scholarly journals New classes of topological crystalline insulators having surface rotation anomaly

2019 ◽  
Vol 5 (12) ◽  
pp. eaat2374 ◽  
Author(s):  
Chen Fang ◽  
Liang Fu
Keyword(s):  
Rotation Axis ◽  
Side Surface ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Rotation Symmetry ◽  
Quantum Device ◽  
Quantum Anomalies ◽  
Topological Crystalline Insulators ◽  
Topological Crystalline Insulator ◽  
Helical Mode

We discover new types of quantum anomalies in two-dimensional systems with time-reversal symmetry (T) and discrete rotation symmetry with order of n = 2, 4, and 6 (Cn). The new anomalous states have n flavors of massless Dirac fermions protected by T and Cn, whereas any two-dimensional lattices having the two symmetries must have a multiple of 4, 8, and 12 Dirac cones for n = 2, 4, and 6, respectively. We show that these anomalous states are physically realized on the surface of new classes of topological crystalline insulators, normal to the rotation axis. Moreover, these topological crystalline insulators support n gapless one-dimensional helical mode on the otherwise fully gapped side surface, connecting the anomalous two-dimensional states on the top and bottom surfaces. The presence of these helical modes enables a new quantum device made from a topological crystalline insulator nanorod, a “helical nanorod,” which has a quantized longitudinal conductance of ne2/h.

scholarly journals Discovery of $${\hat{\boldsymbol{C}}}_2$$ rotation anomaly in topological crystalline insulator SrPb

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Wenhui Fan ◽  
Simin Nie ◽  
Cuixiang Wang ◽  
Binbin Fu ◽  
Changjiang Yi ◽  
...  
Keyword(s):  
Surface States ◽  
Binary Compound ◽  
Dirac Fermions ◽  
Rotation Symmetry ◽  
Angle Resolved Photoemission Spectroscopy ◽  
Topological Crystalline Insulators ◽  
Topological Crystalline Insulator ◽  
Nontrivial Topology ◽  
Bulk Band

AbstractTopological crystalline insulators (TCIs) are insulating electronic states with nontrivial topology protected by crystalline symmetries. Recently, theory has proposed new classes of TCIs protected by rotation symmetries $$\hat C_n$$ C ̂ n , which have surface rotation anomaly evading the fermion doubling theorem, i.e., n instead of 2n Dirac cones on the surface preserving the rotation symmetry. Here, we report the first realization of the $$\hat C_2$$ C ̂ 2 rotation anomaly in a binary compound SrPb. Our first-principles calculations reveal two massless Dirac fermions protected by the combination of time-reversal symmetry $$\hat T$$ T ̂ and $$\hat C_{2y}$$ C ̂ 2 y on the (010) surface. Using angle-resolved photoemission spectroscopy, we identify two Dirac surface states inside the bulk band gap of SrPb, confirming the $$\hat C_2$$ C ̂ 2 rotation anomaly in the new classes of TCIs. The findings enrich the classification of topological phases, which pave the way for exploring exotic behavior of the new classes of TCIs.

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

scholarly journals Two-Dimensional Boron Hydride Sheets: High Stability, Massless Dirac Fermions, and Excellent Mechanical Properties

2016 ◽  
Vol 128 (35) ◽  
pp. 10448-10451 ◽  
Author(s):  
Yalong Jiao ◽  
Fengxian Ma ◽  
John Bell ◽  
Ante Bilic ◽  
Aijun Du
Keyword(s):  
Mechanical Properties ◽  
High Stability ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Boron Hydride

scholarly journals Poly[μ2-aqua-bis[μ4-2-(1H-1,2,3-benzotriazol-1-yl)acetato]dipotassium]

2012 ◽  
Vol 68 (4) ◽  
pp. m379-m379 ◽  
Author(s):  
Qiong Liu
Keyword(s):  
Hydrogen Bonds ◽  
Water Molecule ◽  
Title Compound ◽  
Rotation Axis ◽  
Aqua Ligand ◽  
Octahedral Geometry ◽  
Two Dimensional ◽  
Compound K ◽  
Bridging Ligands ◽  
Carboxylate Groups

In the title compound, [K2(C8H6N3O2)2(H2O)]n, each K+ion is seven-coordinated by one O atom from a bridging water molecule, five carboxylate O atoms and one N atom from a benzotriazole group, forming a distorted mono-capped octahedral geometry. In the crystal, the carboxylate groups act as bridging ligands, forming a two-dimensional polymer parallel to (001). The aqua ligand, which lies on a twofold rotation axis, forms intermolecular O—H...O hydrogen bonds within these layers.

scholarly journals Tris(1,10-phenanthroline-κ2 N,N′)cobalt(II) bis(2,4,5-tricarboxybenzoate) monohydrate

IUCrData ◽  
2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Kai-Long Zhong ◽  
Guo-Qing Cao ◽  
Wei Song ◽  
Chao Ni
Keyword(s):  
Hydrogen Bonds ◽  
Network Structure ◽  
Rotation Axis ◽  
Complex Cation ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Network ◽  
Distorted Octahedral

In the complex cation of the title salt, [Co(C12H8N2)3](C10H5O8)2·H2O, the CoII cation is situated on a twofold rotation axis and is coordinated in a distorted octahedral manner by six N atoms from three chelating 1,10-phenanthroline (phen) ligands. In the crystal, the non-coordinating 2,4,5-tricarboxybenzoate anions interact with each other via O—H...O hydrogen bonds, generating a two-dimensional network parallel to (100). Adjacent sheets are connected by waterO—H...Ocarboxylate hydrogen bonds, resulting in a three-dimensional network structure that surrounds the complex cations.

scholarly journals Itinerant quantum multicriticality of two-dimensional Dirac fermions

2018 ◽  
Vol 97 (20) ◽  
Author(s):  
Bitan Roy ◽  
Pallab Goswami ◽  
Vladimir Juričić
Keyword(s):  
Dirac Fermions ◽  
Two Dimensional

scholarly journals Two-dimensional Dirac fermions on oxidized black phosphorus

2019 ◽  
Vol 21 (43) ◽  
pp. 24206-24211
Author(s):  
Seoung-Hun Kang ◽  
Jejune Park ◽  
Sungjong Woo ◽  
Young-Kyun Kwon
Keyword(s):  
Density Functional Theory ◽  
Ab Initio ◽  
Density Functional ◽  
Density Functional Theory Calculations ◽  
Black Phosphorus ◽  
Inversion Symmetry ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Functional Theory

Using ab initio density functional theory calculations, we find four-fold degenerate Dirac points protected by two nonsymmorphic symmetries in phosphorene oxide with the inversion symmetry broken.

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