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

Flor, G. de la; Orobengoa, D.; Ėvarestov, R. A.; Kitaev, Yu. É.; Taşci, Emre S.; Aroyo, M. I.

doi:10.1107/s1600576719011725

Cited by 12 publications

(8 citation statements)

References 30 publications

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“…As the first step , one finds NM layer groups based on the NM bulk MnO 2 crystal (scanned space group no 136 P 4 2 / mnm ). For this, we used the program SECTIONS from Bilbao Crystallographic Server (BCS). − , This program identifies, for a given nonmagnetic space group, the full set of possible NM layer symmetries of periodic sections defined by their common normal vector and located within the unit cell. The program accepts as input a scanned space group given in any arbitrary setting.…”

Section: Mno2 Monolayers: Dft Calculations and Group-theoretical Anal...mentioning

confidence: 99%

Antiferromagnetism-Induced Spin Splitting in Systems Described by Magnetic Layer Groups

2021

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In this paper, we report the classification of all the 528 magnetic layer groups into seven spin splitting prototypes, in analogy to the similar classification previously reported for the 1651 magnetic space groups [Yuan et al., Phys. Rev. Mat. 2021, 5, 014409]. According to this classification, induced (Pekar−Rashba) spin splitting is possible in the antiferromagnetic monolayers described by magnetic layer groups of type I (no anti-unitary operations) and III, both in the presence and in the absence of the space inversion operation. As one specific application, we have studied theoretically the (110) monolayer of antiferromagnetic (AFM) MnO 2 . Our density functional theory calculations for this structure predicted colossal (on the order of 1 eV) spin splitting in the entire Brillouin zone, similar to the case of the (110) monolayer of AFM MnF 2 which was studied by us earlier. This splitting is much larger compared to the corresponding values for the bulk AFM1 structure of β-MnO 2 , which was rationalized by noting that the (110) monolayer is described by the type I magnetic layer group that does not contain anti-unitary symmetry operations, and therefore, spin splitting is not suppressed anywhere in the entire Brillouin zone, including high-symmetry points and lines.

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Section: Mno2 Monolayers: Dft Calculations and Group-theoretical Anal...mentioning

confidence: 99%

Antiferromagnetism-Induced Spin Splitting in Systems Described by Magnetic Layer Groups

2021

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“…To obtain a complete symmetry-based description, representations relevant to the entire band structure [45] are evaluated and decomposed into building blocks, EBRs. [46][47][48] To this end, the program POLSym [49] is applied. In this program, subroutines based on topological quantum chemistry, [50] which establish symmetry relations between localized and extended crystal states in 2D materials, are incorporated.…”

Section: Symbolmentioning

confidence: 99%

Electronic Band Topology of Monoclinic MoS₂ Monolayer: Study Based on Elementary Band Representations for Layer Groups

