拓樸節線材料之第一原理研究

First-Principles Studies of Topological Nodal-Line Materials

呂驊樵(Hua-Ciao Lyu)

指導教授 ： 周美吟

國立臺灣大學/理學院/物理學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201603233

摘要

最近Cava的實驗團隊藉由X光繞射實驗分析，提出了一個二磷化三鈣(Ca3P2)帶有空缺陷的晶格結構。同時，此結構在虛晶格近似的第一原理計算之下，被預測為狄拉克節線半金屬。以此實驗結論為出發點，且不採用虛晶格近似的情形下，我們探討了晶格空缺陷對於此系統的影響。一旦考慮原子位置的最佳化，虛晶格近似所預測的能帶交合將不復存在。此外我們也發現另一種相同化學計量比的晶格結構，其能量的考慮上是相較更有利的。綜而觀之，此實驗團隊提出的二磷化三鈣是狄拉克節線半金屬，可能不盡正確。為了在真實材料中找到節線半金屬，並有實際的穩定性，我們針對由主族元素所組成的已知穩定結構化合物，做一系統性的篩選。在此材料搜尋中，我們發現在不考量自旋軌道偶合的情況下，鉛化二锶(Sr2Pb)以及部分碳族(矽、鍺、錫)二鋇化物(Ba2X)的能帶結構中，具有狄拉克節線能帶交合。而若考慮自旋軌道偶合效應，將會為能帶結構打開一個小的能隙。其中，能隙大小以二鋇化鍺為最小，並且在室溫中可忽略。因此我們預測，二鋇化鍺可視為近似的節線半金屬。由第一原理性緊束縛模型計算，我們也觀察到了節線半金屬所特有，且極為平坦的鼓面狀表面能帶。

關鍵字

狄拉克節線 ； 拓樸半金屬 ； 貝里相位 ； 鼓面狀表面能帶 ； 第一原理

並列摘要

Recently, a new crystal form of Ca3P2 with vacancies was theoretically predicted as a nodal-line semimetal (NLSM) by means of first-principles calculations within virtual crystal approximation (VCA). Based on the structure, we study the vacancy dependence of the system stability without VCA. It is found that the band dispersion no longer supports a Fermi surface crossing upon local atomic relaxations. On the other hand, we find that there is another crystal structure of the same stoichiometry (Bixbyite structure) that is more energetically favorable than the proposed vacancy model. As a result, we conclude that Ca3P2 in the previously proposed crystal form may not be a realistic candidate for NLSMs. In order to realize NLSMs in materials, we systematically study charge-balanced main group compounds in known stable crystal structures. As it turned out, we find that strontium plumbide (Sr2Pb) and some barium tetragenides (Ba2X, X = Si, Ge, Sn), both in the structure of Pnma/oP12/C12, do exhibit a Fermi surface crossing which is protected by mirror reflection symmetries in the absence of spin-orbit coupling (SOC). When SOC is taken into account, Ba2Ge opens up the smallest gap among those compounds which is negligible at room temperature. Therefore, we predict that Ba2Ge is an approximate NLSM by first-principles calculations. In a slab calculation by an ab initio tight-binding model, we also find that Ba2Ge has nearly flat drumhead surface bands.

並列關鍵字

Dirac nodal-line ； topological semimetals ； Berry phase ； drumhead surface bands ； first-principles

參考文獻

[1] Lilia S. Xie, Leslie M. Schoop, Elizabeth M. Seibel, Quinn D. Gibson, Weiwei Xie, and Robert J. Cava. A new form of Ca3P2 with a ring of Dirac nodes. APL Materials, 3(8):083602, August 2015.

[2] T. B. Massalski, H. Okamoto, and ASM International, editors. Binary alloy phase diagrams. ASM International, Materials Park, Ohio, 2nd ed edition, 1990.

[3] K. Turban and Herbert Schäfer. Notizen: Darstellung und Kristallstruktur des Ba2Ge / Preparation and Crystal structure of Ba2Ge. Zeitschrift für Naturforschung B, 28(3-4):220–222, 2014.

[4] Zhijun Wang, Yan Sun, Xing-Qiu Chen, Cesare Franchini, Gang Xu, Hongming Weng, Xi Dai, and Zhong Fang. Dirac semimetal and topological phase transitions in A3Bi (A = Na, K, Rb). Phys. Rev. B, 85(19):195320, 2012.

[5] Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S.-K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen. Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi. Science, 343(6173):864–867, February 2014.