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A three-dimensional (3D) Dirac semimetal is the 3D analog of graphene whose bulk band shows a linear dispersion relation in the 3D momentum space. Since each Dirac point with four-fold degeneracy carries a zero Chern number, a Dirac…

Mesoscale and Nanoscale Physics · Physics 2014-09-18 Bohm-Jung Yang , Naoto Nagaosa

We propose a novel class of two-dimensional (2D) Dirac materials in the MX family (M=Be, Mg, Zn and Cd, X = Cl, Br and I), which exhibit graphene-like band structures with linearly-dispersing Dirac-cone states over large energy scales…

Materials Science · Physics 2020-05-18 Yan-Fang Zhang , Jinbo Pan , Huta Banjade , Jie Yu , Tay-Rong Chang , Hsin Lin , Arun Bansil , Shixuan Du , Qimin Yan

Electron systems that possess light-like dispersion relations or the conical Dirac spectrum, such as graphene and bismuth, have recently been shown to harbor unusual collective states in high magnetic fields. Such states are possible…

Mesoscale and Nanoscale Physics · Physics 2009-10-08 D. Hsieh , Y. Xia , D. Qian , L. Wray , J. H. Dil , F. Meier , L. Patthey , J. Osterwalder , A. V. Fedorov , H. Lin , A. Bansil , D. Grauer , Y. S. Hor , R. J. Cava , M. Z. Hasan

The graphene family materials are two-dimensional staggered monolayers with a gapped energy band structure due to intrinsic spin-orbit coupling. The mass gaps in these materials can be manipulated on-demand via biasing with a static…

Mesoscale and Nanoscale Physics · Physics 2021-03-18 Rajesh K. Malla , Wilton J. M. Kort-Kamp

Two-dimensional (2D) Dirac-like electron gases have attracted tremendous research interest ever since the discovery of free-standing graphene. The linear energy dispersion and non-trivial Berry phase play the pivotal role in the remarkable…

Two-dimensional (2D) materials with Dirac cones have been intrigued by many unique properties, i.e., the effective masses of carriers close to zero and Fermi velocity of ultrahigh, which yields a great possibility in high-performance…

Materials Science · Physics 2021-02-10 Tao Yang , Xingang Jiang , Wencai Yi , Xiaomin Cheng , Xiaobing Liu

Two-dimensional (2D) carbon materials play an important role in nanomaterials. We propose a new carbon monolayer, named hexagonal-4,4,4-graphyne (H4,4,4-graphyne), which is a nanoporous structure composed of rectangular carbon rings and…

Materials Science · Physics 2018-03-20 Linyang Li , Xiangru Kong , François M. Peeters

Nodal loops in two-dimensional (2D) systems are typically vulnerable against spin-orbit coupling (SOC). Here, we explore 2D systems with a type of doubly degenerate nodal loops that are robust under SOC and feature an hourglass type…

Materials Science · Physics 2019-05-21 Weikang Wu , Yalong Jiao , Si Li , Xian-Lei Sheng , Zhi-Ming Yu , Shengyuan A. Yang

Filling-enforced Dirac semimetals, or those required at specific fillings by the combination of crystalline and time-reversal symmetries, have been proposed and discovered in numerous materials. However, Dirac points in these materials are…

Mesoscale and Nanoscale Physics · Physics 2017-05-26 Steve M Young , Benjamin J. Wieder

Topological phases arise from the elegant mathematical structures imposed by the interplay between symmetry and topology1-5. From gapped topological insulators to gapless semimetals, topological materials in both quantum and classical…

When the spin-orbit coupling (SOC) is absent, almost all the proposed half-metals with the twofold degenerate nodal points at the K (or K') in two-dimensional (2D) materials are misclassified as "Dirac half-metals" owing to the way graphene…

Materials Science · Physics 2023-04-11 Jialin Gong , Guangqian Ding , Chengwu Xie , Jianhua Wang , Ying Liu , Xiaotian Wang , Gang Zhang

Two-dimensional (2D) Dirac states and Dirac points with linear dispersion are the hallmark of graphene, topological insulators, semimetals, and superconductors. Lowering a symmetry by the ferroelectric polarization opens the gap in Dirac…

Mesoscale and Nanoscale Physics · Physics 2025-07-03 Konstantin S. Denisov , Yuntian Liu , Igor Žutić

The remarkable properties of graphene stem from its two-dimensional (2D) structure, with a linear dispersion of the electronic states at the corners of the Brillouin zone (BZ) forming a Dirac cone. Since then, other 2D materials have been…

Materials Science · Physics 2018-11-06 S. Sadeddine , H. Enriquez , A. Bendounan , P. Das , I. Vobornik , A. Kara , A. Mayne , F. Sirotti , G. Dujardin , H. Oughaddou

In the presence of spin-orbit coupling (SOC), achieving both spin and valley polarized Dirac state is significant to promote the fantastic integration of Dirac physics, spintronics and valleytronics. Based on ab initio calculations, here we…

Computational Physics · Physics 2018-12-04 Zhifeng Liu , Wangxiang Feng , Hongli Xin , Yinlu Gao , Pengfei Liu , Yugui Yao , Hongming Weng , Jijun Zhao

Two-dimensional (2D) kagome materials have become a hot research topic in the current scientific community due to their unique electronic structural properties, and the design of novel 2D kagome materials represents a significant…

Materials Science · Physics 2026-04-15 Su-Yang Shen , En-Qi Bao , Xing-Yu Wang , Jiafu Wang , Jun-Hui Yuan

Dirac materials, starting with graphene, have drawn tremendous research interest in the past decade. Instead of focusing on the $p_z$ orbital as in graphene, we move a step further and study orbital-active Dirac materials, where the orbital…

Strongly Correlated Electrons · Physics 2023-01-16 Shenglong Xu , Congjun Wu

This review aims at a theoretical discussion of Dirac points in two-dimensional systems. Whereas Dirac points and Dirac fermions are prominent low-energy electrons in graphene (two-dimensional graphite), research on Dirac fermions in…

Mesoscale and Nanoscale Physics · Physics 2014-10-16 Mark O. Goerbig , Gilles Montambaux

Topological nodal line semimetals, a novel quantum state of materials, possess topologically nontrivial valence and conduction bands that touch at a line near the Fermi level. The exotic band structure can lead to various novel properties,…

The recent detection of the singular diamagnetism of Dirac electrons in a single graphene layer paved a new way of probing 2D quantum materials through the measurement of equilibrium orbital currents which cannot be accessed in usual…

Recently, several new materials exhibiting massless Dirac fermions have been proposed. However, many of these do not have the typical graphene honeycomb lattice, which is often associated with Dirac cones. Here, we present a classification…

Materials Science · Physics 2016-01-12 G. van Miert , C. Morais Smith