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 ΔF_orb[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, -m₁h_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 ΔF_orb[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.