  Kagome metals AV3Sb5 (A = K, Cs, Rb) provide a rich platform for intertwined
orders such as the charge density wave (CDW) and a chiral order with
time-reversal symmetry breaking (TRSB). While early reports of large optical
polarization rotations have been interpreted as the magneto-optic Kerr effect
(MOKE) and as evidence for TRSB, recent dedicated optical rotation and MOKE
experiments have clarified that this large optical rotation originates instead
from an unconventional specular rotation. Yet a critical discrepancy remains
regarding the possible existence of a true spontaneous MOKE signal: in
experiments performed after training with modest magnetic fields of up to 0.3
Tesla, no MOKE signal was detected above the noise floor of 30 nano-radians,
while micro-radian-level signals were found in an experiment using higher
training fields. This raises an intriguing possibility of different zero-field
ground states with opposite time-reversal symmetry properties, because of
different magnetic histories. To unambiguously determine whether a
training-field-dependent spontaneous MOKE signal exists in CsV3Sb5, we conduct
comprehensive MOKE measurements with two Sagnac interferometer setups capable
of both low and high training fields of up to 9 Tesla, and perform careful
analyses of contributions of signals from various optical components. We
conclude that there is no observable spontaneous MOKE signal, hence no optical
evidence for TRSB, regardless of the magnitude of training fields and the speed
of temperature ramping.
