Origin of diverse nematic orders in Fe-based superconductors: 45$^\circ$ rotated nematicity in AFe$_2$As$_2$ (A=Cs, Rb)

The origin of diverse nematicity and their order parameters in Fe-based superconductors have been attracting increasing attention. Recently, a new type of nematic order has been discovered in heavily hole-doped ($n_d=5.5$) compound AFe$_2$As$_2$ (A=Cs, Rb). The discovered nematicity has $B_{2g}$ (=$d_{xy}$) symmetry, rotated by $45^\circ$ from the $B_{1g}$ (=$d_{x^2-y^2}$) nematicity in usual compounds with $n_d\approx6$. We predict that the "nematic bond order", which is the symmetry-breaking of the correlated hopping, is responsible for the $B_{2g}$ nematic order in AFe$_2$As$_2$. The Dirac pockets in AFe$_2$As$_2$ is essential to stabilize the $B_{2g}$ bond order. Both $B_{1g}$ and $B_{2g}$ nematicity in A$_{1-x}$Ba$_x$Fe$_2$As$_2$ are naturally induced by the Aslamazov-Larkin many-body process, which describes the spin-fluctuation-driven charge instability. The present study gives a great hint to control the nature of charge nematicity by modifying the orbital character and the topology of the Fermi surface.