  A rich variety of nematic/smectic orders in Fe-based superconductors is an
important unsolved problem in strongly correlated electron systems. A unified
understanding of these orders has been investigated for the last decade. In
this article, we explain the $B_{1g}$ symmetry nematic transition in
FeSe$_{1-x}$Te$_x$, the $B_{2g}$ symmetry nematicity in AFe$_2$As$_2$ (A=Cs,
Rb), and the smectic state in BaFe$_2$As$_2$ based on the same framework. We
investigate the quantum interference mechanism between spin fluctuations by
developing the density wave equation. The observed rich variety of
nematic/smectic orders is naturally understood in this mechanism. The
nematic/smectic orders depend on the characteristic shape and topology of the
Fermi surface (FS) of each compound. (i) In FeSe$_{1-x}$Te$_x$, each FS is very
small and the dxy-orbital hole pocket is below the Fermi level. In this case,
the small spin fluctuations on three dxz, dyz, and dxy orbitals cooperatively
lead to the $B_{1g}$ nematic order. The experimental Lifshitz transition below
the nematic transition temperature $(T_S)$ is naturally reproduced. (ii) In
BaFe$_2$As$_2$, the dxy-orbital hole pocket emerges around M point, and each FS
is relatively large. The strong spin fluctuations due to the dxy-orbital
nesting give rise to the $B_{1g}$ nematic order and the smectic order, and the
latter transition temperature ($T^*$) exceeds the former one $T_S$. (iii) In
heavily hole-doped AFe$_2$As$_2$, the large dxy-orbital hole pocket and the
four tiny Dirac pockets appear due to the hole-doping. The $B_{2g}$ nematic
bond order emerges on the dxy-orbital hole pocket due to the same interference
mechanism. The present paramagnon interference mechanism provides a unified
explanation of why the variety of nematic/smectic orders in Fe-based
superconductors is so rich, based on the well-established fermiology of
Fe-based superconductors.

Strongly Correlated Electrons;Superconductivity