Electron self-trapping and fluctuation density-of-states tail at the critical point

TL;DR

This paper investigates how electrons become self-trapped due to order-parameter fluctuations at critical points, linking the phenomenon to the Lifshitz tail in the density of states and estimating relevant energies and sizes.

Contribution

It introduces a Feynman path integral method to estimate autolocalization energy and size of self-trapped electrons at critical points, connecting these to critical exponents.

Findings

Self-trapped states are related to Lifshitz tails in the density of states.

Parameters of the density-of-states tail are determined by critical exponents.

Autolocalization energy and size of self-trapped states are estimated.

Abstract

We consider electron self-trapping due to its interaction with order-parameter fluuctuations at the second-order phase-transition or critical point (for example, at the Curie temperature in magnetic or ferroelectric semiconductors). Using Feynman path integral approach the autolocalization energy and the size of the self-trapped state (fluctuon) are estimated. It is shown that the fluctuon states are connected with the Lifshitz tail of the electron density-of-states, the parameters of this tail being determined by the critical exponents.