拓撲扭結态廣泛存在于許多材料的疇壁中，如在石墨烯體系、磁性拓撲絕緣體、類石墨烯的經典波等體系的疇壁中都存在拓撲扭結态。近幾年來，人們通過STM和輸運測量，在雙層石墨烯中證實了拓撲扭結态的存在。另外，在類石墨烯型的經典波體系中，也觀察到了聲波、光子和微波的扭結态。然而，由于拓撲扭結态局域在很小的寬度，因此它的表征是個難題。通常方法中，角分辨光電子能譜隻适用于較大的體系，而介觀輸運測量對于無序較大的情況也無法得到量子化電導。在目前的實驗中，這些拓撲扭結态的電子性質，如扭結态數、色散關系以及相關的幾何相位等，還沒有得到觀察和研究。

最近，beat365官方网站孫慶豐教授和謝心澄教授與西北大學成淑光副教授、蘇州大學江華教授、北京師範大學劉海文教授合作，在石墨烯體系中，通過構建AB幹涉環和利用貝裡位相，提出了對拓撲扭結态的有效調控手段，并實現谷自由度的調控和極化。他們發現，在該體系中谷極化電流的輸運行為可以通過磁場和電場實現周期性的調控，同時呈現AB效應和法布裡-珀羅幹涉效應。在單層石墨烯中，由于隻有一條拓撲扭結态，透射系數随電場或磁場呈現出單周期震蕩行為。而對于雙層石墨烯，由于有兩條拓撲扭結态存在，因此透射系數随電場或磁場呈現出雙周期震蕩行為。另外，他們進一步提出：使用該方案，通過簡單的輸運測量可以獲得拓撲扭結态以下性質：1)高谷極化電流，2) 拓撲扭結态的線性色散關系，3)異質結中準一維拓撲扭結态的數目和 4)狄拉克電子在動量空間旋轉一周的貝裡位相。并且以上性質在有無序存在時也可以很好呈現。此外，他們也指出對于類石墨烯的光子晶體和聲子晶體以及其它二維體系中的拓撲扭結态，以上測量方案均能适用，可以全部或部分地測量以上提到的拓撲扭結态的四個性質。

該工作發表在Phys.Rev.Lett.121,156801(2018)， doi.org/10.1103/PhysRevLett.121.156801。并且文章中的一個圖被放在Phys.Rev.Lett的封面上（見附圖）。

該工作得到了國家重點研發項目(項目批準号2017YFA0303301)、科技部國家重大基礎研究計劃(項目批準号2015CB921102)、中國科學院重點資助項目(項目批準号XDPB08-4)、國家自然科學基金(項目批準号11874298、11822407、11674264、11534001、11574007和11674028)和江蘇省自然基金(項目批準号BK20160007)的支持。

Manipulation and characterization of the topological kink states

The topological kink states are broadly investigated in the domain walls of many materials, such as graphene systems, magnetic topological insulators, classical wave in graphene-type systems and so on. In recent years, the existence of topological kink states has been verified in bilayer graphene by STM and transport measurements. Furthermore, the kink states of sound, photon and microwave are also observed in graphene-type classical wave systems. However, the topological kink states are restricted to a very narrow region, which makes it rather difficult to characterize with common techniques. In general, angle resolved photoemission spectroscopy is only suitable for larger systems, and mesoscopic transport measurements can’t obtain the quantized plateaus of the conductance in large disordered cases. At the present, the properties of the topological kink states, such as the number of kink states, dispersion relation and Berry phase, have not been observed and studied.

Very recently, an important progress is made in topological kink states by Prof. Sun and Prof. Xie at Peking Univ. and the collaborators, Prof. Cheng at Northwest Univ., Prof. Jiang at Soochow Univ. and Prof. Liu at Beijing Normal Univ. In graphene system, by using the Aharanov-Bohm (AB) interferometer and the Berry phase, they propose an effective method to manipulate the topological kink states and then realize the manipulation and polarization of the valley degree of freedom. They show that the transport behavior of valley-polarized current in this system can be controlled periodically by magnetic field and electric field, showing AB effect and Fabry-Perot-type interference. For a monolayer graphene system, because there exists only one topological kink state, the oscillation of the transmission coefficients has a single period with the increase of the electric field or magnetic field. For a bilayer graphene system, there are two topological kink states, so the transmission coefficients have two oscillation periods. In addition, they further propose that by using this proposed method the following properties of topological kink states can be obtained even in the presence of moderate disorder: 1) the nearly pure valley currents obtained, 2) the linear dispersion relation of topological kink states, 3) the number of topological kink states and 4) the pi Berry phase due to the electron evolving along a closed circle in the momentum space. Furthermore, they also point out that this proposed method is also effective to manipulate the topological kink states in classical wave and electronic graphene-type crystalline systems.

These results have been published online in Phys. Rev. Lett. 121, 156801(2018)， doi.org/10.1103/PhysRevLett.121.156801。And one of the figures in this paper is placed on the cover of Phys. Rev. Lett.(see below).

This work was supported by National Key R and D Program of China (2017YFA0303301), NBRP of China (2015CB921102), NSFC (Grants Nos. 11874298, 11822407, 11674264, 11534001, 11574007, and 11674028), NSF of Jiangsu Province, China (Grant No. BK20160007), and the Key Research Program of the Chinese Academy of Sciences (Grant No. XDPB08-4).