Topology in Optical and Transport Responses of Quantum Materials
Quantum mechanics is responsible for a series of remarkable emergent phenomena in solids the most well known of which is superconductivity. The other celebrated manifestation is the quantum Hall effect that is quantized to an astounding precision. Since its discovery theorists have been searching for other possible quantized responses. Topology has been established as the fundamental reason for the quantization and has guided the search ever since. In my talk, I will cover some aspects of how band topology and geometry affect optical responses and hydrodynamics of electron fluids, focusing on two of my results. The first example will be the non-linear chiral photocurrent in Weyl semimetals that has been known to be approximately quantized in the free electron approximation. I will show how electron-electron interaction modifies this result. The other example is the odd viscosity and the dependence of the anomalous Hall conductivity on the gradient of the electric field and their relation to features of the band structure.
Aleksandr is a theoretical physicist studying transport properties of quantum materials, particularly, the role of topology in them. Normally confined to the microscopic world, in quantum materials quantum mechanics manifests itself on the macroscopic scale. This unique feature makes studying them challenging but at the same time promising as these materials can have properties not observed in conventional matter. Two of Aleksandr’s current projects explore the manifestations of band structure topology in transport effects: the first one studies non-linear optical responses in 3D Weyl semimetals that were shown to be quantized similarly to the quantum Hall effect in 2D materials, while the second one focuses on the novel type of hydrodynamic behavior in clean electron systems that arises due to Berry curvature and is drastically different from conventional fluid behaviour. Additionally, he is working on a project that aims to understand quantum chaos and thermalization in isolated quantum many-body systems through time evolution of local operators.