The site-symmetry induced representations of layer groups on the Bilbao Crystallographic Server.

Gemma De La Flor,Robert A Evarestov,Yuri E Kitaev,Emre Tasci,Mois I Aroyo,Danel Orobengoa

doi:10.1107/s1600576719011725

Gemma De La Flor, Robert A Evarestov + Show 4 more

Open Access

https://doi.org/10.1107/s1600576719011725

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Abstract

The section of the Bilbao Crystallographic Server (http://www.cryst.ehu.es) dedicated to subperiodic groups includes a new tool called LSITESYM for the study of materials with layer and multilayer symmetry. This new program, based on the site-symmetry approach, establishes the symmetry relations between localized and extended crystal states using representations of layer groups. The efficiency and utility of the program LSITESYM is demonstrated by illustrative examples, which include the analysis of phonon symmetry in Aurivillius compounds and in van der Waals layered crystals MoS2 and WS2.

Highlights

IntroductionThe site-symmetry method is based on the procedure of induction of representations of the crystal space group from the irreducible representations (irreps) of the site-symmetry groups of the constituent units (atoms, clusters and layers) according to which the local excitations are transformed
The interest in layered and multilayered materials such as graphene (Geim & Novoselov, 2007; Randviir et al, 2014) and van der Waals crystals, e.g. the transition metal dichalcogenide crystal family MeX2 with Me = Nb, Mo, Ta, W, Ti, V, Zr, Hf and X = S, Se, Te (Han et al, 2018; Manzeli et al, 2017; Choi et al, 2017), is constantly growing owing to their interesting properties and possible technological applications
While space groups and their representations describe the symmetry of the bulk electron and phonon states, the layer groups are essential for the description of the electronic structure and the surface states of crystals

Summary

Introduction

The site-symmetry method is based on the procedure of induction of representations of the crystal space group from the irreducible representations (irreps) of the site-symmetry groups of the constituent units (atoms, clusters and layers) according to which the local excitations are transformed In this way, the symmetry of phonon, electron, exciton, biexciton etc. Even though layer groups were described for the first time about a century ago (Weber, 1929; Alexander & Hermann, 1929), it was not until the paper by Zallen et al (1971) that they were applied for the first time for the description of phonon states in layered As2S3 and As2Se3 crystals Afterwards, they were used for modelling atomically clean crystal surfaces (Ipatova & Kitaev, 1985). The procedure of the program for the construction of the induced representations of layer groups is described in detail, and its utility is demonstrated by several examples

General procedure

Application of site-symmetry method to layer groups

The program LSITESYM

Transition metal dichalcogenide layer crystals

Conclusions

Funding information