On Youtube, Ralph S Bacon explored some circuits with MOSFets that would have a micro processor turn off it's own power and possibly also it's other peripherals under program control.
This is a small project demonstrating the use of a IRF7317.
Circuit:
For the test I replaced the battery with a 5V power supply, and for ESP part I used a development board that included a 3.3V power regulator. This doesn't change the working of the circuit, as 3.3V is enough to turn the MOSfets in the IRF7317 on and off. The IRF7317 is an SMD component, so that was soldered to a little breakout board for SO-8 components.
As I used an ESP-01, I used RX as output, as GPIO 0 and 2 need to be High when booting, which may not be the case when used in this circuit.
I made a small sketch that sets the RX pin ( GPIO 3) High, flashes a led on and off 5 times and then sets the RX pin low. See Zelfdover.ino Output of the sketch looks like this:
It looks like this (click on RAW when shown the unattractive GITHUB message) when running the sketch. Max current was about 70 mA while the LED was flashing. After extinguishing itself, I was not able to measure any current, although I used a medium ok multimeter in the uA range. The IRF7317 maintained room temperature, as expected with this minimal power usage.