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Topological insulators are new states of quantum matter which can not 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…

Mesoscale and Nanoscale Physics · Physics 2011-11-09 Xiao-Liang Qi , Shou-Cheng Zhang

Various unusual behaviors of artificial materials are governed by their topological properties, among which the edge state at the boundary of a photonic or phononic lattice has been captivated as a popular notion. However, this remarkable…

Applied Physics · Physics 2025-09-11 Minghong Qi , Dong Wang , Pei-Chao Cao , Xue-Feng Zhu , Cheng-Wei Qiu , Hongsheng Chen , Ying Li

Topological phases, including the conventional first-order and higher-order topological insulators and semimetals, have emerged as a thriving topic in the fields of condensed-matter physics and material science. Usually, a topological…

Mesoscale and Nanoscale Physics · Physics 2021-04-21 Yating Yang , Jiuyang Lu , Mou Yan , Xueqin Huang , Weiyin Deng , Zhengyou Liu

We present a unified framework to systematically embed complex knotted and linked structures, beyond the torus family, into diverse topological phases, including Hopf insulators, classical spin liquids, topological semimetals, and…

Strongly Correlated Electrons · Physics 2025-03-27 Snigdh Sabharwal

Topological phases enable protected transport along the edges of materials, offering immunity against scattering from disorder and imperfections. These phases were suggested and demonstrated not only for electronic systems, but also for…

Topological insulators (TIs) are emerging materials for next-generation low-power nanoelectronic and spintronic device applications. TIs possess non-trivial spin-momentum locking features in the topological surface states in addition to the…

Mesoscale and Nanoscale Physics · Physics 2024-10-11 Anamul Md. Hoque , Lars Sjöström , Dmitrii Khokhriakov , Bing Zhao , Saroj P. Dash

Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry.…

Mesoscale and Nanoscale Physics · Physics 2014-03-25 Yuan-Ming Lu , Dung-Hai Lee

We propose a new type of topological states of matter exhibiting topologically nontrivial edge states (ESs) within gapless bulk states (GBSs) protected by both spin rotational and reflection symmetries. A model presenting such states is…

Mesoscale and Nanoscale Physics · Physics 2019-04-23 Masoud Bahari , Mir Vahid Hosseini

Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice…

Mesoscale and Nanoscale Physics · Physics 2013-02-15 Robert-Jan Slager , Andrej Mesaros , Vladimir Juricic , Jan Zaanen

In a class of systems, there are gapped boundary-localized states described by a boundary Hamiltonian. The topological classification of gapped boundary Hamiltonians, same as the standard tenfold way for gapped bulk states, can lead to the…

Mesoscale and Nanoscale Physics · Physics 2025-06-23 Xun-Jiang Luo , Fengcheng Wu

A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI…

Strongly Correlated Electrons · Physics 2023-02-28 Benjamin Moy , Hart Goldman , Ramanjit Sohal , Eduardo Fradkin

We investigate the Hubbard model on the honeycomb lattice with intrinsic spin orbit interactions as a paradigm for two-dimensional topological band insulators in the presence of interactions. Applying a combination of Hartree-Fock theory,…

Strongly Correlated Electrons · Physics 2015-03-13 Stephan Rachel , Karyn Le Hur

Topology is routinely used to understand the physics of electronic insulators. However, for strongly interacting electronic matter, such as Mott insulators, a comprehensive topological characterization is still lacking. When their ground…

Strongly Correlated Electrons · Physics 2024-08-28 Martina O. Soldini , Ömer M. Aksoy , Titus Neupert

Topological Insulator (TI) has recently emerged as an attractive candidate for possible application to spintronic circuits because of its strong spin orbit coupling. TIs are unique materials that have an insulating bulk but conducting…

Materials Science · Physics 2015-07-31 Ahmed K. Reza , Xuanyao Fong , Zubair Al Azim , Kaushik Roy

Topological materials exhibit edge-localized scattering-free modes protected by their nontrivial bulk topology through the bulk-edge correspondence in Hermitian systems. While topological phenomena have recently been much investigated in…

Mesoscale and Nanoscale Physics · Physics 2020-11-16 Kazuki Sone , Yuto Ashida , Takahiro Sagawa

Topological insulators (TIs) and Weyl semimetals (WSMs) are two realizations of topological matter usually appearing separately in nature. However, they are directly related to each other via a topological phase transition. In this paper,…

Mesoscale and Nanoscale Physics · Physics 2017-03-06 Stefan Juergens , Björn Trauzettel

Topological insulators are promising for spintronics and related technologies due to their spin-momentum-locked edge states, which are protected by time-reversal symmetry. In addition to the unique fundamental physics that arises in these…

Mesoscale and Nanoscale Physics · Physics 2018-12-12 Antonio Russo , Edwin Barnes , Sophia E. Economou

A heterostructure consisting of a topological insulator (TI) nanowire brought into proximity with a superconducting layer provides a promising route to achieve topological superconductivity and associated Majorana bound states (MBSs). Here,…

Mesoscale and Nanoscale Physics · Physics 2022-05-04 Henry F. Legg , Daniel Loss , Jelena Klinovaja

Most topological insulators discovered today in spinful systems can be transformed from topological semimetals (TSMs) with vanishing bulk gap via introducing the spin-orbit coupling (SOC), which manifests the intrinsic links between the…

Topological materials occupy the central stage in the modern condensed matter physics because of their robust metallic edge or surface states protected by the topological invariant, characterizing the electronic band structure in the bulk.…

Mesoscale and Nanoscale Physics · Physics 2021-08-05 Bitan Roy , Vladimir Juricic