Research Projects

The primary objective of this project is to explore, understand and predict Berry curvature and quantum metric induced novel transport and optical phenomena [1–3], and do realistic material specific calculations for these. Our playground to look for these novel phenomena is i) the very popular class of topological materials [4, 5], ii) two dimensional materials with the valley degree of freedom [6], and iii) the recently discovered Moire materials. Band geometric quantities such as the Berry curvature and quantum metric play a very interesting role in these systems to generate completely new transport and optical phenomena in these materials. Such band geometric phenomena are under very active theoretical and experimental investigation. Some very well known examples of band geometric phenomena are the anomalous Hall effect in systems with broken time reversal symmetry, the quantum anomalies related physics in Weyl semimetals, valley polarization related physics in two dimensional materials, and more recently non-linear Hall effects. Collectively, the three fields of i) two dimensional materials, ii) topological materials and iii) Berry curvature in crystalline materials, combine to form the most significant developments in physics in the last few decades. Amongst these, the discovery of two dimensional materials in general and graphene in particular has already been awarded the Nobel prize in physics in 2010 [7]. The discovery of topological materials was awarded the Nobel prize in physics in 2016 [8]. The Berry curvature in a crystalline material is an intrinsic local geometrical property of the electronic wave- function[1–3]. This local geometric property is also connected to the global topological invariants, which can be used to classify integer quantum Hall states, topological insulators or other topological materials [4, 9, 10]. Irrespective of the topology, the presence of a non-zero Berry curvature modifies the semiclassical dynamics of the electron wave packet in a crystal. This has very significant implications and gives rise to new phenomena in electronic transport, optical and other experimental measurements [2, 11, 12]. This is the main fundamental physics concept on which this proposal stands. The project aims to understand the fundamentals for exploring new physics, and predicting new phenomena and connect to experiments. The goal of this proposal is to build on the existing work to develop new theoretical tools for understanding the existence of Berry connection, Berry curvature, quantum metric and their dipoles in crystalline solids, and to explore their role in linear and non-linear electronic (including spin, and heat) transport, and optical properties. The exciting thing is that this will enable us to predict Berry curvature and quantum metric related new transport and optical phenomena in topological and two dimensional materials.