Flexuron, a self-trapped state of electron in crystalline membranes

TL;DR

This paper investigates how electrons can become self-trapped in flexible crystalline membranes due to their interaction with bending fluctuations, leading to the formation of a localized state called a flexuron, with implications for electron density and membrane properties.

Contribution

The study introduces the concept of a flexuron as a self-trapped electron state in membranes and estimates its size and energy using the Feynman path integral approach, highlighting its relation to membrane fluctuations.

Findings

The flexuron size is comparable to the wavelength of membrane fluctuations at the harmonic-anharmonic transition.

Self-trapped states influence the tail of the electron density-of-states distribution.

The asymptotic behavior of the density-of-states tail depends on the renormalized bending rigidity.

Abstract

Self-trapping of an electron due to its interaction with bending fluctuations in a flexible crystalline membrane is considered. Due to the dependence of the electron energy on the corrugations of the membrane, the electron can create around itself an anomalously flat (or anomalously corrugated, depending on the sign of the interaction constant) region and be confined there. Using the Feynman path integral approach, the autolocalization energy and the size of the self-trapped state (flexuron) are estimated. It is shown that typically the size of the flexuron is of the order of the wavelength of fluctuations at the border between harmonic and anharmonic regimes. The flexuron states are connected with the fluctuation tail of the electron density-of-states, the asymptotic behavior of this tail being determined by the exponent of the renormalized bending rigidity.