python pandas how to copy duplicate value to new Column and keep the first duplicate value empty?

I have an dataframe like this

  sku
FAT-001
FAT-001
FAT-001
FAT-002
FAT-002

I want to create another column depend on the duplicate sku value. The first duplicate value must me empty in dup-sku column. I want to keep only duplicate sku in my dup-sku column. So my expected dataframe will be look like this:

  sku        dup-sku
FAT-001      #empty 
FAT-001      FAT-001
FAT-001      FAT-001
FAT-002      #emty  
FAT-002      FAT-002
FAT-003      

The first value of duplicate in dup-sku column must be empty

>Solution :

Would this work for your example ?

df['dup']=df['sku']
df['dup'].loc[~df['sku'].duplicated(keep='first')]=''