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## Polaron
The resulting lattice polarization acts as a potential well that hinders the movements of the charge, thus decreasing its mobility. Polarons have spin, though two close-by polarons are spinless. The latter is called a bipolaron. In materials science, a polaron is formed when a charge within a molecular chain influences the local nuclear geometry, causing an attenuation (or even reversal) of nearby bond alternation amplitudes. This "excited state" possesses an energy level between the lower and upper bands. The concept of a polaron is used while discussing ways for making a polymer electrically conductive. As an example, PPV (poly paraphenylenevinylene), is presently the most popular commercially available conducting polymer. In this it is tried to create an excited state which is then eventually relaxed and the energy is emitted either in a radiative manner (emitting light) or a non radiative manner (vibration etc). One of the simplest ways to create such an "excited state" (i.e. a polaron) is by alternating the bond geometry which is done by doping the polymer. In a bipolaron two charged units exist within a molecular chain. A polaron liquid has been found in doped cuprate perovskites showing high Tc superconductivity. ## Additional recommended knowledge
## Polaron theoryL. D. Landau
The polarization, carried by the longitudinal optical (LO) phonons, is represented by a set of quantum oscillators with frequency ω, the long-wavelength LO-phonon frequency, and the interaction between the charge and the polarization field is linear in the field. This model (which up to now has not been solved exactly) has been the subject of extensive investigations The strength of the electron-phonon interaction is expressed by a dimensionless coupling constant α introduced by Fröhlich The physical properties of a polaron differ from those of a band-carrier. A polaron is characterized by its When the coupling is weak (α small), the self-energy of the polaron can be approximated as
and the polaron mass
When the coupling is strong (α large), a variational approach due to Landau and Pekar indicates that the self-energy is proportional to α² and the polaron mass scales as α⁴. Feynman ## Polaron optical absorptionThe expression for the magnetooptical absorption of a polaron is
Here, ω In the absence of an external magnetic field (ω
A comparison of the DSG results Calculations of the optical conductivity for the Fröhlich polaron performed within the Diagrammatic Quantum Monte Carlo method
The application of a sufficiently strong external magnetic field allows one to satisfy the resonance condition Ω = ω Evidence for the polaron character of charge carriers in AgBr and AgCl was obtained through high-precision cyclotron resonance experiments in external magnetic fields up to 16 T Experimental data on the magnetopolaron effect, obtained using far-infrared photoconductivity techniques, have been applied to study the energy spectrum of shallow donors in polar semiconductor layers of CdTe The polaron effect well above the LO phonon energy was studied through cyclotron resonance measurements, e. g., in II-VI semiconductors, observed in ultra-high magnetic fields ## Polarons in two dimensions and in quasi-2D structuresThe great interest in the study of the two-dimensional electron gas (2DEG) has also resulted in many investigations on the properties of polarons in two dimensions
It has been shown that simple scaling relations exist, connecting the physical properties of polarons in 2D with those in 3D. An example of such a scaling relation is
where () and () are, respectively, the polaron and the electron-band masses in 2D (3D). The effect of the confinement of a Fröhlich polaron is to enhance the Also in 2D systems cyclotron resonance is a convenient tool to study polaron effects. Although several other effects have to be taken into account (nonparabolicity of the electron bands, many-body effects, the nature of the confining potential, etc.), the polaron effect is clearly revealed in the cyclotron mass. An interesting 2D system consists of electrons on films of liquid He For GaAs/Al In GaAs/AlAs quantum wells with sufficiently high electron density, anticrossing of the cyclotron-resonance spectra has been observed near the GaAs transverse optical (TO) phonon frequency rather than near the GaAs LO-phonon frequency Besides optical properties ## Extensions of the polaron conceptSignificant are also the extensions of the polaron concept: acoustic polaron, piezoelectric polaron, electronic polaron, bound polaron, trapped polaron, spin polaron, molecular polaron, solvated polarons, polaronic exciton, Jahn-Teller polaron, small polaron, bipolarons and many-polaron systems The possibility that polarons and bipolarons play a role in high- A new aspect of the polaron concept has been investigated for semiconductor nanostructures: the exciton-phonon states are not factorizable into an adiabatic product Ansatz, so that a In biophysics Davydov soliton is a propagating along the protein α-helix self-trapped amide I excitation that is a solution of the Davydov Hamiltonian. The mathematical techniques that are used to analyze Davydov's soliton are similar to some that have been developed in polaron theory. In this context the Davydov soliton corresponds to a ## References and notes**^**Landau LD (1933). "Über die Bewegung der Elektronen in Kristalgitter".*Phys. Z. Sowjetunion***3**: 644-645.- ^
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Categories: Condensed matter physics | Ions |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Polaron". A list of authors is available in Wikipedia. |