The roots of polaron theory

In his review of the book Polarons by David Emin (Physics Today, October 2014, page 54 ), Jozef Devreese properly emphasizes the role of large polarons as both a general theoretical concept and a physical object. Polarons are electrons dressed by a cloud of virtual phonons in solids. To the best of our knowledge, they present the first example of propagating self-localized excitations in a quantum field theory. Devreese lists brilliant theorists who were inspired by the theory of polarons and significantly contributed to it, but he makes a serious omission when it comes to the roots of the polaron theory and the very origin of the term “polaron.”

The general idea of electron trapping by a crystal lattice goes back to the seminal 1933 paper by Lev Landau. ¹ That paper, which Devreese mentions, is primarily concerned with the resulting lattice defects, such as color centers in sodium chloride. Landau does not specify the trapping mechanism and contrasts a trapped electron with what he refers to as a freely moving electron.

The polaron was proposed, and the term coined, by Solomon Pekar. In two papers ² published in 1946, he developed a self-consistent theory of a large polaron as a spontaneously trapped state of an electron strongly coupled to the induced polarization of atomic displacements in an ionic crystal. In his initial papers, Pekar considered polaron states to be “local,” but in the follow-up papers ³ he identified polarons, rather than band electrons, as charge carriers in ionic crystals. That concept was developed and substantiated in a joint 1948 paper by Landau and Pekar in which they calculated the effective mass of a large, strongly coupled polaron. ⁴ Regarding the role of polarons as charge carriers, that paper states that Pekar proposed “a new point of view concerning the electron conduction of ionic crystals. According to it, the current carrier is just a polaron, rather than a free electron in the conduction band.”

The paper by Landau and Pekar appeared at the time of burgeoning progress in quantum electrodynamics (QED). In contrast to QED, the polaron theory is free from divergences, and the renormalized electron energy and mass remain finite. Also in contrast to QED, the polaron theory was initially a strong-coupling theory. For those reasons, it attracted much attention beyond the condensed-matter community. The extension to intermediate and weak coupling quickly followed. ⁵ Today the physics of polarons continues to thrive and expand into new areas.