High-order coupling between CDW and PDW in transition-metal dichalcogenide

Intertwined states of quantum matter are at the focus of modern physics. Among them, charge density wave (CDW) and Cooper-pair density wave (PDW), that originate from modulated chemical potential and pairing potential in real space respectively, are two pearls on the crown. Recently, the PDW state was observed in NbSe₂, where a global δφ≅±2π/3 phase difference between the PDW and CDW states was disclosed, leaving the interaction between them to be unsolved [1]. To clarify this issue, we carefully measured PDW and CDW states in defect-free regions by atomic-resolution scanned Josephson-tunneling microscopy. We detected a 2π/3 phase sum of the three components of the CDW order simultaneously accompanied with a 2π/3 phase difference between each CDW and PDW component. The linear coupling in the Ginzburg-Landau-Wilson model among CDW, PDW and s-wave superconducting states seems unable to explain these data. Hence, we explore a high order coupling term with the form of Δ_S^*Δ_PⁱΔ_C^-jΔ_C^-k(i, j, k = Q₁, Q₂, Q₃ and i≠j≠k), in pursuit of the phase difference issue. This is a new route to investigating the interactions between novel ordered states in transition-metal dichalcogenides as well as other quantum matter.



[1] X.L. Liu et al., Science 372, 1447–1452 (2021).