I thought the Persians wore their armour under their robes
Herodotus book 9 Persian wars
"As the barbarians continued charging in divisions, the horse
of Masistius, which was in front of the others, received an arrow in his
flank, the pain of which caused him to rear and throw his rider. Immediately
the Athenians rushed upon Masistius as he lay, caught his horse, and when
he himself made resistance, slew him. At first, however, they were not
able to take his life; for his armour hindered them. He had on a breastplate
formed of golden scales, with a scarlet tunic covering it. Thus the blows,
all falling upon his breastplate, took no effect, till one of the soldiers,
perceiving the reason, drove his weapon into his eye and so slew him."
So you would have to find historical justification for putting it over the robes.