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Journal ArticleDOI

Solitons in polyacetylene

18 Jun 1979-Physical Review Letters (American Physical Society)-Vol. 42, Iss: 25, pp 1698-1701
TL;DR: In this paper, the authors present a theoretical study of soliton formation in long-chain polyenes, including the energy of formation, length, mass, and activation energy for motion.
Abstract: We present a theoretical study of soliton formation in long-chain polyenes, including the energy of formation, length, mass, and activation energy for motion. The results provide an explanation of the mobile neutral defect observed in undoped ${(\mathrm{CH})}_{x}$. Since the soliton formation energy is less than that needed to create band excitation, solitons play a fundamental role in the charge-transfer doping mechanism.
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TL;DR: In this paper, the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations, are discussed.
Abstract: This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

20,824 citations


Cites background from "Solitons in polyacetylene"

  • ...…and, as in the Figure 12 (Color online) Sket h of the three inequivalent ori-entations of graphene layers with respe t to ea h other. ase of other arbon based systems su h as polya ethy-lene (Su et al., 1979, 1980), it an lead to soliton-likeex itations (Hou et al., 2007; Ja kiw and Rebbi, 1976)....

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Journal ArticleDOI
TL;DR: Topological superconductors are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors and are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time reversal symmetry.
Abstract: Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

11,092 citations

Journal ArticleDOI
TL;DR: Electronic Coupling in Oligoacene Derivatives: Factors Influencing Charge Mobility, and the Energy-Splitting-in-Dimer Method 3.1.
Abstract: 2.2. Materials 929 2.3. Factors Influencing Charge Mobility 931 2.3.1. Molecular Packing 931 2.3.2. Disorder 932 2.3.3. Temperature 933 2.3.4. Electric Field 934 2.3.5. Impurities 934 2.3.6. Pressure 934 2.3.7. Charge-Carrier Density 934 2.3.8. Size/molecular Weight 935 3. The Charge-Transport Parameters 935 3.1. Electronic Coupling 936 3.1.1. The Energy-Splitting-in-Dimer Method 936 3.1.2. The Orthogonality Issue 937 3.1.3. Impact of the Site Energy 937 3.1.4. Electronic Coupling in Oligoacene Derivatives 938

3,635 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the parity of the occupied Bloch wave functions at the time-reversal invariant points in the Brillouin zone greatly simplifies the problem of evaluating the topological invariants.
Abstract: Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$ topological invariants, which characterize the ground state. In two dimensions, there is a single ${Z}_{2}$ invariant that distinguishes the ordinary insulator from the quantum spin-Hall phase. In three dimensions, there are four ${Z}_{2}$ invariants that distinguish the ordinary insulator from ``weak'' and ``strong'' topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the two-dimensional quantum spin-Hall phase and the three-dimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the ${Z}_{2}$ invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wave functions at the time-reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials that are strong topological insulators, including the semiconducting alloy ${\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x}$ as well as $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}$ and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.

3,349 citations

Journal ArticleDOI
TL;DR: In this paper, a detailed review of the role of the Berry phase effect in various solid state applications is presented. And a requantization method that converts a semiclassical theory to an effective quantum theory is demonstrated.
Abstract: Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.

3,344 citations


Cites background from "Solitons in polyacetylene"

  • ...If ∆ = 0 it reduces to the celebrated Su-Shrieffer-Heeger model (Su et al., 1979)....

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  • ...Examples include spin-orbit coupled systems (Culcer et al., 2003; Liu et al., 2008), linearly conjugated diatomic polymers (Rice and Mele, 1982; Su et al., 1979), one-dimensional ferroelectrics (Onoda et al., 2004b; Vanderbilt and King-Smith, 1993), graphene (Haldane, 1988; Semenoff, 1984), and…...

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