PhD Thesis defense: Quantum simulation of two-dimensional electronic lattices

PhD Program

Miguel Angel Jiménez Herrera
CFM Auditorium
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PhD Thesis defense: Quantum simulation of two-dimensional electronic lattices

Electronic quantum simulator / Topology / Topological quantum chemistry

Supervisors: Dario Bercioux (Ikerbasque Research Associate) and Aitzol Garcia-Etxarri (Ikerbasque Research Fellow)

This thesis addresses the quantum simulation of two-dimensional electronic lattices using the CO/Cu(111) quantum simulating platform. First of all, we introduce the methods used in the three results chapters. They are all based on the solution of the Schrödinger equation for an electron in the presence of a confining potential through the plane wave expansion method. Likewise, we establish predictions by writing a tight-binding Hamiltonian for each system.

In the first chapter of results (Chapter 3) we study the kagome lattice subject to a distortion applied to the hopping integrals, which allows us to distinguish two different phases: one topologically trivial and the other topologically non-trivial. Through topological invariants and symmetry markers, we characterize each phase to study the origin of the zero-energy modes that are localized in the corners of a finite-size flake realizing the non-trivial topologically phase. In the next chapter of results, we study the spectrum of a lattice belonging to a non-symmorphic space group and what are the effects of breaking these symmetries on the energy spectrum. Thus, we can describe the physics of the lattice in terms of phase diagrams based on the position of the energy gap. Additionally, we study the lattice in finite-size geometries, such as are nano-ribbons, with a single periodic dimension, or forming molecules, where there is no periodic dimension.

Finally, the last chapter of results collects the research on the fragile topology carried out on a two-dimensional latteice based on the kagome lattice. Again, By studying different geometries and applying topological invariants and symmetry markers, we are able to characterize the fragile topology of the lattice and study the breaking of the bulk-boundary correspondence in different geometries.