Topology in relativistic semimetals (TOPREL)

• Applicant: Dr. Tobias Meng
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 452557895

This project will explore electronic properties of relativistic topological materials. One important goal is to put transport in topological semimetals on a firmer theoretical footing. Another important aspect is to build connections between Dirac materials and the theory of relativity, which will generate new interpretations for transport phenomena in terms of black hole physics and curved spacetimes. Finally, our work will aim at predicting new topological phases created by dissipation in semimetals. In particular, we will improve on the existing approached based on effective non-hermitian Hamiltonians by using more realistic and well-controlled approaches.In a first work package, we will study transport in inhomogeneous topological semimetals and semimetal heterostructures with a focus on inhomogeneous Weyl node tilts. By exploiting a mapping of Weyl and Dirac Hamiltonians to curved spacetimes, and by deriving a semiclassical description of transport using real space Berry phases, we will develop a new theoretical formalism that allows to design transport properties of topological semimetals for uses in sensors, in electron lensing, and as novel topolectric circuit elements.In a second work package, we study thermoelectric transport quantities such as electrical conductivity, electronic thermal conductivity, and the Seebeck coefficient of Weyl semimetals by exactly solving the Boltzmann transport equations in realistic models. We will explore the effect of long range impurity scattering and implement realistic Hamiltonians (e.g. for WTe2 and ZrSiSe), for which we interface our transport theory with density functional theory (DFT) calculations.In a third work package, we will consider Dirac and Weyl semimetals as well as nodal-line semimetals in two or three dimensions which are subject to dissipation due to mechanisms like disorder, electron-electron or electron-phonon interactions. We will revisit the results obtained recently using effective non- hermitian Hamiltonians using alternative more accurate techniques. One objective is to obtain a more realistic picture of experimentally relevant semimetals. Another objective is to discover novel topological phases for open quantum systems in these materials and to elucidate their experimental signatures.In a fourth work package, we will study electron transport in quantum materials with strong Coulomb interactions using the theory of hydrodynamic transport in the semiclassical regime. The hydrodynamic equations inherit important properties from the quantum mechanical band structure such as the Dirac spectrum as well as Berry curvature terms. The objective of this work package is thus to investigate the interplay between topologically nontrivial band structures and strong electronic interactions on the transport properties.

• DFG Programme: Research Grants
• International Connection: Luxembourg
• Cooperation Partners: Dr. Eddwi Hesky Hasdeo; Professor Dr. Thomas L. Schmidt