Topological Modes in Bidimensional Dirac Materials

Vasco Castanheira da Silva Ramos dos Santos

Key information

Authors:

Vasco Castanheira da Silva Ramos dos Santos (Vasco Castanheira da Silva Ramos dos Santos)

Supervisors:

Pedro Afonso Cosme e Silva; Hugo Fernando Santos Terças (Hugo Fernando Santos Terças)

Published in

November 21, 2025

Abstract

This work explores the hydrodynamic properties of two-dimensional magnetized Dirac materials, to demonstrate their utility in achieving ultra-fast signal propagation. Using a theoretical description based on electronic fluid dynamics that incorporates the presence of Hall viscosity, complemented with numerical simulations, we start by performing a topological analysis on the bulk bands of the conductor, categorized through their respective Chern numbers, serving as an important guide to the upcoming analysis of finding topologically protected solutions. Using such results, we fully characterize the spectrum of solutions in an inviscid linearized picture in the edge of a magnetized domain, and on the interface between two domains with opposite magnetic field configurations. We proceed with the inclusion of Hall viscosity, which yields new results, such as chiral solutions that can either propagate along or against the electron gyromotion for different wavenumbers. Finally, focusing also the nonlinear regime, we recover the full model and study new shock wave phenomena. Those follow a Burgers-like equation along the interface, which we derived, and our numerical simulations evince that such nonlinear chiral modes travel with low attenuation and steady propagation.