# Flexoelxctricity of the distorted twist bend nematic phase

## TL;DR

This paper extends the symmetry-based elastic theory of the twist-bend nematic phase to include flexoelectricity, explaining the increased polarization and predicting new behaviors at phase transition points.

## Contribution

It introduces a theoretical model incorporating flexoelectric effects in the twist-bend nematic phase, predicting increased flexoelectric coefficients and new active modes at phase transition.

## Key findings

- Flexoelectric coefficient increases at the nematic to twist-bend transition.
- A new flexoelectric mode becomes active at the phase transition.
- The model predicts possible unwinding of the helix leading to a splay-bend nematic phase.

## Abstract

Mesogenic dimers in the twist-bend nematic phase exhibit much higher flexoelectric polarization than in their uniform nematic phase. In order to theoretically investigate this data, we extend the symmetry based linear elastic theory of the twist-bend nematic phase developed in Phys. Rev. E 92, 030501(R) 2015, by including flexoelectricity under the action of an external electric field perpendicular to the helical axis. We show that at the nematic towards twist-bend nematic transition, a new flexoelectric mode becomes active. Consequently, the present model predicts the increase of the effective flexoelectric coefficient when the system is entering the twist-bend nematic phase. The influence of the flexoelectric coupling on the equilibrium wavevector and the spontaneous heliconical tilt angle are investigated. The electroclinic coefficient is calculated. Finally we argue that the helix could be unwound giving rise to a splay-bend nematic phase.