Wave vector star channel and star channel group in the reciprocal lattice space of crystal

TL;DR

This paper introduces a novel method for identifying wave vector star channels in crystal reciprocal space, emphasizing the role of symmetry in phase transitions and defining the wave vector star channel group for analyzing translational symmetry breaking.

Contribution

It proposes a new approach to determine wave vector star channels considering symmetry breaking and introduces the concept of wave vector star channel group for comprehensive analysis.

Findings

Phase transitions are driven by symmetry-compatible arm combinations.

Wave vector star channel group leaves the channel invariant.

Method applicable to all Lifshitz wave vector stars in 230 space groups.

Abstract

In the paper, a new method determining the wave vector star channel in the reciprocal lattice space of crystal in the light of the translational symmetry breaking is proposed, and, in order to consider the phase transitions according to the wave vector star channel, the conception of wave vector star channel group is adopted. By this method, it is revealed that the phase transitions in crystal are induced not by any arbitrary combinations of arms of the given star, but by the selected combinations of arms which are satisfied by symmetry of the parent phase. The wave vector star channel group is defined as the set of elements of space group leaving the wave vector star channel invariant. We show that the conception of wave vector star channel group can be efficiently used in studying the translational symmetry breaking related to all the Lifshitz wave vector stars of 230 space groups.