A hearing memorandum is required at the Portland, Maine ODAR. Written by the claimant's representative, the hearing memorandum sets forth the background facts of the case, a description of the medical evidence, and (most importantly) a "theory of the case," with an analysis of the claim at each step of the sequential evaluation process.
The memorandum, which I write in the form of a letter to the judge, is typically filed 7 to 10 days ahead of the hearing. That way, it is in the record when the judge looks at the file to prepare for the hearing.
The hearing memorandum does more than educate the judge in advance of the hearing. Since the memorandum stays in the record, the judge can refer back to it after the hearing, when the representative's great opening statement has been long forgotten.
A hearing memorandum helps the lawyer as well. Writing the memorandum will give you an improved command of the evidence, and will help you to focus on the hearing issues. You will be better prepared for the hearing, and better able to illuminate for the judge the path to granting benefits.
The word is spreading. Judges from New Hampshire and Massachusetts conduct hearings in Maine from time to time, and have found the hearing memorandums to be helpful. Those judges are starting to request hearing memorandums for their own cases.
{update: Here is a sample hearing brief}