Strong competition between $\Theta_{II}$-loop-current order and $d$-wave charge order along the diagonal direction in a two-dimensional hot spot model

摘要: We study the fate of so-called $\Theta_{II}$-loop-current order that breaks both time-reversal and parity symmetries in a two-dimensional hot spot model with antiferromagnetically mediated interactions, using Fermi surfaces relevant to phenomenology cuprate superconductors. start from three-band Emery describing hopping holes CuO$_{2}$ plane includes two parameters $t_{pp}$ $t_{pd}$, local on-site Coulomb interactions $U_{d}$ $U_{p}$ nearest-neighbor $V_{pd}$ couplings between fermions copper [Cu$(3d_{x^{2}-y^{2}})$] oxygen [O$(2p_{x})$ O$(2p_{y})$] orbitals. By focusing on lowest-energy band, we proceed decouple interaction Cu orbital spin channel Hubbard-Stratonovich transformation arrive at interacting part spin-fermion model. also introduce parameter order. In this way, are able construct consistent mean-field theory describes strong competition composite made quadrupole-density-wave $d$-wave pairing fluctuations proposed Efetov \emph{et al.} [Nat. Phys. \textbf{9}, 442 (2013)] is argued be for explaining important aspects physics pseudogap phase displayed underdoped cuprates.