Tunable Nodal Dirac Semimetals Demonstrate Enhanced Second and Third-Order Nonlinear Hall Responses

The behaviour of electrons in novel materials is driving a search for new electronic properties, and recent work focuses on understanding nonlinear Hall effects in a class of materials called Dirac semimetals. Akash Dey, from the National Institute of Science Education and Research, and colleagues investigate how these effects arise in materials where the electronic structure can be tuned to create different types of nodes, points or lines where electrons behave in unusual ways. This research demonstrates that the strength of these nonlinear Hall responses depends critically on the type of node present, with single-node semimetals exhibiting enhanced second-order effects and line-node materials displaying a significantly larger third-order response, particularly when the material’s energy levels are finely tuned. These findings advance our understanding of electron behaviour in these materials and could pave the way for new electronic devices that exploit these nonlinear effects.

Nonlinear Hall Effects in Dirac Semimetal Phases

This research investigates nonlinear Hall responses in two-dimensional materials tunable to exhibit different Dirac semimetal phases, including single nodes, double nodes, and nodal rings. The team demonstrates that the second-order Hall effect, arising from the Berry curvature dipole, is strongest in the single-node phase and vanishes in the nodal-ring phase due to restored inversion symmetry. Conversely, the third-order Hall effect, originating from Berry connection polarizability, is significantly enhanced in the nodal-ring semimetal, particularly when the material’s energy levels are close to the band edges.

The differing strengths of these responses are attributed to the unique distribution of Berry connection polarizability in each phase, with the nodal-ring phase exhibiting a highly localized concentration near the nodal ring. Importantly, the study reveals that these nonlinear Hall effects occur intrinsically within all nodal phases, without requiring any tilting or warping of the material’s electronic structure. The authors note that the third-order Hall response in the nodal-ring phase decreases as the energy level moves away from the band edge, a limitation related to the concentration of Berry connection polarizability. This work highlights the potential of tunable two-dimensional semimetals for controlling quantum geometry-driven transport phenomena, offering a pathway towards novel electronic devices and a deeper understanding of fundamental material properties.