Recent experiments on vanadium-based nonmagnetic kagom\'e metals
AV3βSb5β (A= K, Rb, Cs) revealed evidence for possible spontaneous
time-reversal symmetry (TRS) breaking in the charge density wave (CDW) ordered
state. The long-sought-after quantum order of loop currents has been suggested
as a candidate for the TRS breaking state. However, a microscopic model for the
emergence of the loop-current CDW due to electronic correlations is still
lacking. Here, we calculate the susceptibility of the real and imaginary bond
orders on the kagom\'e lattice near van Hove filling, and reveal the importance
of next-nearest-neighbor Coulomb repulsion V2β in triggering the instability
toward imaginary bond ordered CDW. The concrete effective single-orbital
t-V1β-V2β model on the kagom\'e lattice is then studied, where t and
V1β are the hopping and Coulomb repulsion on the nearest-neighbor bonds. We
obtain the mean-field ground states, analyze their properties, and determine
the phase diagram in the plane spanned by V1β and V2β at van Hove filling.
The region dominated by V1β is occupied by a 2a0βΓ2a0β real CDW
insulator with the inverse of Star-of-David (ISD) bond configuration.
Increasing V2β indeed drives a first-order transition from the ISD to
stabilized loop-current insulators that exhibit four possible current patterns
of different topological properties, leading to orbital Chern insulators. We
then extend these results away from van Hove filling and show that the
loop-current states survive in the lightly doped orbital Chern insulators, and
give rise to emergent Chern Fermi pockets carrying large Berry curvature and
orbit magnetic moment. Our findings provide a concrete model realization of the
loop-current Chern metal at the mean-field level for the TRS breaking normal
state of the kagom\'e superconductors.Comment: 11 pages, 6 figure