The nonlinear Hall effect in two dimensional moiré superlattices

The Hall effect refers to the generation of a voltage in a direction perpendicular to the applied current. Since its discovery in 1879, the Hall effect family has become a huge group, and its in-depth study is an important topic in the field of condensed matter physics. The newly discovered nonlinear Hall effect is a new member of the Hall effects. Unlike most of the previous Hall effects, the nonlinear Hall effect does not need to break the time-reversal symmetry of the system but requires the spatial inversion asymmetry. Since 2015, the nonlinear Hall effect has been predicted and confirmed to exist in several kinds of materials with nonuniform distribution of Berry curvature of the energy bands. Experimentally, when a longitudinal ac electric field is applied, a transvers Hall voltage will be generated, with its amplitude proportional to the square of the driving current. Such nonlinear Hall signal contains two components: one is an ac transverse voltage that oscillates at a frequency that twice of the driving current, and the other is a DC signal converted from the injected current. Although the history of the nonlinear Hall effect is only a few years, its broad application prospects in the fields of wireless communication, energy harvesting, and infrared detectors have been widely recognized. The main reason is that the frequency doubling and rectification of electrical signals via the nonlinear Hall effect are achieved by the inherent quantum properties of the material - the Berry curvature dipole moment, and therefore do not have the thermal voltage thresholds and/or the transition time characteristic of semiconductor junctions/diodes. Unfortunately, the existence of the Berry curvature dipole moment has more stringent requirements on the lattice symmetry of the system in addition to the space inversion breaking, and the available materials are very limited. This greatly reduces the chance to optimize the signal of the nonlinear Hall effect and limits the application and development of the nonlinear Hall effect. The rapid development of van der Waals stacking technology in recent years provides a new way to design, tailor and control the symmetry of lattice, and prepare artificial moiré crystals with certain physical properties. Recently, both theoretical and experimental studies on graphene superlattices and transition metal chalcogenide superlattices have shown that artificial moiré superlattice materials can have larger Berry curvature dipole moments than natural non-moiré crystals, which has obvious advantages in generating and manipulating the nonlinear Hall effect. On the other hand, abundant strong correlation effects have been observed in two dimensional superlattices. The study of the nonlinear Hall effect in two-dimensional moiré superlattices can not only give people a new understanding of the momentum space distribution of Berry curvatures, contributing to the realization of more stable topological transport, correlation insulating state and superfluidity state, but also expand the functional space of moiré superlattice materials which are promising for the design of new electronic and optoelectronic devices. This review paper firstly introduces the birth and development of the nonlinear Hall effect and discusses the two mechanism of the nonlinear Hall effects: Berry curvature dipole moment and disorder. Subsequently, this paper summaries some properties of two-dimensional moiré superlattices which are essential in realizing the nonlinear Hall effect: considerable Berry curvature, symmetry breaking, strong correlation effect and tunable band structure. Next, this paper reviews the theoretical and experimental progress of the nonlinear Hall effects in graphene and transition metal chalcogenide superlattices. Finally, the future research directions and potential applications of the nonlinear Hall effect based on moiré superlattice materials are prospected.