UC Santa Barbara

The discovery of $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) compounds with a kagome net structure has unveiled their intriguing properties including superconductivity and unique topological characteristics in their electronic structure. These materials also exhibit charge density wave (CDW) ordering, which manifests as a distortion known as a breathing mode in the kagome layers. It has been proposed that this CDW ordering arises from nesting effects between saddle points on the Fermi surface.

To contribute to the evolving understanding of this fascinating class of materials, this thesis presents a comprehensive exploration of diverse kagome materials. The focus lies on conducting calculations that delve into the Fermi surface nesting and Lindhard susceptibility of CsV$_3$Sb$_5$, a prominent member of the $A$V$_3$Sb$_5$ family. Furthermore, the thesis thoroughly investigates the coupling between CDW and superconducting (SC) states through experimental and computational approaches, particularly by introducing hole doping into the systems. The resulting phase diagrams for $A$V$_3$Sb$_5$ unveil the profound impact of slight carrier doping on the SC and CDW orders in these materials. In addition, this thesis presents a comprehensive study of other kagome-based materials, such as the members of the \textit{A}\textit{M}$_3$\textit{X}$_4$ family, including a focused analysis of YbV$_3$Sb$_4$ and EuV$_3$Sb$_4$. The research also delves into the properties of the $R$V$_6$Sn$_6$ compounds, characterized by a vanadium kagome-based structure, and investigates the intriguing characteristics of the $RM_3Pn_3$ family featuring a triangular lattice, which shares similar signatures of instabilities.

Throughout the thesis, a spotlight is cast on various aspects, including Fermi surface nesting-driven instabilities, CDW phenomena, and magnetic behaviors within these materials. Meticulous experimental investigations and advanced theoretical analyses offer valuable insights into the complex interplay between electronic structures, CDW ordering, and superconductivity. The findings challenge previous assumptions and classifications, emphasizing the critical role of electron-phonon interactions and complex electronic correlations in shaping the observed behaviors of these materials. Overall, this dissertation contributes to a deeper understanding of the kagome materials and underscores the potential of these materials for realizing exotic electronic states and offers new avenues for exploring their unique physical phenomena.