Microscopic origin of period-four stripe charge-density-wave in kagome metal CsV$_3$Sb$_5$

Abstract

The interplay between unconventional density waves and exotic superconductivity has attracted growing interest. Kagome superconductors $A\rm{V}_3\rm{Sb}_5$ ($A = \rm{K}, \rm{Rb}, \rm{Cs}$) offer a platform for studying quantum phase transitions and the resulting symmetry breaking. Among these quantum phases, the $4a_0$ stripe charge-density-wave (CDW) has been widely observed for $A=\rm{Rb}$ and $\rm{Cs}$ by scanning tunneling microscopy (STM) and nuclear magnetic resonance (NMR) measurements. However, the microscopic origin of the $4a_0$ stripe CDW remains elusive, and no theoretical studies addressing this phenomenon have been reported so far. In this paper, we propose a microscopic mechanism for the emergence of the $4a_0$ stripe CDW. We analyze the CDW instability in the 12-site kagome lattice Hubbard model with the $2\times2$ bond order driven by the paramagnon-interference mechanism by focusing on the short-range magnetic fluctuations due to the geometrical frustration of kagome lattice. We reveal that the nesting vector of the reconstructed Fermi surface, formed by the $2\times 2$ bond order, gives rise to a $4a_0$-period CDW. Remarkably, the obtained stripe CDW is composed of both the off-site hopping integral modulations and on-site potentials. The real-space structure of the stripe CDW obtained here is in good qualitative agreement with the experimentally observed stripe pattern.