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Daniel Passos

Daniel Passos
Daniel Jorge da Silva Passos
PhD Student (Theory)
MSc in Physics (Specialization in Experimental Physics)


I am a PhD student, working under the supervision of Prof. Lopes dos Santos. My research is on Condensed Matter Physics (Theory). My main focus is on optical properties of two-dimensional materials, with an emphasis on the effects of twisted layers and Moiré potentials. I am currently pursuing two topics:

Gauge invariance in the density matrix formalism

(This work is being done in collaboration with Gonçalo Ventura and Prof. João Viana.)

The density matrix formalism provides a method for computing the optical conductivity and nonlinear optical response functions by making an expansion of the density matrix operator on the perturbation. There are, however, two ways to define the perturbation, either by the scalar potential (length gauge) or by the vector potential (velocity gauge). These two equivalent choices of gauge for the electromagnetic field have in practice led to different results. We have been working to clarify the differences in the two approaches and, by making use of a second gauge principle, to provide formal simplifications of the calculations.

Optical properties of twisted bilayer graphene

Two dimensional materials are a current research frontier in condensed matter physics. More than a decade after the discovery of graphene, several other 2D crystals have been produced and analyzed (theoretically and experimentally) and the more exciting prospects seem to come from their combination in Van Der Waals heterostructures. Often in the assembly of such layered systems, rotational disorder has been observed, with one layer being rotated relative to the next, leading to complex crystals structures and long-wavelength potentials (Moiré potentials). These twisted layered systems form by themselves a new kind of crystal. My PhD topic is on exploring the optical properties of these twisted two-dimensional crystals, with a focus on plasmonics of twisted bilayer graphene, which stands as a prototype of such systems.