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Publication# Topological states on the breathing kagome lattice

Résumé

We theoretically study the topological properties of the tight-binding model on the breathing kagome lattice with antisymmetric spin-orbit coupling (SOC) between nearest neighbors. We show that the system hosts nontrivial topological phases even without second-nearest-neighbor hopping and that the weakly dispersing band of the kagome lattice can become topological. The main results are presented in the form of phase diagrams, where the Z(2)( )topological index is shown as a function of SOC (intrinsically allowed and Rashba) and lattice trimerization. In addition, exact diagonalization is compared with effective low-energy theories around the high-symmetry points. We find that the weakly dispersing band has a very robust topological property associated with it. Moreover, the Rashba SOC can produce a topological phase rather than hinder it, in contrast to the honeycomb lattice. Finally, we consider the case of a fully spin polarized (ferromagnetic) system, breaking time-reversal symmetry. We find a phase diagram that includes systems with finite Chern numbers. In this case too, the weakly dispersing band is topologically robust to trimerization.

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Diagramme de phase

Un diagramme de phase, ou diagramme de phases, est une représentation graphique utilisée en thermodynamique, généralement à deux ou trois dimensions, représentant les domaines de l'état physique (ou

Topological order

In physics, topological order is a kind of order in the zero-temperature phase of matter (also known as quantum matter). Macroscopically, topological order is defined and described by robust ground

Système

Un système est un ensemble d' interagissant entre eux selon certains principes ou règles. Par exemple une molécule, le système solaire, une ruche, une société humaine, un parti, une armée etc.
Un s

We have obtained the zero-temperature phase diagram of the kagomé antiferromagnet with Dzyaloshinskii-Moriya interactions in Schwinger-boson mean-field theory. We find quantum phase transitions (first or second order) between different topological spin-liquid and Néel-ordered phases (either the √3×√3 state or the so-called Q=0 state). In the regime of small Schwinger-boson density, the results bear some resemblances with exact diagonalization results and we briefly discuss some issues of the mean-field treatment. We calculate the equal-time structure factor (and its angular average to allow for a direct comparison with experiments on powder samples), which extends earlier work on the classical kagomé to the quantum regime. We also discuss the dynamical structure factors of the topological spin-liquid and the Néel-ordered phases.

2010Fernando Gargiulo, Oleg Yazyev

Dislocations and grain boundaries are intrinsic topological defects of large-scale polycrystalline samples of graphene. These structural irregularities have been shown to strongly affect electronic transport in this material. Here, we report a systematic investigation of the transmission of charge carriers across the grain-boundary defects in polycrystalline graphene by means of the Landauer-Buttiker formalism within the tight-binding approximation. Calculations reveal a strong suppression of transmission at low energies upon decreasing the density of dislocations with the smallest Burgers vector b = (1,0). The observed transport anomaly is explained from the point of view of resonant backscattering due to localized states of topological origin. These states are related to the gauge field associated with all dislocations characterized by b = (n,m) with n - m not equal 3q (q is an element of Z). Our work identifies an important source of charge-carrier scattering caused by the topological defects present in large-area graphene samples produced by chemical vapor deposition.

The topology of the electron wavefunctions in certain band insulators can give rise to novel topological phases. Materials harbouring such topological phases are termed topological insulators (TI). A gapped bulk electronic spectrum, described by a topological invariant, and gapless boundary modes, tend to characterize the non-trivial topology. This work describes a theoretical investigation of the Z2 topological insulator phase in Bi2Se3 and Bi2Te3, and the topological crystalline insulator (TCI) phase in SnTe, subject to nanoscale confinement. Specifically, it details the electronic structure, and properties of low-dimensional nanostructures derived from the bulk topological phase. For the bismuth chalcogenides, a first principles methodology is applied to compute the energetics of high-index surfaces, followed by an analysis of the electronic properties of corresponding topological surface state charge carriers. Our calculations find several stable terminations of high-index surfaces, which can be realized at different values of the chemical potential of one of constituent elements. For the uniquely defined stoichiometric termination, the Dirac fermion surface states exhibit a strong anisotropy, with a clear dependence of Fermi velocities and spin polarization on the surface orientation. Non-stoichiometric surfaces undergo self-doping effects, which results in the presence of topologically trivial mid-gap states. These findings guide the construction of Bi2Se3 nanostructures of a nanowire (NW) and nanoribbon (NR) morphology. A tight-binding formalism is utilised to study, firstly, the impact of finite-size effects on the electronic spectrum of each nanostructure. Secondly, the effects of confinement on the topological properties of two-dimensional (2D) Dirac fermion surface states. Quantum confinement around each nanostructure perimeter entails the formation of a series of discrete one-dimensional (1D) sub-bands in the bulk gap. An analysis of how the band gap varies as a function of nanostructure dimensions finds that the dependence is highly sensitive to nanostructure morphology. We reveal a clear correspondence between the spin helicity of the 2D surface Dirac cone and the spin properties of the 1D sub-bands. This is exemplified in the real space spin textures of each nanostructure. For the NW morphology, this correspondence gives rise to an energy dependent spin polarization density. Whereas for the NR morphology the presence of two separate surface types results in a more complex relationship. Finally, via a similar tight-binding formalism, we establish how the crystal-symmetry-dependent topological phases of SnTe (001) thin films are exhibited in lower dimensional nanowires. SnTe (001) thin films, defined by either mirror or glide symmetry, realise distinct 2D TCI phases. As the band dispersion of NWs are characterised by which of these symmetry classes they belong to, we subsequently connect the distinctive NW surface states to the respective parent 2D TCI phase. Lastly, we show that the robust topological protection offered by the mirror symmetry protected 2D TCI phase is manifested in robust surface states of NWs of equivalent symmetry.