New Horizons in Quantum Transport: From band structure geometry to emergent curved spacetime

The theory of electrical, thermoelectric and magnetoelectric transport lies at the core of condensed matter research, because it allows to probe many ground state properties as well as dynamical and temperature-dependent features and harness them for advancing technology. Due to the progress in precision and resolution of experimental techniques, formerly inaccessible nonlinear and nonlocal effects take an increasingly central role. However, this pace is not matched in theory, where the physical understanding of response phenomena beyond the local and linear approximation remains fragmented. The advent of new quantum materials makes it necessary to take our understanding of transport theory to the next level.Here, I propose a universal and intuitive approach to quantum transport based on wavepacket deformations which allows the organization and prediction of complex transport phenomena with the help of geometric band structure properties. The goal of this research program is to develop this concept into a powerful and applicable tool in order to accelerate our comprehension of novel transport phenomena and prediction of new ones. To this end, using diagrammatic methods I will generalize the concept of the anomalous quasiparticle motion to all orders in the response, thereby significantly expanding on the concept of Berry curvatures. Connecting wavepacket deformations with gravitational phenomena, I will recast the theory of quantum transport in terms of a motion in curved spacetime. I will apply these concepts to novel flatband platforms by employing an innovative mapping of the quasiparticle flow between real and momentum space. Such powerful technology will enable the creation and investigation of dynamical gravitational fields in a condensed matter setting. The geometric formulation of quantum transport will reshape our understanding of condensed matter physics and lead to the discovery of new phenomena like gravitational anomalies in quantum materials.