Database: legislator
Question: Among the Independent senators that started their term in 2011 and onwards, what are the official full names of the senators that caucused with the Democrat?
SQL: SELECT T1.official_full_name FROM current AS T1 INNER JOIN `current-terms` AS T2 ON T1.bioguide_id = T2.bioguide WHERE T2.party = 'Independent' AND strftime('%Y', T2.start) >= '2011' AND T2.type = 'sen' AND T2.caucus = 'Democrat'