Polaron

A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. The polaron concept was proposed by Lev Landau in 1933 and Solomon Pekar in 1946 to describe an electron moving in a dielectric crystal where the atoms displace from their equilibrium positions to effectively screen the charge of an electron, known as a phonon cloud. This lowers the electron mobility and increases the electron's effective mass. 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. Major theoretical work has focused on solving Fröhlich and Holstein Hamiltonians. This is still an active field of research to find exact numerical solutions to the case of one or two electrons in a large crystal lattice, and to study the case of many interacting electrons. Experimentally, polarons are important to the understanding of a wide variety of materials. The electron mobility in semiconductors can be greatly decreased by the formation of polarons. Organic semiconductors are also sensitive to polaronic effects, which is particularly relevant in the design of organic solar cells that effectively transport charge. Polarons are also important for interpreting the optical conductivity of these types of materials. The polaron, a fermionic quasiparticle, should not be confused with the polariton, a bosonic quasiparticle analogous to a hybridized state between a photon and an optical phonon. The energy spectrum of an electron moving in a periodical potential of rigid crystal lattice is called the Bloch spectrum, which consists of allowed bands and forbidden bands. An electron with energy inside an allowed band moves as a free electron but has an effective mass that differs from the electron mass in vacuum. However, a crystal lattice is deformable and displacements of atoms (ions) from their equilibrium positions are described in terms of phonons.