  We study the interplay of attractive electron interactions and topological
states in strained kagome lattices with spin-orbit coupling via a Hubbard
Hamiltonian in the mean-field approximation. In the unstrained lattice, there
is a topological phase transition from a quantum spin Hall state to a charge
density wave (CDW) with increasing interaction strength. Upon applying a
uniform uniaxial strain to the lattice, we find a new phase with coexisting
CDWs and topological states. For increasing interaction strength or strain, the
system is driven into a pure CDW, signaling topological phase transitions. The
directionality (nematicity) of the CDW is controlled by the direction of the
applied strain. When $s$ wave electronic pairing is allowed, the system
develops a superconducting order beyond a threshold attraction, which is
totally suppressed by the onset of a CDW with increasing interaction. Most
interestingly, moderate strain allows the coexistence of superconductivity and
CDWs for a range of interaction values. This illustrates how electronic
interactions and single-particle topological structures compete to create
unusual correlated phases in kagome systems.
