To impeach means to formally accuse an official of a crime. Who has the "sole power of impeachment" in the Constitution?

No one

Explanation:

No one person can impeach a sitting president. The Speaker of the House, however, can call for an impeachment investigation. After that a committee is formed to investigate the crimes of the President. But the "impeachment" doesn't begin until the House of Representatives votes to impeach a president. A simple majority is all it takes to have a President impeached.

House of Representatives "shall have the sole Power of Impeachment" and that "the Senate shall have the sole Power to try all Impeachments"