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Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which…

Mesoscale and Nanoscale Physics · Physics 2009-11-11 Liang Fu , C. L. Kane

Based on first-principles calculations and symmetry-based indicator analysis, we find a class of topological crystalline insulators (TCIs) with $C_2$ rotation anomaly in a family of Zintl compounds, including…

Materials Science · Physics 2019-08-14 Tan Zhang , Changming Yue , Tiantian Zhang , Simin Nie , Zhijun Wang , Chen Fang , Hongming Weng , Zhong Fang

We introduce a lattice field theory that describes the transition between a superfluid (SF) and a bosonic topological Mott Insulator (tMI) -- a $U(1)$ symmetry protected topological phase labeled by an integer level $k$ and possessing an…

Strongly Correlated Electrons · Physics 2021-12-07 Michael A. DeMarco , Ethan Lake , Xiao-Gang Wen

In typical topological insulator (TI) systems the TI is bordered by a non-TI insulator, and the surrounding conventional insulators, including vacuum, are not generally treated as part of the TI system. Here, we implement the first material…

We introduce a novel class of interaction-enabled topological crystalline insulators in two- and three-dimensional electronic systems, which we call "topological crystalline magnet." It is protected by the product of the time-reversal…

Strongly Correlated Electrons · Physics 2017-03-08 Haruki Watanabe , Liang Fu

By means of first-principles calculations and crystal structure searching techniques, we predict that a new NaCaBi family crystallized into the ZrBeSi-type structure (\ie $P6_{3}/mmc$) are strong topological insulators (STIs). Taking…

Materials Science · Physics 2021-03-29 Dexi Shao , Zhaopeng Guo , Xianxin Wu , Simin Nie , Jian Sun , Hongming Weng , Zhijun Wang

A topological crystalline insulator (TCI) is a new phase of topological matter, which is predicted to exhibit distinct topological quantum phenomena, since space group symmetries replace the role of time-reversal symmetry in the…

Ferroelectric higher-order topological insulators (HOTIs) exhibit tunable physical properties arising from the interplay between ferroelectric polarization and band topology. This work investigates the topological origin of two classes of…

Materials Science · Physics 2026-04-21 YingJie Hu , Heng Gao , Yabei Wu , Wei Ren

Topological crystalline insulators (TCI) are unique systems where a band inversion that is protected by crystalline mirror symmetry leads to a multiplicity of topological surface states. Binary SnTe is an attractive lead-free TCI compound;…

Alternating current (ac) circuits can have electromagnetic edge modes protected by symmetries, analogous to topological band insulators or semimetals. How to make such a topological circuit? This paper illustrates a particular design idea…

Mesoscale and Nanoscale Physics · Physics 2018-12-12 Erhai Zhao

We consider a thin film of a topological insulator (TI) sandwiched between two ferromagnetic (FM) layers. The system is additionally under an external gate voltage. The surface electron states of TI are magnetized due to the magnetic…

Mesoscale and Nanoscale Physics · Physics 2023-09-19 Piotr Pigoń , Anna Dyrdał

The bulk-boundary correspondence of the second-order topological insulator (SOTI) has been well established, but a universal transport signature for open systems is still absent. For a variety of SOTIs induced by applying in-plane magnetic…

Mesoscale and Nanoscale Physics · Physics 2023-11-07 Yuxiong Long^§ , Miaomiao Wei^§ , Fuming Xu , Jian Wang

Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of…

Mesoscale and Nanoscale Physics · Physics 2018-06-05 Frank Schindler , Ashley M. Cook , Maia G. Vergniory , Zhijun Wang , Stuart S. P. Parkin , B. Andrei Bernevig , Titus Neupert

We present a novel class of topological insulators, termed the Takagi topological insulators (TTIs), which is protected by the sublattice symmetry and spacetime inversion ($\mathcal P\mathcal T$) symmetry. The required symmetries for the…

Mesoscale and Nanoscale Physics · Physics 2021-10-29 Jia-Xiao Dai , Kai Wang , Shengyuan A. Yang , Y. X. Zhao

Ferromagnetism in topological insulators (TIs) opens a topologically non-trivial exchange band gap, providing an exciting platform to manipulate the topological order through an external magnetic field. Here, we experimentally show that the…

The tunability of topological surface states and controllable opening of the Dirac gap are of great importance to the application of topological materials. In topological crystalline insulators (TCIs), crystal symmetry and topology of…

Materials Science · Physics 2018-10-17 Feng Wei , Chieh-Wen Liu , Da Li , Chun-Yang Wang , Hong-Rui Zhang , Ji-rong Sun , Xuan P. A. Gao , Song Ma , Zhidong Zhang

In two dimensions, intrinsic second-order topological insulators (SOTIs) are characterized by topological corner states that emerge at the intersections of distinct edges with reversed mass signs, enforced by spatial symmetries. Here, we…

Materials Science · Physics 2024-06-21 Z. J. Chen , S. G. Xu , Z. J. Xie , H. Xu , H. M. Weng

Conventional topological insulators support boundary states that have one dimension lower than the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order…

Mesoscale and Nanoscale Physics · Physics 2020-07-24 Avik Dutt , Momchil Minkov , Shanhui Fan

In a topological insulator (TI), if its spin-orbit coupling (SOC) strength is gradually reduced, the TI eventually transforms into a trivial insulator beyond a critical point of SOC, at which point the bulk gap closes: this is the standard…

Materials Science · Physics 2016-09-08 Maryam Salehi , Hassan Shapourian , Nikesh Koirala , Matthew J. Brahlek , Jisoo Moon , Seongshik Oh

We explore a large family of one-dimensional (1D) topological crystalline insulators (TCIs) classified by $\mathbb{Z}$ invariants protected by space-time inversion symmetry. This finding stands in marked contrast to the conventional…

Mesoscale and Nanoscale Physics · Physics 2025-07-03 Ling Lin , Yongguan Ke , Chaohong Lee