Quantum Mechanics of Interacting Electron Fluid in Berry-curved Materials

Non-technical summary

This award supports theoretical studies of experimentally measurable manifestations of quantum mechanics in the collective behavior of electrons in solids. Quantum mechanics has proven crucial to explaining the behavior of this electron fluid. However, more often than not, macroscopic properties (e.g., electrical conduction) of the electron fluid can be described quite classically.

For instance, the equations describing viscous flow of the electronic liquid are very similar to those that describe water, showing essentially classical behavior. The present project goes beyond this traditional point of view in developing a quantum theory for electron flow.

The Principal investigator will focus on the interaction of magnetic order with higher-energy states in three-dimensional analogs of graphene, called Weyl and Dirac semimetals. He will study electron motion in the presence of a magnetic field on the edge of a two-dimensional "topological insulator" and deviations from the classical equations for viscous fluid flow. These topics will bring out the quantum effects in solids as a characterization tool for their microscopic properties.

The research will involve graduate and undergraduate students and will facilitate their training in modern methods of condensed-matter theory. The educational efforts will also be directed toward implementation of modern classroom techniques (e.g. the "flipped" classroom) into the teaching practices of the PI. The outreach program will be directed toward training high-school students and acquainting them with the demands and traditions of higher education.

Technical summary

The objective of this proposal is to provide theoretical insights into the interaction of electronic degrees of freedom with macroscopic order parameters as well as transport and hydrodynamic properties of the interacting electronic fluid in (disordered) gapless topological phases, with a strong focus on experimentally observable phenomena. The research program contains three main thrusts.

The common thread connecting these thrusts is the quantum mechanics of electrons on the lattice, manifested through geometric phases. The thrusts are

1. Anomaly-induced electric control of magnetic degrees of freedom in Weyl materials: the PI will develop the theory of interaction between the electronic degrees of freedom of a topological metal with a macroscopic magnetization. Specifically, he will focus on i) the anomaly-induced magnetic anisotropy for anomaly detection and magnetization control, ii) the theory of current-induced spin torques in 3D topological metals, and iii) the manifestations of band topology in textured magnetic phases and magnetic excitations.

2. Nonlinear transport and magnetotransport phenomena in Weyl and other geometric metals: the PI will study nonlinear phenomena rooted in band geometry (not having classical "Drude" analogs) in 3D and 1D gapless systems. The specific directions will include i) developing a general theory of E2B-corrections to transport in metals, ii) non-linear anomalous Hall effect in disordered Weyl semimetals, and iii) the theory of kinetic magnetoelectric effect and nonlinear transport on 1D topological and Rashba edges.

3. Anomalous hydrodynamics in crystals: the PI will develop the theory of quantum effects in electron-electron collisions and their influence on electronic hydrodynamics. The specific directions PI Pesin will pursue within this thrust focus on i) anomalous transport in the hydrodynamic regime, in particular in multi-valley Berry-curved (semi-)conductors, ii) the anomalous Hall viscosity from electron-electron collisions in gapless systems, and iii) chiral vortical effect in crystals.

The methods of the project will include standard tools of many-body theory, including the Keldysh diagrammatic technique and the quantum kinetic equation approach to quantum transport, as well as some numerical modeling. The results of the program will be used to provide guidance for materials research, paying particular attention to the realistic aspects of systems with nontrivial topology.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.