石墨烯是由sp²杂化的碳原子组成的具有六角蜂窝结构的层状二维材料。其独特的原子排布，使其载流子在狄拉克点附近具有类似于光子的线性能量色散关系，这与无质量狄拉克费米子的行为一致。无质量狄拉克费米子作为一种相对论性质的粒子，将表现出很多新奇的物理效应，例如克莱因隧穿效应，半整数量子霍尔效应，非零贝里相位等。
  当体系尺寸与电子的德布罗意波长可比拟时，可以观测到量子受限效应。量子受限的引入可以使材料产生非常丰富有趣的量子现象。倘若对石墨烯中的狄拉克费米子进行限制，预计将会产生不同于传统半导体量子点的很多新奇的物理现象。通过这些量子现象一方面可以揭示受限（准）粒子的物理本质，例如，在石墨烯量子点中所观测到的克莱因隧穿效应就直接揭示了其载流子的相对论属性。更有趣的是，在量子受限情况下可以实现材料本身所不具备的新奇量子物态，例如实现对体系贝里相位的调控，并进一步调控量子受限能级。因此，对石墨烯中狄拉克费米子量子受限行为的研究一直是理论和实验的关注重点。
  本文针对这一课题，利用不同方法在石墨烯中引入量子受限，再结合低温扫描隧道显微镜（STM）和扫描隧道谱（STS）技术，系统地研究了受限狄拉克费米子的电学性质，并对其进行了调控。具体的研究内容和结果如下：
1. 在单层石墨烯量子点中通过调控贝里相位来调控受限能谱
  贝里相位是材料的固有属性，对于揭示微观体系中新奇量子现象和探索新物态等方面至关重要。在这一部分工作中，我们主要针对贝里相位的探测和调控两部分内容进行研究。在探测方面，传统的测量方法主要是通过输运实验中的Shubnikov-de Haas（SdH）量子振荡来实现，这需要制作器件，对样品要求较高。基于此，我们发展了利用STM测量隧穿磁导振荡的方法来探测材料体系的贝里相位，这就克服了输运测量中的一些限制，有望在更多的二维材料中得到广泛应用。在调控方面，人们普遍认为材料的贝里相位是一个常数，通常不会被改变，实际上，贝里相位取决于动量空间中对闭合路径贝里曲率的曲面积分，这就意味着如果能够控制电子轨迹，就可以实现对其贝里相位的调控。而在石墨烯电受限量子点中，可以通过引入磁场来调控电子轨迹，提供了一个调控贝里相位的平台。基于此，我们在单层石墨烯中引入了电受限量子点，结合磁场，系统研究了贝里相位的演化及其对能谱的调控作用。我们发现当改变磁场时，准束缚态动量空间轨迹会从不包含狄拉克点转变为包含狄拉克点，使贝里相位实现从0到π的跳变，进而导致量子干涉条件发生改变，使得跳变后的量子受限能谱多出一套束缚态能级，并对应于±m角动量简并度的解除。这提供了一个全新的手段来调控量子点电学性质。
2. 在双层石墨烯量子点中贝里相位连续变化导致的谷极化能谱
  在双层石墨烯量子点中，由于贝里曲率分布与单层石墨烯不同，改变运动轨迹会使贝里相位从0到2π连续变化，连续变化的贝里相位会产生与单层石墨烯截然不同的实验结果，但仍缺乏直接的实验证据。在这部分工作中，我们在双层石墨烯中引入电受限量子点，通过提高STS测量的信噪比，成功观测到一系列几乎等间距的束缚态。进一步地，我们间隔0.05 T磁场进行了精细STS测量，研究束缚态在磁场下的演化，发现了贝里相位从π到2π连续变化导致的谷极化受限能谱，能谱在磁场下连续演化。这一结果为双层石墨烯量子点中贝里相位的连续变化提供了直接证据，而连续变化的贝里相位也对能谱产生了重要影响，导致了和’谷简并度的解除，实现了对谷自由度的操控，为能谷电子学中谷极化量子态的实现提供了全新思路。
3. 磁场可调的具有谷差异的赝磁场受限
  引入量子受限可在材料体系中产生一系列有趣的量子现象。然而，能实现量子受限的有效方法并不多，在连续体系里，静电势受限几乎是实验上唯一可选的方法。在这一部分工作中，我们提出可以利用空间分布不均匀的赝磁场在石墨烯中实现量子受限。我们利用衬底和石墨烯热膨胀系数的差异，在石墨烯中形成了周期性一维应变结构，利用STM探测到应变较大的赝磁场区域和应变较小的受限区域。由于赝磁场受限不依赖于电势的变化，因此可以对电子和空穴产生同样的限制作用，这一点与电受限有很大的不同。更有趣的是，由于赝磁场不破坏时间反演对称性，因此在石墨烯的两个谷中具有相反的符号，当叠加一个真实磁场时，两个谷中载流子感受到的有效磁势垒将会不同，此时可实现具有谷差异的全新量子受限，为操控谷自由度提供了一种新的途径。

  Graphene is a layered two-dimensional (2D) material with a hexagonal honeycomb lattice composed of sp² hybridized carbon atoms. Its linear energy dispersion in low energy zone determines that the charge carries in graphene are massless Dirac fermions, which exhibit many interesting properties, such as Klein tunneling effect, half-integer quantum Hall effect and non-zero Berry phase.
