Non-Bloch Band Theory of Non-Hermitian Systems

1. Auflage 2022
ISBN: 978-981-19-1857-5
Verlag: Springer Nature Singapore

Buch, Englisch, 92 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 336 g

Reihe: Springer Theses

This book constructs a non-Bloch band theory and studies physics described by non-Hermitian Hamiltonian in terms of the theory proposed here.

In non-Hermitian crystals, the author introduces the non-Bloch band theory which produces an energy spectrum in the limit of a large system size. The energy spectrum is then calculated from a generalized Brillouin zone for a complex Bloch wave number. While a generalized Brillouin zone becomes a unit circle on a complex plane in Hermitian systems, it becomes a circle with cusps in non-Hermitian systems. Such unique features of the generalized Brillouin zone realize remarkable phenomena peculiar in non-Hermitian systems. 

Further the author reveals rich aspects of non-Hermitian physics in terms of the non-Bloch band theory. First, a topological invariant defined by a generalized Brillouin zone implies the appearance of topological edge states. Second, a topological semimetal phase with exceptional points appears, The topological semimetal phase is unique to non-Hermitian systems because it is caused by the deformation of the generalized Brillouin zone by changes of system parameters. Third, the author reveals a certain relationship between the non-Bloch waves and non-Hermitian topology.

Zielgruppe

Research

Autoren/Hrsg.

Yokomizo, Kazuki

Fachgebiete

• Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde

Inhaltsverzeichnis

Introduction.- Hermitian Systems and Non-Hermitian Systems.- Non-Hermitian Open Chain and Periodic Chain.- Non-Bloch Band Theory of Non-Hermitian Systems and Bulk-Edge Correspondence.- Topological Semimetal Phase With Exceptional Points in One-Dimensional Non-Hermitian Systems.- Non-Bloch Band Theory in Bosonic Bogoliubov-de Gennes Systems.- Summary and Outlook.

Über Autor(innen)

Kazuki Yokomizo is a postdoctoral researcher at the Condensed Matter Theory Laboratory, RIKEN Cluster for Pioneering Research. He received his Ph.D. in science from Tokyo Institute of Technology in December 2020. He was awarded a Research Fellowship for Young Scientists (PD) by the Japan Society for the Promotion of Science.