Nonlinear Hall effects in two-dimensional moire 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 Hall effects. Unlike most of 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 observed in several kinds of materials with a nonuniform distribution of the Berry curvature of energy bands. Experimentally, when a longitudinal alternating current (AC) electric field is applied, a transverse Hall voltage will be generated, with its amplitude proportional to the square of the driving current. Such a nonlinear Hall signal contains two components: one is an AC transverse voltage oscillating at twice the frequency of the driving current, and the other is a direct current (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 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 some nonlinear Hall effects are achieved by an inherent quantum property 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 for the lattice symmetry breaking of the system apart from the spatial inversion breaking, and the materials available are largely 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 brand new way to design, tailor and control the symmetry of lattice, and to prepare artificial moire crystals with certain physical properties. Recently, both theoretical results and experimental studies on graphene superlattices and transition metal dichalcogenide superlattices have shown that artificial moire superlattice materials can have larger Berry curvature dipole moments than those in natural non-moire 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 moire 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 states and superfluidity states, but also expand the functional space of moire 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 two mechanisms of the nonlinear Hall effect: the Berry curvature dipole moment and the disorder. Subsequently, this paper summaries some properties of two-dimensional moire superlattices which are essential in realizing the nonlinear Hall effect: considerable Berry curvatures, symmetry breaking effects, strong correlation effects and tunable band structures. Next, this paper reviews theoretical and experimental progress of nonlinear Hall effects in graphene and transition metal dichalcogenides superlattices. Finally, the future research directions and potential applications of the nonlinear Hall effect based on moire superlattice materials are prospected.