Research Projects

The Hall effect and its quantized cousins are of fundamental importance in condensed matter and materials physics. Very recently, it has been realized that time-reversal symmetry breaking in not an essential requirement to obtain the Hall effect, provided one goes beyond linear response – this has been termed the non-linear Hall effect and has connections to dipole moments of the Berry curvature. A major challenge in this nascent field has been the small values of non-linear Hall signals, with the effect limited to very low temperatures. This necessitates a search for materials and mechanisms to achieve large non-linear Hall signals, preferably at ambient conditions in order to better understand this new phenomenon and harness its full potential for applications. The origin of our current proposal lies in our realization, based on preliminary work, that remarkably large values of non-linear Hall signals may be achieved close to topological phase transitions in different material platforms. At present, this is one mechanism to enhance the non-linear Hall signals, and it will be our goal to find other such mechanisms, including strain engineering or doping strategies. Furthermore, since only a handful of materials have been found to show measurable values of non-linear Hall signals, our aim is to design material systems – including heterostructures and superlattices – to obtain improved non-linear Hall materials. The non-linear Hall effect beyond second order is largely unexplored. We will identify and predict materials systems with response beyond second order and delineate the symmetry requirements for such physics. Further, almost all the studies till date have focused on two-dimensional materials, and three-dimensional systems, which offer more flexibility in terms of symmetry constraints, remain unexplored. Our study will broaden the scope to include such three-dimensional materials and establish the symmetry requirements to obtain non-linear Hall effect. In a nutshell, our project aims at discovery of mechanisms to enhance non-linear Hall effect and design of material systems which exhibit this effect, using symmetry analyses, state-of-the-art first-principles methods, ab-initio derived tight-binding models, and low-energy effective Hamiltonians. This will establish them as a new class of multifunctional materials and pave the way for realizing their potential applications in the non-linear regime.