Masters Thesis Defense by Frederik Alexander Stege Philipsen

Title: Consequences of time-reversal symmetry breaking states of the kagome superconductors

Abstract: The interplay between lattice geometry and complex many-body interactions creates an ideal setting for the emergence of exotic collective phenomena. In particular, the kagome lattice, with its inherently intricate geometry, offers a unique platform for realizing novel and unconventional states of matter. Accordingly, the synthesis and subsequent discovery of superconductivity in the Kagome metals AV_3Sb_5 (A = K, Cs, Rb) have attracted significant interest from the scientific community — especially following recent indications of time-reversal symmetry breaking within the superconducting stat, potentially pointing toward a chiral $d$-wave order parameter.

Motivated by these findings, this thesis explores the consequences of superconductivity being governed by such a chiral state. To this end, we first examine the influence of the Kagome lattice structure on the electronic states and on the symmetries allowed for the superconducting order. This is followed by the development of a self-consistent method for calculating the superconducting order parameter in both momentum and real space on the Kagome lattice. 

Using this framework, we identify the conditions under which a chiral d-wave state becomes energetically favorable. We then study its real-space response to impurity scattering, as well as the formation of vortices under an externally applied magnetic field. Through this analysis, we uncover direct observable consequences of the superconducting order exhibiting a chiral d-wave symmetry. 

With this work, we aim to contribute to the ongoing efforts to characterize the superconducting state realized in the AV3Sb5 Kagome metals.