石墨烯是一種無質量的狄拉克費米子系統，在動量空間中具有狄拉克點。石墨烯因具有自旋軌道耦合（SOC），也首次被確定為量子自旋霍爾（QSH）絕緣體，它能在狄拉克點處打開帶隙。這一發現給人以新的啟發，即研究石墨烯QSH效應有可能實現其在量子計算和自旋電子學方面的應用。盡管人們已在HgTe量子阱中觀察到了QSH效應，但由于石墨烯的SOC強度太小（~1μeV），無法在實驗可實現的溫度范圍內誘導出拓撲絕緣體相。

來自韓國建國大學的Hoonkyung Lee領導的研究小組利用原子模擬進行了系統的結構搜索和幾何優化，以探索和設計能夠容納量子自旋霍爾相的原子級層狀碳材料（2D材料）。從二維sp²-sp²雜化網絡開始，原子模擬提供了31個碳層，這些碳層都具有各種類型無質量的狄拉克錐，同時包括各向同性或各向異性的狄拉克錐，以及共存的具有不同各向異性的不對稱狄拉克錐。此外，他們還發現了21個沒有自旋軌道耦合的狄拉克費米子系統，其中的19個有可能成為量子自旋霍爾絕緣體，卻具有相當大的自旋軌道耦合。這些結果表明利用第一性原理可以預測各種無質量狄拉克錐的碳基系統，同時也為揭示二維材料中實現狄拉克錐提供了可行路線。

該文近期發表于npj Computational Materials 4: 54 (2018)，英文標題與摘要如下，點擊左下角“閱讀原文”可以自由獲取論文PDF。

Design of 2D massless Dirac fermion systems and quantum spin Hall insulators based on sp–sp²  carbon sheets 

Minwoo Park, Youngkuk Kim & Hoonkyung Lee 

Graphene is a massless Dirac fermion system, featuringDirac points in momentum space.It was also firstidentified as a quantum spin Hall (QSH) insulator when considering spin–orbitcoupling (SOC), which opens a band gap at the Dirac points. This discovery hasinitiated new research efforts to study the QSH effect, towards its applicationfor quantum computing and spintronics. Although the QSH effect has beenobserved in HgTe quantum wells, the SOC strength of graphene is too small (~1μeV)to induce the topological insulator phase in an experimentally achievabletemperature regime. Here, we perform a systematic atomistic simulation to designtwo-dimensional sp–sp²hybrid carbon sheets to discover new Diracsystems, hosting the QSH phase. 21 out of 31 newly discovered carbon sheets areidentified as Dirac fermion systems without SOC, distinct from graphene in thenumber, shape, and position of the Dirac cones occurring in the Brillouin zone.Moreover, we find 19 out of the 21 new Dirac fermion systems become QSHinsulators with a sizable SOC gap enhanced up to an order of meV, thus allowingfor the QSH effect at experimentally accessible temperatures. In addition,based on the 26 Dirac fermion systems, we make a connection between the numberof Dirac points without SOC and the resultant QSH phase in the presence of SOC.Our findings present new prospects for the design of topological materials withdesired properties.