Remember, people no longer live on the surface, but in high altitudes where oxygen should be thinner.  However, everyone seems to be relatively fine.  So maybe, one of the reasons why people have left the surface, is because there's just too much of an abundance of oxygen down at the surface. 

So far the answer seems to be None

Or he had it covered because of his relationship with Luccio.  I'm not sure why he'd be keeping it from her, but he seemed to be keeping it from everyone except Molly.  If Luccio is popping in and out, he might have just had it covered so that she wouldn't spot it if she came in while he was in the basement with the hatch door open. 

Of course, that might intrigue her more than anything, and intriguing the captain of the wardens about what you're up to in your secret sub-basement lair doesn't sound like a good idea.

But with his brother missing and being tortured by one of the most evil beings Harry's ever laid his Sight on, he settles for tracking spells using the copper circle?  And completely neglects to mention LC in text, or even explain why it isn't used? 

That doesn't make any sense.