Recently, Professor Hai-Zhou Lu’s group from the Shenzhen Institute for Quantum Science and Engineering (SIQSE) and the Department of Physics at the Southern University of Science and Technology (SUSTech) published two papers about progress in the quantum theory of the nonlinear Hall effect. The first article, entitled “Quantum theory of the nonlinear Hall effect,” was published in Nature Communications. The second article, entitled “Nonlinear Hall effects,” is an invitational perspective paper published in Nature Reviews Physics.

In the first article, Professor Hai-Zhou Lu’s group has made progress on the quantum theory of the nonlinear Hall effect. The nonlinear Hall effect is a new type of Hall effect, which can exist in time-reversal symmetric systems and is sensitive to spatial symmetry. Therefore, it can be used to probe phase transitions induced by spontaneous symmetry breaking, such as ferroelectric or nematic transitions.

The nonlinear Hall effect is convenient to be measured using the lock-in technique and can be realized in many 2D and 3D topological materials, thus can be an active research field. The nonlinear Hall effect is a quantum transport phenomenon that has a deep connection with the Berry curvature. However, a full quantum description is still absent. Prof. Hai-Zhou Lu’s group constructed a quantum theory of the nonlinear Hall effect by using the diagrammatic technique, highlighting the quantum nature of this effect and the inadequacy of the semiclassical theory. This work can be useful for future theoretical and experimental investigations.

Figure 1. Feynman diagrams for the nonlinear Hall conductivity

In the other article, Professor Hai-Zhou Lu’s group was invited to write a perspective about the recent progress on the nonlinear Hall effects, which includes discussions on the problems and outlooks of this field, therefore can be useful for investigations.

Figure 2. The nonlinear Hall effect and its generalizations

For the first paper, Dr. Zongzheng Du from SIQSE at SUSTech is the first author, while Prof. Hai-Zhou Lu from SUSTech is the corresponding author. The co-authors include Chun-Ming Wang from Shanghai Normal University, Dr. Hai-Peng Sun from SUSTech, and Academician X. C. Xie from Peking University. For the second paper, Dr. Zongzheng Du is the first author, while Prof. Hai-Zhou Lu is the corresponding author. The co-author is Academician X. C. Xie.

Paper links:

Nature Communications: https://www.nature.com/articles/s41467-021-25273-4

Nature Reviews Physics: https://www.nature.com/articles/s42254-021-00359-6