Any statewide elected official can be impeached. The process, similar to the process to impeach a president, requires that the Assembly adopt a resolution to impeach and that the Senate hold the trial.
We (the common citizens) can only recall such officers, since our liberal legislature won't impeach or convict one of their own. Obviously, recall and impeachment have different standards/requirements.
CALIFORNIA CODES
GOVERNMENT CODE
SECTION 3020-3040
3020. State officers elected on a statewide basis, members of the State Board of Equalization, and judges of state courts are subject to impeachment for misconduct in office.