Apply for a National Science Foundation Graduate Research Fellowship. These are open to citizens and permanent residents and are among the leading sources of graduate science scholarships in the U.S. They provide a stipend of $30,000 and $10,500 for tuition and fees per year for three years, as well as $1,000 for international travel. To apply, provide a personal statement, a description of previous research, a research plan, three reference letters, transcripts and scores from the Graduate Record Examination.
Apply to private donors such as the Hertz Foundation and Bell Labs. Many corporations in the fields of engineering and technology offer PhD scholarships in physics to promote research and development that in turn helps their bottom line. For instance, the Hertz Foundation Offers PhD fellowships in physical sciences to U.S. citizens and permanent residents with excellent academic credentials and technical abilities.
Expand your horizons and consider going abroad to pursue a PhD. Many foreign universities offer PhD scholarships in physics that are open to all nationalities. For instance, the University of Tokyo's scholarship program for international students is called the "PhD Program at Frontier Physics Research Centers" program. The University of St. Andrews, UK, offers PhD scholarships to foreign students through several sources, including the Nicol Trust.