拓扑扭结态广泛存在于许多材料的畴壁中，如在石墨烯体系、磁性拓扑绝缘体、类石墨烯的经典波等体系的畴壁中都存在拓扑扭结态。近几年来，人们通过STM和输运测量，在双层石墨烯中证实了拓扑扭结态的存在。另外，在类石墨烯型的经典波体系中，也观察到了声波、光子和微波的扭结态。然而，由于拓扑扭结态局域在很小的宽度，因此它的表征是个难题。通常方法中，角分辨光电子能谱只适用于较大的体系，而介观输运测量对于无序较大的情况也无法得到量子化电导。在目前的实验中，这些拓扑扭结态的电子性质，如扭结态数、色散关系以及相关的几何相位等，还没有得到观察和研究。

最近，kaiyun体育官方网站孙庆丰教授和谢心澄教授与西北大学成淑光副教授、苏州大学江华教授、北京师范大学刘海文教授合作，在石墨烯体系中，通过构建AB干涉环和利用贝里位相，提出了对拓扑扭结态的有效调控手段，并实现谷自由度的调控和极化。他们发现，在该体系中谷极化电流的输运行为可以通过磁场和电场实现周期性的调控，同时呈现AB效应和法布里-珀罗干涉效应。在单层石墨烯中，由于只有一条拓扑扭结态，透射系数随电场或磁场呈现出单周期震荡行为。而对于双层石墨烯，由于有两条拓扑扭结态存在，因此透射系数随电场或磁场呈现出双周期震荡行为。另外，他们进一步提出：使用该方案，通过简单的输运测量可以获得拓扑扭结态以下性质：1)高谷极化电流，2) 拓扑扭结态的线性色散关系，3)异质结中准一维拓扑扭结态的数目和 4)狄拉克电子在动量空间旋转一周的贝里位相。并且以上性质在有无序存在时也可以很好呈现。此外，他们也指出对于类石墨烯的光子晶体和声子晶体以及其它二维体系中的拓扑扭结态，以上测量方案均能适用，可以全部或部分地测量以上提到的拓扑扭结态的四个性质。

该工作发表在Phys.Rev.Lett.121,156801(2018)， doi.org/10.1103/PhysRevLett.121.156801。并且文章中的一个图被放在Phys.Rev.Lett的封面上（见附图）。

该工作得到了国家重点研发项目(项目批准号2017YFA0303301)、科技部国家重大基础研究计划(项目批准号2015CB921102)、中国科公司重点资助项目(项目批准号XDPB08-4)、国家自然科学基金(项目批准号11874298、11822407、11674264、11534001、11574007和11674028)和江苏省自然基金(项目批准号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).