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

We consider electron self-trapping due to its interaction with order-parameter fluctuations at the second-order phase transition or critical point (for example, at the Curie temperature in magnetic or ferroelectric semiconductors). Using the 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.