研究人员开发磁开关打开或关闭一种奇怪的量子性质

诸平

据美国国家标准与技术研究院（National Institute of Standards and Technology）2017年5月25日提供的信息，由美国国家标准与技术研究院、美国马兰兰大学（University of Maryland）、麻省理工学院（Massachusetts Institute of Technology）、哈佛大学（Harvard University）、中国南方科技大学（South University of Science and Technology of China）、瑞士洛桑联邦理工学院（école Polytechnique Fédérale de Lausanne）以及日本国立材料科学研究院（National Institute for Materials Science, Tsukuba）的研究人员合作，开发出一种磁开关，可以打开或者关闭一种奇怪的量子属性。相关研究结果于2017年5月26日在《科学》（Science）杂志最新一期发表——F. Ghahari, D. Walkup, C. Gutiérrez, J. F. Rodriguez-Nieva, Y. Zhao, J. Wyrick, F. D. Natterer, W. G. Cullen, K. Watanabe, T. Taniguchi, L. S. Levitov, N. B. Zhitenev, J. A. Stroscio. An on/off Berry phase switch in circular graphene resonators. Science, 26 May 2017, 356(6340): 845-849. DOI: 10.1126/science.aal0212.图1就是在环形石墨烯谐振器中电子轨迹的三维透视图及其在水平面的投影图示。一个弱磁场将经典类型的原子轨道(左图所示)扭曲成具有外侧环路的跳跃型(右图所示)。因为石墨烯中电子的波函数是生俱来的拓扑贝里相（topological Berry phase）,它们之间的过渡是涉及到在量子力学的能量水平上突然跳跃。

Fig. 1 Three-dimensional renderings of electron trajectories in circular graphene resonators, and their projections on the horizontal plane. A weak magnetic field warps the classic type of atomic orbit (left) into the skipping type with outer loops (right). Because of the topological Berry phase inherent to electron’s wavefunctions in graphene, the transition between them involves a sudden jump in the quantum-mechanical level energy. Credit: Christopher Gutiérrez, Jon Wyrick, CNST/NIST

当一个芭蕾舞演员单脚旋转时,快速旋转一周,她看起来就像她刚刚开始那样。但对于电子和其他亚原子粒子来说事实并非如此,因为它们遵守的规则是量子理论。当一个电子围绕一个封闭的路径循环一周时,终点也是始点,其物理状态与其离开时可能是相同的，但是也可能是不同的。

现在,由美国国家标准与技术研究院(NIST)的科学家领导的一个跨国研究小组，已经开发出一种方法来控制此结果。他们开发了可以打开和关闭这个神秘的量子行为的首例开关。此发现有望为量子理论基础提供新见解，并可能导致新的量子电子设备。

为了研究此量子性质,NIST的物理学家和研究员 Joseph A. Stroscio和他的同事们研究了将电子驱赶到石墨烯纳米级范围内的特殊轨道，时电子围绕石墨烯样品中心的轨道运行，就像电子围绕原子中心的轨道运行一样。石墨烯中电子运行一周之后，在其轨道上运行的电子通常会保持其相同的物理性质。但是,当一个应用磁场达到某个临界值时,它的作用就像是一个开关,使电子运行一周之后，不仅轨道的形状发生变化,而且会导致电子具有不同的物理特性。

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The newly developed quantum switch relies on a geometric property called the Berry phase, named after English physicist Sir Michael Berry who developed the theory of this quantum phenomenon in 1983. The Berry phase is associated with the wave function of a particle, which in quantum theory describes a particle's physical state. The wave function—think of an ocean wave—has both an amplitude (the height of the wave) and a phase—the location of a peak or trough relative to the start of the wave cycle.

      These images show the orbital paths of electrons trapped within a circular region within graphene. In the classical orbit (top image), an electron that travels in a complete circuit has the same physical state as when it started on the path. However, when an applied magnetic field reaches a critical value, (bottom image), an electron completing a circuit has a different physical state its original one. The change is called a Berry phase and the magnetic field acts as a switch to turn on the Berry phase. The result is that the electron is raised to a higher energy level. Credit: Christopher Gutiérrez, Daniel Walkup/NIST    

When an electron makes a complete circuit around a closed loop so that it returns to its initial location, the phase of its wave function may shift instead of returning to its original value. This phase shift, the Berry phase, is a kind of memory of a quantum system's travel and does not depend on time, only on the geometry of the system—the shape of the path. Moreover, the shift has observable consequences in a wide range of quantum systems.

Although the Berry phase is a purely quantum phenomenon, it has an analog in non-quantum systems. Consider the motion of a Foucault pendulum, which was used to demonstrate Earth's rotation in the 19th century. The suspended pendulum simply swings back and forth in the same vertical plane, but appears to slowly rotate during each swing—a kind of phase shift—due to the rotation of Earth beneath it.

Since the mid-1980s, experiments have shown that several types of quantum systems have a Berry phase associated with them. But until the current study, no one had constructed a switch that could turn the Berry phase on and off at will. The switch developed by the team, controlled by a tiny change in an applied magnetic field, gives electrons a sudden and large increase in energy.

Several members of the current research team—based at the Massachusetts Institute of Technology and Harvard University—developed the theory for the Berry phase switch.

To study the Berry phase and create the switch, NIST team member Fereshte Ghahari built a high-quality graphene device to study the energy levels and the Berry phase of electrons corralled within the graphene.

       Three-dimensional renderings of electron trajectories in circular graphene resonators, and their projections on the honeycomb lattice (shadows). A weak magnetic field warps the classic type of atomic orbit (left) into the skipping type with outer loops (right). Because of the topological Berry phase inherent to electron’s wavefunctions in graphene, the transition between them involves a sudden jump in the quantum-mechanical level energy. Credit: Christopher Gutiérrez, Jon Wyrick, CNST/NIST    

First, the team confined the electrons to occupy certain orbits and energy levels. To keep the electrons penned in, team member Daniel Walkup created a quantum version of an electric fence by using ionized impurities in the insulating layer beneath the graphene. This enabled a scanning tunneling microscope at NIST's nanotechnology user facility, the Center for Nanoscale Science and Technology, to probe the quantum energy levels and Berry phase of the confined electrons.

The team then applied a weak magnetic field directed into the graphene sheet. For electrons moving in the clockwise direction, the magnetic field created tighter, more compact orbits. But for electrons moving in counterclockwise orbits, the magnetic field had the opposite effect, pulling the electrons into wider orbits. At a critical magnetic field strength, the field acted as a Berry phase switch. It twisted the counterclockwise orbits of the electrons, causing the charged particles to execute clockwise pirouettes near the boundary of the electric fence.

Ordinarily, these pirouettes would have little consequence. However, says team member Christopher Gutiérrez, "the electrons in graphene possess a special Berry phase, which switches on when these magneticallyinduced pirouettes are triggered."

When the Berry phase is switched on, orbiting electrons abruptly jump to a higher energy level. The quantum switch provides a rich scientific tool box that will help scientists exploit ideas for new quantum devices, which have no analog in conventional semiconductor systems, says Stroscio.