Electronic – No output from AOZ3103DI buck converter

It appears that the problem was with the shape of the traces on my PCB. The following PCB design works correctly:

Unfortunately I still do not understand the real reasons behind this well enough to explain it, but I think it has to do with parasitic capacitance and inductance of the traces at high frequencies. It appears that at 1MHz these things really do matter, which also explains why I had so much trouble with the breadboard earlier.

It's going to be a crappy switch mode converter design because you have the FET connected as a source follower: -

If FET has a gate threshold voltage of (say) 4 volts then you cannot get any voltage out of the source higher than 30V from your circuit. Also, with it in this configuration the rise and fall times of the FET are totally limited by the rise and fall times of the op-amp delivering the "square wave". As the op-amp has 2.5 volts per micro second slew rate, it makes for a pretty ineffective switcher.

The rise time for a 30V change is 12 us. Fall time is also 12 us. Given that you would want these times to be less than 5% of a cycle time, this makes the best effective switching frequency about 2 kHz.

Fix the design either by using a P channel device or use a proper driver chip. Also, be aware that the LT1677 has diode clamps across its inputs hence, if you have 4V on one input, the other input is constrained to levels between 3V and 5V - this might answer one of the issues mentioned in the question.