Topological Semimetals Studied by Ab Initio Calculations

Hirayama, Motoaki; Okugawa, Ryo; Murakami, Shuichi

doi:10.7566/jpsj.87.041002

Cited by 53 publications

(52 citation statements)

References 102 publications

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“…In other cases a formal topological number can be defined in terms of energy band symmetry quantum numbers. Many of these tools have been implemented in ab initio band structure calculations (30,31,32). Density functional theory (DFT) within the single particle approximation provides a good description of weakly correlated electronic systems and has proven to be instrumental in finding material realizations of TSMs.…”

Section: Introductionmentioning

confidence: 99%

Topological Semimetals from First Principles

Gao

Venderbos

Kim

et al. 2019

Annu. Rev. Mater. Res.

193

118

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We review recent theoretical progress in the understanding and prediction of novel topological semimetals. Topological semimetals define a class of gapless electronic phases exhibiting topologically stable crossings of energy bands. Different types of topological semimetals can be distinguished based on the degeneracy of the band crossings, their codimension (e.g. point or line nodes), as well as the crystal space group symmetries on which the protection of stable band crossings relies. The dispersion near the band crossing is a further discriminating characteristic. These properties give rise to a wide range of distinct semimetal phases such as Dirac or Weyl semimetals, point or line node semimetals, and type-I or type-II semimetals. In this review we give a general description of various families of topological semimetals with an emphasis on proposed material realizations from first-principles calculations. The conceptual framework for studying topological gapless electronic phases is reviewed, with a particular focus on the symmetry requirements of energy band crossings, and the relation between the different families of topological semimetals is elucidated. In addition to the paradigmatic Dirac and Weyl semimetals, we pay particular attention to more recent examples of topological semimetals, which include nodal line semimetals, multifold fermion semimetals, triple-point semimetals. Less emphasis is placed on their surface state properties, responses to external probes, and recent experimental developments. 1 arXiv:1810.08186v1 [cond-mat.mes-hall]

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Section: Introductionmentioning

confidence: 99%

Topological Semimetals from First Principles

Gao

Venderbos

Kim

et al. 2019

Annu. Rev. Mater. Res.

193

118

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“…Studies on the topology of band structures in k space reveal various nontrivial phases of insulators and semimetals [1][2][3]. In recent years, higher-order topological phases have attracted high attention, where higher-order topological states appear due to nontrivial bulk topology.…”

Section: Introductionmentioning

confidence: 99%

Higher-order topological crystalline insulating phase and quantized hinge charge in topological electride apatite

Hirayama

Takahashi

Matsuishi

et al. 2020

Phys. Rev. Research

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In some kind of three-dimensional higher-order topological insulators, bulk and surface electronic states are gapped, while there appear gapless hinge states protected by spatial symmetry. Here we show by ab initio calculations that the La apatite electride is a higher-order topological crystalline insulator. It is a one-dimensional electride, in which the one-dimensional interstitial hollows along the c axis support anionic electrons, and the electronic states in these one-dimensional channels are well approximated by the one-dimensional Su-Schrieffer-Heeger model. When the crystal is cleaved into a hexagonal prism, the 120 • hinges support gapless hinge states, with their filling quantized to be 2/3. This quantization of the filling comes from a topological origin. We find that the quantized value of the filling depends on the fundamental blocks that constitute the crystal. The apatite consists of the triangular blocks, which is crucial for giving nontrivial fractional charge at the hinge.

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“…[16][17][18] Nodal-line semimetals where the conduction and valence bands touch each other along a line in the three-dimensional Brillouin zone have aroused broad interest in the possibility of topologically nontrivial states. [19][20][21][22][23][24][25][26][27][28] The crystal of metal dithiolene complex [Pd(dddt) 2 ] is an insulator at ambient pressure. The application of hydrostatic pressure using the DAC technique suppressed resistivity and activation energy.…”

Section: Introductionmentioning

confidence: 99%

Novel Dirac Electron in Single-Component Molecular Conductor [Pd(dddt)₂] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate)

Kato

Suzumura

2017

J. Phys. Soc. Jpn.

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Dirac electrons in a single-component molecular conductor [Pd(dddt) 2 ] (dddt=5,6dihydro-1,4-dithiin-2,3-dithiolate) under pressure have been examined using a tight-binding model which consists of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) functions in four molecules per unit cell. The Dirac cone between the conduction and valence bands originates from the property that the HOMO has ungerade symmetry and the LUMO has gerade symmetry. The Dirac point forms a loop in the three-dimensional Brillouin zone, which is symmetric with respect to the plane of k y = 0, where k y is the intralayer momentum along the molecular stacking direction, i.e., with the largest (HOMO-HOMO, LUMO-LUMO) transfer energy. The parity at time reversal invariant momentum (TRIM) is calculated using the inversion symmetry around the lattice point of the crystal. It is shown that such an exotic Dirac electron can be understood from the parity of the wave function at the TRIM and also from an effective Hamiltonian. Recently, a Dirac electron was found in the single-component molecular conductor [Pd(dddt) 2 ] (dddt=5,6-dihydro-1,4-dithiin-2,3-dithiolate), which shows a constant resistivity with decreasing temperature under pressure. 4, 5) Based on first-principles calculation, which shows the existence of a Dirac cone, 6) a tight-binding model of [Pd(dddt) 2 ] consisting of highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO)functions in four molecules per unit cell was proposed. 7) In the crystal, there are two crystallographically independent layers given by layers 1 and 2 (Fig. 1), and the Dirac cone originates from the HOMO-based band in layer 1 and the LUMO-based band in layer 2. 4) The interplay *

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Topological Semimetals Studied by Ab Initio Calculations

Cited by 53 publications

References 102 publications

Topological Semimetals from First Principles

Topological Semimetals from First Principles

Higher-order topological crystalline insulating phase and quantized hinge charge in topological electride apatite

Novel Dirac Electron in Single-Component Molecular Conductor [Pd(dddt)₂] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate)

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Topological Semimetals Studied by Ab Initio Calculations

Cited by 53 publications

References 102 publications

Topological Semimetals from First Principles

Topological Semimetals from First Principles

Higher-order topological crystalline insulating phase and quantized hinge charge in topological electride apatite

Novel Dirac Electron in Single-Component Molecular Conductor [Pd(dddt)2] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate)

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Novel Dirac Electron in Single-Component Molecular Conductor [Pd(dddt)₂] (dddt = 5,6-dihydro-1,4-dithiin-2,3-dithiolate)