PhD Thesis defense: Symmetry-breaking and topology in correlated and amorphous matter

PhD Program

Daniel Muñoz Segovia
CFM Auditorium
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PhD Thesis defense: Symmetry-breaking and topology in correlated and amorphous matter

Supervisors: Fernando de Juan (DIPC, Ikerbasque Research Associate) and Adolfo G. Grushin.

In this thesis, we use the tools of symmetries and topology to analyze different phases and phase transitions in three different systems. First, we study the commensurate charge density wave (CDW) state in 1T-TiSe2. Motivated by the conflicting experimental claims regarding the symmetry of the CDW state, we develop a theory wherein electron doping induces two transitions to CDW states breaking the threefold rotational symmetry (C3) of the lattice. In particular, using k.p, tight-binding and mean-field calculations, we find that the C3-symmetric CDW, which is stable at low doping, undergoes a transition first to a nematic CDW and finally to a stripe CDW. Given the uncontrolled electron doping in realistic samples, our theory can reconcile the experimental observations. Then, we examine the superconducting state of monolayer 2H-NbSe2. Based on the unconventional twofold-anisotropic in-plane critical magnetic field and on the scanning tunneling microscopy (STM) evidence for a bosonic mode linked to the superconducting state, we study the superconducting collective modes that emerge in the presence of a subleading unconventional pairing. As long as the interaction in the subleading channel remains attractive, we find a well-defined Leggett mode that renormalizes the electronic spectral function and is compatible with the STM experiments. Finally, we address the problem of efficiently identifying topological phases in noncrystalline materials, where a rich variety of topological phases appear, but there is no efficient and generic topological marker due to the absence symmetry indicators. Here, we introduce the structural spillage, a new topological indicator compatible with first-principles calculations, which measures the band inversions between the noncrystalline system and a reference crystal. We show that the structural spillage correctly reproduces the topological phase diagram of tight-binding models of amorphous 2D Bismuth.