Hydrodynamic approach to quantum dynamics in electronic systems

• Applicant: Privatdozent Dr. Boris Narozhny
• Subject Area: Theoretical Condensed Matter Physics
• Term: from 2021 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 466540346

Comprehensive understanding of quantum dynamics in novel and unconventional materials is one of the major outstanding issues in condensed matter physics. The project is devoted to the theoretical study of the possible hydrodynamic behavior of charge carriers in topological materials and strongly correlated systems. The aim of the project is to gain physical insight into the fundamental problem of the interplay of strong electron-electron interactions (and corresponding correlations) and disorder as well as its manifestations in observable transport phenomena.Traditional transport theory is based on the quasiparticle paradigm. In conventional conductors, the system of weakly interacting quasiparticles can be described with the help of the kinetic equation. At the semiclassical level, the common “tau-approximation” for the collision integral leads to the Drude-like description of transport phenomena with the central quantity being the quasiparticle mean free time or “lifetime”. In strongly correlated systems, the quasiparticle approach may fail, e.g., in the “strange metal” phase of unconventional superconductors or twisted bilayer graphene. Moreover, even if quasiparticles can be defined the semiclassical kinetic approach may fail in multi-component systems with non-Abelian degrees of freedom (e.g., spin or isospin) due to the purely quantum nature of the latter. The ultimate goal of this project is to develop a macroscopic theory of electronic transport in strongly correlated systems and to investigate the possibility of the hydrodynamic behavior (testing the conjectures based on the holographic approach).The major direction of this project is quantum dynamics in topological materials, an actively developing field of condensed matter physics with several high-profile experiments showing hints of the hydrodynamic behavior. Especially interesting in this context is the interplay of topological band structure and electron-electron interactions (responsible for establishing the local equilibrium underlying the usual hydrodynamic theory). Developing a coherent picture of macroscopic transport involving the effects of non-trivial, multi-component band structure, electronic correlations, and weak disorder represents the long-term goal of the project. The objectives of the project are expected to be particularly relevant to engineering and functionalization of novel materials. Methodologically, the project aims at developing a theoretical framework for studying macroscopic transport properties based on the microscopic approach to the quantum kinetic theory in the spirit of the linear response theory developed by the applicant in the context of graphene.

• DFG Programme: Research Grants