[{"product_name":"A","product_type":[{"name":"Metal"},{"name":"Wood"},{"name":"Carbon"}],},{"product_name":"B","product_type":[{"name":"Metal"},{"name":"Iron"}],},{"product_name":"C","product_type":[{"name":"Metal"},{"name":"Wood"}],},{"product_name":"D","product_type":[{"name":"Wood"}],}]

db.collection.find({"product_type.name":{$in:["Metal"]}})