Can cops search my home with 14yr old permisson home alone?:
No. Cops need the permission of the owner of the house to search it without a warrant or reasonable suspicion that someone's life was in danger.

Edit: I wanted to add that it is disturbing how many people are saying your brother could let the police in. It is completely illegal. How could any reasonable person think that a 14 year-old, clearly not an adult, could have authority to consent?