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Electron energy bands of crystalline solids generically exhibit degeneracies called band-structure nodes. Here, we introduce non-Abelian topological charges that characterize line nodes inside the momentum space of crystalline metals with…

Mesoscale and Nanoscale Physics · Physics 2019-12-05 QuanSheng Wu , Alexey A. Soluyanov , Tomáš Bzdušek

Topological nodal-line semimetals (NLSMs) are a new family of topological materials characterized by electronic band crossings that form lines in the Brillouin zone. These NLSMs host exotic nodal-line structures and exhibit distinct…

Strongly Correlated Electrons · Physics 2025-10-30 Po-Yao Chang

Magnetic topological semimetals (TSMs) are topological quantum materials with broken time-reversal symmetry (TRS) and isolated nodal points or lines near the Fermi level. Their topological properties would typically reveal from the…

Materials Science · Physics 2019-10-08 Jinyu Zou , Zhuoran He , Gang Xu

Topological nodal line semimetals are characterized by the crossing of the conduction and valence bands along one or more closed loops in the Brillouin zone. Usually, these loops are either isolated or touch each other at some highly…

Strongly Correlated Electrons · Physics 2017-07-12 Wei Chen , Hai-Zhou Lu , Jing-Min Hou

A prominent feature of some one-dimensional non-Hermitian systems is that all right-eigenstates of the non-Hermitian Hamiltonian are localized in one end of the chain. The topological and trivial phases are distinguished by the emergence of…

Mesoscale and Nanoscale Physics · Physics 2019-07-17 Motohiko Ezawa

Nodal links are special configurations of band degeneracies in the momentum space, where nodal line branches encircle each other. In PT symmetric systems, nodal lines can be topologically characterized using the eigenvector frame rotations…

Among different topological and related phases of condensed matter, nodal semimetals occupy a special place - the electronic band topology in these materials is related to three-dimensional bulk, rather than to surface, states. A great…

Mesoscale and Nanoscale Physics · Physics 2021-04-28 A. V. Pronin , M. Dressel

Nodal loop semimetals are close descendants of Weyl semimetals and possess a topologically dressed band structure. We argue by combining the conventional theory of magnetic oscillation with topological arguments that nodal loop semimetals…

Strongly Correlated Electrons · Physics 2018-05-16 László Oroszlány , Balázs Dóra , József Cserti , Alberto Cortijo

Nodal-line semimetals (NLSMs) contains Dirac/Weyl type band-crossing nodes extending into shapes of line, loop and chain in the reciprocal space, leading to novel band topology and transport responses. Robust NLSMs against spin-orbit…

Topological metals and semimetals (TMs) have recently drawn significant interest. These materials give rise to condensed matter realizations of many important concepts in high-energy physics, leading to wide-ranging protected properties in…

Weyl semimetals are examples of a new class of topological states of matter which are gapless in the bulk with protected surface states. Their low energy sector is characterized by massless chiral fermions which are robust against…

Strongly Correlated Electrons · Physics 2015-06-22 Michael Phillips , Vivek Aji

Non-Abelian toplogical superconductors are characterized by the existence of {zero-energy} Majorana fermions bound in the quantized vortices. This is a consequence of the nontrivial bulk topology characterized by an {\em odd} Chern number.…

Strongly Correlated Electrons · Physics 2013-01-14 Jian-Hua Jiang , Si Wu

Among topological materials, nodal loop semimetals (NLSMs) are arguably the most topologically sophisticated, with their valence and conduction bands intersecting along arbitrarily intertwined nodes. But unlike the well-known topological…

Mesoscale and Nanoscale Physics · Physics 2020-07-29 Ching Hua Lee , Han Hoe Yap , Tommy Tai , Gang Xu , Xiao Zhang , Jiangbin Gong

The topological nodal-line semimetal state, serving as a fertile ground for various topological quantum phases, where a topological insulator, Dirac semimetal, or Weyl semimetal can be realized when the certain protecting symmetry is…

We review the recent, mainly theoretical, progress in the study of topological nodal line semimetals in three dimensions. In these semimetals, the conduction and the valence bands cross each other along a one-dimensional curve in the…

Mesoscale and Nanoscale Physics · Physics 2017-01-10 Chen Fang , Hongming Weng , Xi Dai , Zhong Fang

Nodal-line semimetals are topological semimetals in which band touchings form nodal lines or rings. Around a loop that encloses a nodal line, an electron can accumulate a nontrivial $\pi$ Berry phase, so the phase shift in the Shubnikov-de…

Mesoscale and Nanoscale Physics · Physics 2018-04-10 Cequn Li , C. M. Wang , Bo Wan , Xiangang Wan , Hai-Zhou Lu , X. C. Xie

The nodal line semimetals have attracted much attention due to their unique topological electronic structure and exotic physical properties. A genuine nodal line semimetal is qualified by the presence of Dirac nodes along a line in the…

Topological Dirac semimetals with accidental band touching between conduction and valence bands protected by time reversal and inversion symmetry are at the frontier of modern condensed matter research. Theoretically one can get Weyl and/or…

We report the experimental and theoretical studies of a magnetic topological nodal line semimetal candidate HoSbTe. Single crystals of HoSbTe are grown from Sb flux, crystallizing in a tetragonal layered structure (space group: P4/nmm,…

Topological nodal-line semimetals are characterized by one-dimensional Dirac nodal rings that are protected by the combined symmetry of inversion $\mathcal{P}$ and time-reversal $\mathcal{T}$. The stability of these Dirac rings is…

Mesoscale and Nanoscale Physics · Physics 2018-05-02 W. B. Rui , Y. X. Zhao , Andreas P. Schnyder