The interplay between topology, geometry and correlations in novel materials

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In this project we will consider hydrodynamic electron transport in various strongly-correlated 2Dmaterials. The goal is to derive equations describing the motion of electrons in these systems andsolve them for certain simple geometries. An intriguing possibility is to combine the somewhat"semiclassical" hydrodynamic description with the quantum nature of particles, which are in factcharacterized by discrete spin, pseudospin, valley, layer degrees of freedom. These are, quitegenerally, coupled to the particle kinetic momentum and endow electrons with non-trivial Berryphases. In turn, when the electron momentum varies (as a consequence of external potentials orcollisions), particles "skew" in the orthogonal direction, producing measurable effects. The interplaybetween strong correlations, hydrodynamic transport and the Berry phases of particles in twisted 2Dmaterials is a new and unexplored field.In this project we will:- derive equations of motions for electron in twisted bilayer graphene, both in flat and upper bands,where mobility is very high, accounting for the role of strong interactions, band renormalization,and the coupling between pseudospin/layer/valley indices with kinetic momentum;- solve the above-derived equations in simple but experimentally relevant geometries (channels,constrictions, etc.), addressing a wide range of densities and temperatures - from Fermi liquid toelectron-hole-plasma regime;- understand how Berry phases impact on the collision integral and therefore on viscositiesappearing in electrons' hydrodynamic equations. We will therefore study the emergence of "twobodyside jump" phenomena and calculate transport coefficients and relaxation times;- extend these results to other flat-band materials, such as transition-metal dichalcogenides, whereelectrons feature spin-orbit coupling and describe a new regime for spintronics.During this project the student will gain a knowledge of 2D materials, modern theory of transport andhydrodynamics, all of them hot research topics at the moment. Moreover, he/she will learn how toemploy modern field theoretical methods (Green functions, perturbation theory, Keldysh) to tacklemany-body transport problems in condensed matter physics. Finally, he/she will also develop and/orenhance computational skills by using Mathematica/Python to solve some of the problem numerically.