Milošević

Popović

Nikolić

et al. 2020

Physica Rapid Research Ltrs

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Layered structures of group-VI transition-metal dichalcogenides (TMDs) MX 2 (M ¼ Mo, W; X ¼ Te, Se, S) [1,2] are of particular importance in both fundamental research and novel device design, because these compounds manifest a variety of quantum phenomena and combine technologically relevant and complementary physical properties, thus promising applications in optoelectronics, valleytronics, spintronics, energy storage, and energy harvesting. [1,3-7] The most studied compound among these group-VI TMDs, molybdenum disulfide or MoS 2 , exists as several polytypes. Even a single three-atoms-thick MX 2 sheet occurs in many different forms: semiconducting hexagonal 1H, metallic octahedral 1T, semimetallic monoclinic 1T 0 , and slightly distorted polymorphic forms of the latter (1T 00 and 1T 000[7]). Whereas the 1H phase is stable, the 1T phase is very unstable and undergoes Peierls transition to the metastable 1T 0 phase, which, together with 1T 00 and 1T 000 , embedded mainly in the 1H phase, [8] can be obtained via chemical exfoliation. Phase-controlled large-scale growth of μm-sized layered group-VI TMDs and synthesis of 1T 0-MoS 2 crystals of high purity have also been reported recently, [9] whereas from a theoretical perspective, a potassiumassisted chemical vapor deposition method for the phase-selective growth of 1T 0-MoS 2 monolayers and 1T 0 /2H heterophase bilayers has been proposed. [10] Nevertheless, despite these past efforts, 1T 0-MX 2 monolayers remain difficult to obtain experimentally, and therefore, measurements are usually performed on multilayers [11] and then, with the help of theoretical considerations and numerical calculations, extrapolated to the monolayer level. Meanwhile, structural phase transitions between different polytypes can be realized via diverse methods: alkali-metal intercalation, strain engineering, electron-beam and high-energy laser irradiation, argon plasma treatment, controlled chemical vapor deposition growth, [12-19] etc. In previous years, TMDs have attracted considerable research interest for their applications as solid lubricants, [20] catalytic materials, [21] and high-performance transistors, [3] whereas, nowadays, layered TMDs have become a focus of research primarily as strong photoluminescent materials [4,22] that could host nontrivial topological phases. [12,23-34] On the basis of the calculated Z 2 topological index, which characterizes time-reversal-invariant systems, [35] layered 1T 0 TMDs have been predicted to exhibit the quantum-spin Hall (QSH) effect, [36] and thus, construction of a field-effect transistor that would be based on the reversible topological phase transition [33] has been proposed. [23] In contrast, 1T 0 molybdenum ditelluride (MoTe 2) has quite recently been theoretically characterized as a Z 4-nontrivial higher order topological insulator. [26] Experimental verification of the QSH effect in 2D crystals of atomic-scale thickness is a challenging task, aimed at observation of phenomena that are considered characteristic for the

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“…In fact, for each LG there are supergroups among the space groups, and data for the supergroup (irreducible domains, IRs, etc.) can in principle be used [3] to derive the corresponding data for the LG [4]. Being cumbersome, this procedure is not straightforward and therefore, IRs of LGs have been derived independently [5].…”

Section: Introductionmentioning

confidence: 99%

“…Being cumbersome, this procedure is not straightforward and therefore, IRs of LGs have been derived independently [5]. More than a decade ago Bilbao crystallographic server [6,7] devoted a section to the LGs, which has recently been amended by the band representations, being induced from the representations of the site symmetry groups [4]. However, a bunch of information is still missing, and the present paper is aimed at completing the field.…”

Section: Introductionmentioning

confidence: 99%

Irreducible and site symmetry induced representations of single/double ordinary/gray layer groups

Nikolić,

Milošević,

Vuković

et al. 2021

Preprint

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Considered are eighty sets of layer groups, each set consisted of four groups: ordinary single and double, and gray single and double layer group. Structural properties of layer groups (factorization onto cyclic subgroups and existence of grading according to the sequence of halving subgroups) enable efficient symbolic computation (by POLSym code) of the relevant properties, real and complex irreducible and allowed (half-)integer (co-)representations in particular. This task includes, as the first step, classification of the irreducible domains based on the group action in Brillouin zone combined with torus topology. Also, the band (co-)representations induced from the irreducible (co-)representations of Wyckoff position stabilizers (site symmetry groups) are decomposed onto the irreducible components. These, and other layer group symmetry related theoretical data relevant for physics, layered materials in particular, are tabulated and made available through the web site.

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

Cited by 12 publications

References 30 publications

Antiferromagnetism-Induced Spin Splitting in Systems Described by Magnetic Layer Groups

Antiferromagnetism-Induced Spin Splitting in Systems Described by Magnetic Layer Groups

Electronic Band Topology of Monoclinic MoS₂ Monolayer: Study Based on Elementary Band Representations for Layer Groups

Irreducible and site symmetry induced representations of single/double ordinary/gray layer groups

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

Cited by 12 publications

References 30 publications

Antiferromagnetism-Induced Spin Splitting in Systems Described by Magnetic Layer Groups

Antiferromagnetism-Induced Spin Splitting in Systems Described by Magnetic Layer Groups

Electronic Band Topology of Monoclinic MoS2 Monolayer: Study Based on Elementary Band Representations for Layer Groups

Irreducible and site symmetry induced representations of single/double ordinary/gray layer groups

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Electronic Band Topology of Monoclinic MoS₂ Monolayer: Study Based on Elementary Band Representations for Layer Groups