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狄拉克錐

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石墨烯的電子能帶結構中的各向同性狄拉克錐
2012年4月24日,麻省理工學院在其官方首頁報道了唐-崔瑟豪斯理論 (Tang-Dresselhaus Theory),該機構的科學家唐爽崔瑟豪斯夫人 (Mildred Dresselhaus) 在各項異性狄拉克錐方面取得突破,將引領半導體行業的晶片設計和熱電能源領域。


狄拉克錐是一種特殊二維材料中的電子能帶結構,在此結構中,電子具有像光一樣的相對論性質。科研人員認為狄拉克錐可能是通向未來超級晶片量子計算機超導和桌面相對論技術的路徑。[1][2][3][4]

典型的狄拉克錐材料包括石墨烯拓撲絕緣體薄膜和其他新型納米材料[1][5][6] 這些特殊二維材料中電子的能量動量具有線性的色散關係,因此其費米能級附近的電子能帶結構呈現出上下兩個錐體,分別代表電子和空穴。兩個錐體的頂端剛好相連,形成「零帶隙」的半金屬相.

狄拉克錐的名字來源於狄拉克方程,由保羅·狄拉克 (Paul Dirac) 提出,用以統一描述物質的量子力學效應和相對論效應。狄拉克錐可以是各向同性,也可是各向異性的。石墨烯中存在各向同性的狄拉克錐,由飛利浦·華萊士英語P. R. Wallace (P. R. Wallace) 於1947提出[7],並由諾貝爾物理學獎得主安德烈·海姆 (Andre Geim) 和康斯坦丁·諾沃肖洛夫 (Konstantin Novoselov) 於2005年首次在實驗中觀察到。[8] 麻省理工學院唐爽崔瑟豪斯夫人(Mildred Dresselhaus)於2012年在其唐-崔瑟豪斯理論 (Tang-Dresselhaus Theory) 中首次提出了系統性構建各向異性狄拉克錐的方法。[9][10][11]

描述

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量子力學中,狄拉克錐描述 [12]價帶和導帶的能量在二維晶格k空間中,除了零維狄拉克點所在的位置外,其他任何動量的價帶和導帶能量都不相等。由於是錐型,電傳導可以用無質量費米子電荷載流子來描述,在理論上這種情況可由相對論性的狄拉克方程來處理。 [13]無質量費米子可以導致各種奇異的量子霍爾效應、或是拓撲材料中的磁電效應和超高載流子遷移率[14] [15]在 2008-2009 年實驗上使用角分辨光電子能譜(ARPES) 對鉀-石墨插層化合物KC 8 [16]和幾種鉍基合金的狄拉克錐進行了觀察。[17] [18] [15]

狄拉克錐是二維材料 (像是單層石墨烯)或拓撲絕緣體的表面態的特徵。狄拉克錐在材料中是線性色散關係,由能量與晶體動量的兩個分量k xk y來描述。然而,這個概念可以擴展到三維材料,其中狄拉克半金屬由能量與k xk yk z的線性色散關係來定義。在動量空間中,色散關係為超圓錐體,它具有雙重簡併能帶,也在狄拉克點相交。 [15]狄拉克半金屬同時包含時間反演對稱性和空間反演對稱性;當其中一個對稱性被破壞時,狄拉克點可以分裂成兩個外爾點,材料變成外爾半金屬。 [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] 在2014年,實驗上利用ARPES對狄拉克半金屬砷化鎘 的能帶結構進行了直接觀測。 [30] [31] [32]

模擬系統

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已在許多物理系統實現狄拉克點,例如等離子體學、聲子學或納米光子學(微腔、 [33]光子晶體[34] )。

參看

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參考文獻

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