Our group observed direct evidence of the novel three-dimensional quantum Hall effect based on Weyl orbits in topological semi metallic cadmium arsenide nanosheets. On December 17th, the relevant research findings were published online in Nature (DOI: 10.1038/s41586-018-0798-3) under the title “Quantum Hall effect based on Weyl orbitals in Cd3As2”. Professor Faxian Xiu is the corresponding author, the doctoral student of our group Cheng Zhang is the first author, and Fudan alumni, Cornell postdoctoral student Yi Zhang, and another doctoral student of our group Xiang Yuan are the co first authors.
The quantum Hall effect is one of the most important scientific discoveries in the field of condensed matter physics since the 20th century, and so far there have been four Nobel Prizes (1985, 1998, 2010, and 2016) directly related to it. Simply put, electrons in a two-dimensional system undergo cyclotron motion under a strong magnetic field, forming a size independent quantized resistance at the edges. This process does not involve energy dissipation and belongs to a topological non mediocre boundary state. In recent years, a large number of important physical discoveries have been made based on this novel boundary state, such as the quantum anomalous Hall effect reported by Academician Qikun Xue of Tsinghua University in 2013 and the one-dimensional chiral Mayolana fermion reported by Academician Kanglong Wang of the University of California, Los Angeles in 2017. Therefore, the quantum Hall effect is considered the cornerstone of the flourishing research on topological electronic states in recent years. Due to its non-trivial topological properties and non-dissipative properties, the quantum Hall effect has potential application value in topological quantum computing and low-power electronic devices. It has been widely studied since its discovery in the 1980s and is an evergreen tree in the fields of physics and electronic science and engineering.
An important prerequisite for the current research on the quantum Hall effect system is that it must be a two-dimensional system to ensure that electrons can undergo fully insulated two-dimensional cyclotron motion under a magnetic field. Only electrons that are rebounded at the edges cannot undergo complete cyclotron motion and participate in conductivity, forming a quantized resistance through the mechanism of ballistic transport. However, in the work of our group, innovative use was made of a new electronic orbital based on the surface state of the Wail semi metal, successfully achieving a quantum Hall effect in a three-dimensional system. Weyl semi metal is a type of semi metal with energy bands at intersections. The excitation of low energy electrons near the intersection conforms to the so-called Weyl equation, and the corresponding quasi particles belong to massless and chiral Weyl Fermions. Topological semi metals have many novel physical properties, such as linear dispersion of the energy band, which leads to very high carrier mobility and extremely large magnetoresistance, resulting in chiral anomalies in external fields. Our group has conducted extensive preliminary research on these novel characteristics in the field of topological semi metals in recent years.
In addition, topological semimetals also have an important feature - Fermi arc surface states. The conventional Fermi surface that does not reach the boundary of the Brillouin zone is closed, while the Fermi arc here is an unclosed curve. This unique property is often used as an important indicator for confirming topological semi metals in research and has a wide range of applications in photoelectron spectroscopy experiments. Under a magnetic field, electrons in a regular band will undergo a cyclotron motion along the closed curve of the Fermi surface cross-section in the inverted space. For Fermi arcs, the two endpoints ultimately connect to the Weyl point of the body state, so they will not form a cyclotron orbit under normal circumstances. The Ashvin Vishwanath research group at the University of California, Berkeley proposed that in a low dimensional system, if the Fermi arcs on the upper and lower surfaces can couple under a magnetic field to form a closed loop, it is used to connect the chiral energy levels of the body state that also pass through the Wail point, just like constructing a wormhole connecting different surfaces in a crystal, which can allow electrons to freely tunnel. This theory was validated by an experimental research group in 2016 by measuring the quantum oscillations of the corresponding coupling orbitals in the cadmium arsenide micrometer structure. In 2017, our group successfully observed the quantum Hall effect using higher quality cadmium arsenide nanosheets, which was published in Nature Communications 8, 1272 (2017). However, at that time, there was still a lack of direct experimental evidence for the three-dimensional characteristics of this effect. In this study, we innovatively further utilized wedge-shaped samples to achieve controllable thickness changes, which resulted in different tunneling times for the Weyl orbits in different thickness regions, leading to changes in the corresponding orbital states. By measuring the corresponding quantum Hall resistance, it was found that the energy of the cyclotron orbit can be directly controlled by the sample thickness, which is completely different from the conventional quantum Hall effect based on two-dimensional surface states. At the same time, by changing the direction of the magnetic field, it was found that the orbital energy was also affected by the relative position of the magnetic field and crystal direction, breaking the mirror symmetry that two-dimensional systems should have. Based on these two important evidence, the experiment successfully demonstrated that the quantum Hall effect in cadmium arsenide nanostructures originates from the three-dimensional Weyl orbits. The theoretical mechanism for the generation of this new type of Weyl orbital quantum Hall effect is due to the fact that the two surface gyroscopes perfectly match the two-dimensional gyroscopes required for normal quantum Hall effects. At the same time, the vertical tunneling process is based on the chiral Landau energy level unique to Weyl semimetals, which can provide a non-dissipative channel without damaging the original quantized boundary states. On the other hand, the unique tunneling process in the Weyl orbits further provides a mechanism for controlling the phase and energy of electronic states through thickness, making this new three-dimensional quantum Hall effect more promising for research.
Figure. Physical mechanism of three-dimensional quantum Hall effect based on Weyl orbits
Paper link: https://www.nature.com/articles/s41586-018-0798-3
