Topics on space groups treated in Volumes A1 and E of <i>International Tables for Crystallography</i>

Lattice translation symmetry gives rise to a large class of "weak" topological insulators (TIs), characterized by translation-protected gapless surface states and dislocation bound states. In this work we show that space group symmetries lead to constraints on the weak topological indices that define these phases. In particular, we show that screw rotation symmetry enforces the Hall conductivity in planes perpendicular to the screw axis to be quantized in multiples of the screw rank, which generally applies to interacting systems. We further show that certain 3D weak indices associated with quantum spin Hall effects (class AII) are forbidden by the Bravais lattice and by glide or even-fold screw symmetries. These results put strong constraints on weak TI candidates in the experimental and numerical search for topological materials, based on the crystal structure alone.

show abstract

“…To get a nontrivial weak index, we 035115-3 [53]; "all" means all the eight possible values are allowed.…”

Section: A Constraints From Bravais Latticementioning

confidence: 99%

Space group constraints on weak indices in topological insulators

2017

View full text Add to dashboard Cite

show abstract

“…In accordance with Volume A1 of International Tables for Crystallography (Wondratschek & Mü ller, 2004), conventional bases for lattice-type pairs L 1 and L 2 have been chosen in Tables 3 and 4 Table 4 Metric relations between the conventional unit cells of lattice types related by normal subgroups, i.e. joined by full lines in Fig.…”

Section: Metric Relations Between Conventional Bases Of 'Neighbouringmentioning

confidence: 99%

“…we shall make use of information given in ITC-A or, in more detail, in Volume A1 of International Tables for Crystallography (Wondratschek & Mü ller, 2004).…”

Section: Introductionmentioning

confidence: 99%

Partial order among the 14 Bravais types of lattices: basics and applications

Grimmer

2015

Acta Cryst Sect A

View full text Add to dashboard Cite

Neither International Tables for Crystallography (ITC) nor available crystallography textbooks state explicitly which of the 14 Bravais types of lattices are special cases of others, although ITC contains the information necessary to derive the result in two ways, considering either the symmetry or metric properties of the lattices. The first approach is presented here for the first time, the second has been given by Michael Klemm in 1982. Metric relations between conventional bases of special and general lattice types are tabulated and applied to continuous equi-translation phase transitions.

show abstract

“…A useful group-subgroup relationship [29,30] between the structural models under consideration was established (see Fig. 4).…”

Section: Crystal Structure Of Lamg 3-x Ge 2 (τ 5 ) As √3a×√3a×2c Supementioning

confidence: 99%

Phase equilibria in the La–Mg–Ge system at 500°C and crystal structure of the new ternary compounds La11Mg2Ge7 and LaMg3−xGe2

Negri

Solokha

Skrobańska

et al. 2014

Journal of Solid State Chemistry

View full text Add to dashboard Cite

show abstract

Topics on space groups treated in Volumes A1 and E of International Tables for Crystallography

Cited by 18 publications

References 0 publications

Space group constraints on weak indices in topological insulators

Space group constraints on weak indices in topological insulators

Partial order among the 14 Bravais types of lattices: basics and applications

Phase equilibria in the La–Mg–Ge system at 500°C and crystal structure of the new ternary compounds La11Mg2Ge7 and LaMg3−xGe2

Contact Info

Product

Resources

About