  When the length scale of the system is comparable to the de Broglie wavelength of the particle, the quantum confinement effect takes place and generates many exotic quantum phenomena. Quantum confinement in graphene is expected to introduce many novel physical properties different from traditional semiconductor quantum dots (QDs). Through these quantum phenomena, on the one hand, the physical nature of confined (quasi-)particles can be revealed. For example, experimental evidence of the Klein tunneling in electronic junctions of graphene directly reveals the relativistic nature of its carriers. On the other hand, it is more interesting that in the case of quantum confinement, exotic quantum states beyond that of the parent materials can be realized. For instance, the Berry phase of confined (quasi-)particles in graphene electronic junctions can be tuned by external magnetic fields, resulting in novel Berry-phase-induced energy spectra in the confined junctions (In contrast, the Berry phase in pristine graphene is a constant). Therefore, the study of quantum confinement in graphene has attracted much attention both in experiment and in theory.
  In this thesis, we use different methods to introduce quantum confinement in graphene. We have systematically studied and tuned the electrical properties of confined Dirac fermions by using the scanning tunneling microscope (STM) and scanning tunneling spectroscopy (STS). The main results are obtained as follows:
1. Tuning the energy spectrum in monolayer graphene quantum dots via tunable Berry phase 
  Berry phase is an intrinsic property of materials, which is very important for revealing novel quantum phenomena and exploring new states of matter in microscopic systems. Two results will be introduced in this part. One is the measurement of Berry phase, the other is to tune Berry phase by using magnetic fields. In previous study, the Berry phase is mainly measured through Shubnikov-de Haas (SdH) quantum oscillation in transport experiments, which requires high-quality samples and devices. Here, we develop a method to measure the tunneling magneto-conductance oscillations by STM to directly detect the Berry phase of a material. Our method overcomes some limitations in transport measurements and is expected to be widely used in more two-dimensional materials. Usually, it is believed that the Berry phase of a material is a fixed constant. In fact, Berry phase is the integral of the Berry curvature over the area circled by the closed path in momentum space, which means that if the electron trajectory can be controlled, its Berry phase can be controlled. In a graphene QD, a magnetic field can well control the trajectories and thus the Berry phase for individual confined states. Therefore, we introduce quantum confinement in monolayer graphene (MLG), combined with magnetic fields, to systematically study the evolution of the Berry phase and its effect on the energy spectrum. It is found that when the magnetic field is increased, the momentum-space loop will change from not closing the Dirac point to enclosing the Dirac point, which makes the Berry phase jumps from 0 to π at a critical magnetic field. Then the quantum interference conditions are changed, which will suddenly lift the degeneracy of the quasibound states with opposite angular momenta ±m.
2. Realizing valley-polarized energy spectra in bilayer graphene quantum dots via continuously tunable Berry phases
  For the bilayer graphene (BLG), the Berry curvature distribution is different from that of monolayer graphene, so that changing the trajectory will continuously tune the Berry phase from 0 to 2π. The continuous change of Berry phase will produce completely different quasibound states evolution from that of monolayer graphene, but direct experimental evidence is still lacking. In this part, we first introduce a p-n junction quantum dot in bilayer graphene, and successfully observe a series of confined states by improving the signal-to-noise ratio in the tunneling spectra. Further, we study the evolution of the quasibound states in magnetic fields (the magnetic field interval is 0.05 T), and find large and tunable valley-polarized energy spectra. This result provides direct evidence for the continuously changing Berry phase in bilayer graphene quantum dots, which also has an important impact on the energy spectra, leading to the lifting of the and ’ valley degeneracy. Our result realizes the manipulation of the valley degrees of freedom, shedding light on graphene-based valleytronics.
3. Magnetic field-tunable valley-contrasting pseudomagnetic confinement
  Introducing quantum confinement is an efficient way to realize novel quantum phenomena, both revealing the physics of confined (quasi-)particles and enabling exotic quantum states beyond that of the parent materials. However, the efficient way to introduce quantum confinement is rare, and in most experiments, electrostatic potential is the only available way to realize quantum confinement in a continuous system. In this part, we show a different type of quantum confinement induced by inhomogeneous pseudomagnetic fields in graphene. Here we use STM to demonstrate that one-dimensional (1D) periodic graphene ripples, arising from differences in the thermal expansion coefficients of the substrate and graphene, with well-defined pseudomagnetic field regions and confined regions. Unlike the electrostatic potential, which mainly confines either electrons or holes, the pseudomagnetic fields can introduce a confinement simultaneously for both electrons and holes. Since the pseudomagnetic field does not violate time-reversal symmetry of graphene, and thus has opposite signs in the graphene’s two valleys, the total effective magnetic fields in the two valleys become unequal by applying external magnetic fields. By that we realize valley-contrasting spatial confinement and field-tunable valley-polarized confined states, providing a new way to manipulate the degree of freedom of the valley.