<i>d</i>- and <i>p</i>-wave Quantum Liquid Crystal Orders in Cuprate Superconductors, <i>κ</i>-(BEDT-TTF)₂X, and Coupled Chain Hubbard Models: Functional-renormalization-group Analysis

Unconventional symmetry breaking without spin order,such as the rotational (=nematic or smectic) orders well spontaneous loop-current orders, have been recently reported in cuprate superconductors and their related materials.They are theoretically represented by non-$A_{1g}$ self-energy, which we call form factor $f_{k,q}$.In this paper, analyze typical Hubbard models applying renormalization-group (RG) method, find that various unconventional ordering emerges due to quantum interference among fluctuations. Due mechanism,nematic ($q=0$) smectic ($q \ne 0$)bond with $d$-wave appear $f_{k,q}\propto \cos k_x - k_y$ both cuprates $\kappa$-(BEDT-TTF)$_2$X. The derived bond naturally explain pseudogap behaviors these compounds. also induces current odd-parity factor. For example, emergence of charge $p$-wave geometrically frustrated models. Thus, rich phase transitions $d$- factors driven paramagnon many low-dimensional