Topological Matter -  Topological Insulators, Skyrmions and Majoranas

Blügel, Stefan; Schäpers, Thomas; Ando, Yoichi; Mokrousov, Yuriy

Book/Proceedings

FZJ-2017-02620

Topological Matter - Topological Insulators, Skyrmions and Majoranas

Blügel, S. (Editor)FZJ* ; Mokrousov, Y. (Editor)FZJ* ; Schäpers, T.FZJ* ; Ando, Y. (Editor)

2017
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag Jülich
ISBN: 978-3-95806-202-3

Lecture Notes of the 48th IFF Spring School 2017, Jülich, Germany, 27 Mar 2017 - 7 Apr 2017 Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Schriften des Forschungszentrums Jülich. Reihe Schlüsseltechnologien / Key Technologies 139, getr. Zählung (2017)

Please use a persistent id in citations: http://hdl.handle.net/2128/22133

Abstract: Condensed matter physics is currently undergoing a revolution through the introduction of concepts arising from topology that are used to characterize physical states, fields and properties from a completely different perspective. With the introduction of topology, the perspective is changed from describing complex systems in terms of local order parameters to a characterization by global quantities, which are measured nonlocally and which endow the systems with a global stability to perturbations. Prominent examples are topological insulators, skyrmions and Majorana fermions. Since topology translates into quantization, and topological order to entanglement, this ongoing revolution has impact on fields like mathematics, materials science, nanoelectronics and quantum information resulting in new device concepts enabling computations without dissipation of energy or enabling the possibility of realizing platforms for topological quantum computation, and ultimately reaching out into applications. Thus, these new exciting scientific developments and their applications are closely related to the grand challenges in information and communication technology and energy saving. Topology is the branch of mathematics that deals with properties of spaces that are invariant under smooth deformations. It provides newly appreciated mathematical tools in condensed matter physics that are currently revolutionizing the field of quantum matter and materials. Topology dictates that if two different Hamiltonians can be smoothly deformed into each other they give rise to many common physical properties and their states are homotopy invariant. Thus, topological invariance, which is often protected by discrete symmetries, provides some robustness that translates into the quantization of properties; such a robust quantization motivates the search and discovery of new topological matter. So far, the mainstream of modern topological condensed matter physics relies on two profoundly different scenarios: the emergence of the complex topology either in real space, as manifested e.g. in non-trivial magnetic structures or in momentum space, finding its realization in such materials as topological and Chern insulators. The latter renowned class of solids attracted considerable attention in recent years owing to its fascinating properties of spin-momentum locking, emergence of topologically protected surface/edge states governed by Dirac physics, as well as the quantization of Hall conductance and the discovery of the quantum spin Hall effect. Historically, the discovery of topological insulators gave rise to the discovery of a whole plethora of topologically non-trivial materials such asWeyl semimetals or topological superconductors, relevant in the context of the realization of Majorana fermions and topological quantum computation. [...]

Contributing Institute(s):

Research Program(s):

899 - ohne Topic (POF3-899) (POF3-899)

Appears in the scientific report 2017

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Institutssammlungen > IAS > IAS-1
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Institutssammlungen > PGI > PGI-1
Institutssammlungen > PGI > PGI-9
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Linked articles:

Contribution to a conference proceedings/Contribution to a book DiVincenzo, D. (Corresponding author)FZJ*
Topological quantum computing
2017Topological Matter - Topological Insulators, Skyrmions and Majoranas
48th IFF Spring School 2017, JülichJülich, Germany, 27 Mar 2017 - 7 Apr 20172017-03-272017-04-07 Jülich : Verlag Forschungszentrum Jülich, Schlüsseltechnologien/Key Technologies 139, (2017)2017 BibTeX | EndNote: XML, Text | RIS

Contribution to a conference proceedings/Contribution to a book Bihlmayer, G. (Corresponding author)FZJ*
Band structure from first-principles and relativistic effects
201748th IFF Spring School 2017 " Topological Matter - Topological Insulators, Skyrmions and Majoranas ", ed. S. Blügel, Y. Mokrousov, T. Schäpers, Y. Ando,
IFF Spring School, JülichJülich, Germany, Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Schriften des Forschungszentrums Jülich Reihe Schlüsseltechnologien / Key Technologies 139, A3-A3.40 (2017)2017 BibTeX | EndNote: XML, Text | RIS

Contribution to a book Mokrousov, Y. (Corresponding author)FZJ*
Berry phase in quantum mechanics
201748th IFF Spring School 2017 " Topological Matter - Topological Insulators, Skyrmions and Majoranas ", ed. S. Blügel, Y. Mokrousov, T. Schäpers, Y. Ando, Germany : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Schriften des Forschungszentrums Jülich Reihe Schlüsseltechnologien / Key Technologies 139, A6-A6.30 (2017)2017 BibTeX | EndNote: XML, Text | RIS

Contribution to a book Aguilera, I. (Corresponding author)FZJ* ; Friedrich, C.FZJ*
Quasiparticle band structure of topological insulators: Relativistic GW approximation
201748th IFF Spring School 2017 "Topological Matter - Topological Insulators, Skyrmions and Majoranas", ed. S. Blügel, Y. Mokrousov, T. Schäpers, Y. Ando, Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Schriften des Forschungszentrums Jülich Reihe Schlüsseltechnologien / Key Technologies 139, B3-B3.30 (2017)2017 BibTeX | EndNote: XML, Text | RIS

Contribution to a book Rüssmann, P.FZJ* ; Mavropoulos, P. (Corresponding author)FZJ*
Quasiparticle interference at surfaces of topological insulators
201748th IFF Spring School 2017 " Topological Matter - Topological Insulators, Skyrmions and Majoranas ", ed. S. Blügel, Y. Mokrousov, T. Schäpers, Y. Ando, Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Schriften des Forschungszentrums Jülich Reihe Schlüsseltechnologien / Key Technologies 139, B5-B5-21 (2017)2017 BibTeX | EndNote: XML, Text | RIS

Contribution to a book Kiselev, N. (Corresponding author)FZJ* ; Zimmermann, B.FZJ* ; Chico, J.FZJ*
Atomistic and micromagnetic models of magnetism
201748th IFF Spring School 2017 " Topological Matter - Topological Insulators, Skyrmions and Majoranas ", ed. S. Blügel, Y. Mokrousov, T. Schäpers, Y. Ando, Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Schriften des Forschungszentrums Jülich Reihe Schlüsseltechnologien / Key Technologies 139, C1-C1.20 (2017)2017 BibTeX | EndNote: XML, Text | RIS

Contribution to a book Blügel, S. (Corresponding author)FZJ*
Non-collinear magnetism in density functional theory
201748th IFF Spring School 2017 " Topological Matter - Topological Insulators, Skyrmions and Majoranas ", ed. S. Blügel, Y. Mokrousov, T. Schäpers, Y. Ando, Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Schriften des Forschungszentrums Jülich Reihe Schlüsseltechnologien / Key Technologies 139, C5-C5.45 (2017)2017 BibTeX | EndNote: XML, Text | RIS

Contribution to a book Chico, J. (Corresponding author)FZJ* ; Kiselev, N.FZJ* ; Zimmermann, B.FZJ*
Skyrmion dynamics
201748th IFF Spring School 2017 " Topological Matter - Topological Insulators, Skyrmions and Majoranas ", ed. S. Blügel, Y. Mokrousov, T. Schäpers, Y. Ando, Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Schriften des Forschungszentrums Jülich Reihe Schlüsseltechnologien / Key Technologies 139, C9-C9.20 (2017)2017 BibTeX | EndNote: XML, Text | RIS

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