Drastic magnetic-field-induced chiral current order and emergent current-bond-field interplay in kagome metals

In kagome metals, the chiral current order parameter η with time-reversal-symmetry-breaking is the source of various exotic electronic states, while the method of controlling the current order and its interplay with the star-of-David bond order ϕ are still unsolved. Here, we reveal that tiny uniform orbital magnetization M orb [ η , ϕ ] is induced by the chiral current order, and its magnitude is prominently enlarged under the presence of the bond order. Importantly, we derive the magnetic-field ( h z )-induced Ginzburg–Landau (GL) free energy expression Δ F [ h z , η , ϕ ] ∝ − h z M orb [ η , ϕ ] , which enables us to elucidate the field-induced current-bond phase transitions in kagome metals. The emergent current-bond- h z trilinear coupling term in the free energy, − m 1 h z η · ϕ , naturally explains the characteristic magnetic-field sensitive electronic states in kagome metals, such as the field-induced current order and the strong interplay between the bond and current orders. The GL coefficients of Δ F [ h z , η , ϕ ] derived from the realistic multiorbital model are appropriate to explain various experiments. Furthermore, we discuss the field-induced loop current orders in the square lattice models that have been studied in cuprate superconductors.