In a two mover, a self block is a move that restricts the black King's movement. The blocking of a square in the bK's field may allow white to relinquish guard on that square or interfere with guard on the square. We begin with arguably the most famous mate in two problem of all time.
Here it is. Quite possibly the most perfect two move problem ever composed. Not only does it accomplish the task record of eight overall self-blocks, but it is a mutate with two changes and a wonderful step back key.
1...d6,S4 else 2.e6
1...R else 2.Be4
Here the composer achieves 8 self-blocks with 6 of them coming on a single square d4. The give and take key sets things into motion.
Here is a classic and one of my all time favorite problems. The theme is not really about self-blocks, in fact there are only three self-blocks in the solution. Two of them are absolutely spectacular and the key is wonderful. Notice that the bQ pins wSb7 and its release would mate with Sd6. The key neutralizes this, but provides two spectacular unpinning, white interference, self-blocking variations after 1...Qd4 and 1...Qe5.
The idea is that the wSb7 must pick which of the wR's lines to close based on which square the bQ is blocking. Oh and the key rook must stop on d7 instead of d8 because 1...Qf2 must leave the wSb7 somewhere to go! Some how, Ellerman makes an open board for white crowded.
Another classic! The date is early, but the problem is perfect. The wK closes 4 different lines based on self-blocks. Chalk this one up to a problem I wish I would have composed. A nice waiting key and excellent accuracy in nine variations.
A knight can only guard two squares in the kings field, and so only two self-blocks by a bS are possible. Double this and you have what is called the Horseblock theme. Here is a fine example with a half-pin and changes.
1...Sd else 2.Rxe6
Here is another block buster (pun intended). Here we have four self-blocks changed from set to actual play. On top of this two of those are transferred giving the Rukhlis theme.
Here is a nice more-mover with a self block theme. White would like to play 1.exd3 followed by d4 and be done with it. The problem is Black has the strong defense 1...a1=Q. So White must first lure the newly promoted bQ out of the way. Watch the magic unfold with switchbacks galore:
2.Sh7+ ...Ke5 (switchbacks)
6.Sb5+ ...Ke5 (switchbacks)
Here is my own problem where I attain four self-blocks on the corners. There is relevant set play and a close try and changes throughout. Enjoy.