贝里相最初是由贝里提出的，当系统的外参量Rt经过绝热演化后回到初始值时本征波函数累积的相位即为贝里相。贝里相对材料的拓扑性质有很重要的作用，与量子霍尔效应、轨道磁矩等一系列现象密切相关。通常认为，测量材料的贝里相需要借助于外磁场，利用磁场下电子的回旋运动实现电子在动量空间的闭合运动轨迹。2005年，A. K. Geim和P. Kim课题组通过强磁场下输运实验首次证实单层石墨烯电子波函数的贝里相为π。最近，C. Dutreix课题组最近的实验表明，在没有外加磁场时也可以测量石墨烯的贝里相。当石墨烯中存在单个氢原子吸附时，由于局域存在子格对称性的破缺，会发生谷内散射和谷间散射，导致赝自旋方向改变，使氢原子附近形成Friedel振荡。在实空间中，会诱导形成额外的谷间散射条纹，这与石墨烯的贝里相对应，在实验上通过对石墨烯的STM图像的分析也验证了上述结论。该工作为石墨烯中贝里相的测量提供了全新的方法，对我们之后的研究具有十分重大的意义。

Berry phase was first proposed by Berry. It is a geometrical phase accumulated by the wave function after the parameterR(t) of the system return to the initial value along an adiabatic cycle. Berry phase plays a very important role in the topological properties of materials, and is closely related to a series of phenomena such as quantum Hall effect and orbital magnetic moment. It is generally believed that the necessary condition for measuring the Berry phase of materials is to take advantage of external magnetic field to force the electrons circling around a closed loop. In 2005, for the first time, the research groups of A. K. Geim and P. Kim confirmed the existence of π Berry phase in graphene monolayer via the transport experiment under high magnetic field. Recent experiments by the C. Dutreix group have shown that the Berry phase of graphene can be measured without an external magnetic field. When there is a single hydrogen atom chemisorbed on graphene, the localized sublattice symmetry is broken and leads to the complex intravalley and intervalley scattering, which will further cause the nonzero rotational pseudospin and Friedel oscillation near the hydrogen atom. In the real space, it exhibits the additional wavefronts that correspond to the Berry phase of graphene, which have also been verified experimentally via the fast Fourier transform (FFT) filtered scanning tunnelling microscopy (STM) images of graphene. This work provides a new method for the measurement of the Berry phase in graphene, which is of a great significance for our subsequent research.