Prediction of $d$-wave bond-order and pseudogap in organic superconductor $\kappa$-(BEDT-TTF)$_2$X: Similarities to cuprate superconductors

Rich pseudogap phenomena due to unconventional orders, such as the inter-site order parameter called the bond-order (BO), attract increasing attention in condensed matter physics. Here, we investigate the occurrence of the unconventional orders in organic superconductor $\kappa$-(BEDT-TTF)$_2$X in an unbiased way, based on the combination of the functional renormalization group (fRG) method and the density-wave equation method. We revealed the strong development of the $d$-wave BO instability at wavelength $q=Q_{\rm B}=(\delta,\delta)$ ($\delta=0.38\pi$). Its origin is novel quantum interference among incommensurate paramagnons with $Q_{\rm S}^{\pm}\approx(\pi \pm \delta/2,\pi \pm \delta/2)$. The present prediction leads to the emergence of the Fermi arc structure and pseudogap in $\kappa$-(BEDT-TTF)$_2$X. The d-wave BO fluctuations at $q=Q_{\rm B}$ reinforce the $d$-wave superconducting state.