Polaron

A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material.

The general concept of a polaron has been extended to describe other interactions between the electrons and ions in metals that result in a bound state, or a lowering of energy compared to the non-interacting system.

However, a crystal lattice is deformable and displacements of atoms (ions) from their equilibrium positions are described in terms of phonons.

While polaron theory was originally developed for electrons, there is no fundamental reason why it could not be any other charged particle interacting with phonons.

Indeed, other charged particles such as (electron) holes and ions generally follow the polaron theory.

[7] Usually, in covalent semiconductors the coupling of electrons with lattice deformation is weak and polarons do not form.

The Fröhlich Hamiltonian for a single electron in a crystal using second quantization notation is: The exact form of γ depends on the material and the type of phonon being used in the model.

and by its characteristic response to external electric and magnetic fields (e. g. dc mobility and optical absorption coefficient).

of the charge carrier without self-induced polarization:[20] 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.

Later, Lieb and Thomas[22] gave a shorter proof using more conventional methods, and with explicit bounds on the lower order corrections to the Landau–Pekar formula.

Experimentally more directly accessible properties of the polaron, such as its mobility and optical absorption, have been investigated subsequently.

For polar crystals the value of the polaron binding energy is strictly determined by the dielectric constants

is smaller than the hopping integral t the large polaron is formed for some type of electron-phonon interactions.

A comparison of the DSG results [34] with the optical conductivity spectra given by approximation-free numerical [35] and approximate analytical approaches is given in ref.

[36] Calculations of the optical conductivity for the Fröhlich polaron performed within the Diagrammatic Quantum Monte Carlo method,[35] see Fig.

The application of a sufficiently strong external magnetic field allows one to satisfy the resonance condition

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.[38] The all-coupling magneto-absorption calculated in ref.,[33] leads to the best quantitative agreement between theory and experiment for AgBr and AgCl.

This quantitative interpretation of the cyclotron resonance experiment in AgBr and AgCl[38] by the theory of Peeters[33] provided one of the most convincing and clearest demonstrations of Fröhlich polaron features in solids.

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.

[39] 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.

[40] The resonant polaron effect manifests itself when the cyclotron frequency approaches the LO phonon energy in sufficiently high magnetic fields.

This formula was derived and extensively discussed in[41][42][43] and was tested experimentally for example in photodoped parent compounds of high temperature superconductors.

[44] The 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.

[9] These extensions of the concept are invoked, e. g., to study the properties of conjugated polymers, colossal magnetoresistance perovskites, high-

[9][59][60] 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 non-adiabatic treatment is needed.

[61] The non-adiabaticity of the exciton-phonon systems leads to a strong enhancement of the phonon-assisted transition probabilities (as compared to those treated adiabatically) and to multiphonon optical spectra that are considerably different from the Franck–Condon progression even for small values of the electron-phonon coupling constant as is the case for typical semiconductor nanostructures.

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 polaron that is (i) large so the continuum limit approximation in justified, (ii) acoustic because the self-localization arises from interactions with acoustic modes of the lattice, and (iii) weakly coupled because the anharmonic energy is small compared with the phonon bandwidth.

[63] This allows the hitherto inaccessible strong coupling regime to be studied, since the interaction strengths can be externally tuned through the use of a Feshbach resonance.

[64][65] The existence of the polaron in a Bose–Einstein condensate was demonstrated for both attractive and repulsive interactions, including the strong coupling regime and dynamically observed.