the top band is the conduction band. Electrons in the conduction band are free to move and can contribute to conduction.

Exciton Formation

The absorption of an incident photon with sufficient energy leads to the promotion of a valence electron to the conduction band. This process leaves behind an absence of negative charge in the valence band which can be modelled as the introduction of a positive charge, known as a hole and is shown in Figure 2.

Figure 2: A valence electron absorbs energy from an incident photon and is promoted to the conduction band. This process creates an electron-hole pair.

Following this process, both the hole and electron occupy the same point in space. Due to their opposite electric charges, there is a Coulomb attraction binding the two together within the material. The electron-hole pair can be modelled as a quasiparticle known as an exciton. If the ambient thermal energy of the surroundings is less than the exciton binding energy, the exciton will be stable and contribute to the optical properties of the material.

Types of Exciton

Excitons can be dichotomised according to the length of the bond between the electron-hole pair, known as the exciton radius. Excitons with a radius much larger than the distance between atoms in the solid are known as free excitons. Free excitons can be modelled in a similar way to positronium, an electron-positron molecule, and are delocalised from their original atomic sites with ease.

Excitons with a radius of the order of atomic spacing are known as bound excitons. Such excitons remain fixed to their original atomic positions. Whilst not free to move through the substance, bound excitons can deviate slightly from their origin by hopping from one atomic site to another.

The binding energy of a free exciton is small. Temperatures of around 100K are usually sufficient to break such bonds meaning free excitons are not found in most materials at reasonable temperatures. In contrast, bound excitons can boast much higher binding energies. Such bonds are often capable of existing at room temperature, meaning most solids in the everyday world will feature bound excitons.

Detecting Excitons

Optical absorption both creates excitons and can be used to detect them. Photons will be absorbed by a material if sufficiently energetic to instigate transitions. The exciton binding energies are much lower than typical bandgap values, meaning absorption will occur at lower photon energy in the presence of excitons. By measuring the frequency of such photons, the exciton binding energy can be calculated.

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