Operational Amplifier Single Supply Negative Output
If it is only necessary to drive the MOSFET for a brief moment, you can use a concept like this:







simulate this circuit &ndash; Schematic created using CircuitLab

While the output of the comparator is high, the capacitor gets charged. Then when the output of the comparator switches LOW, the capacitor is still charged and the right plate will be pushed below 0V. The capacitor cannot discharge through the diode so it will stay charged for a while with only leakage current flowing.

Usability depends on exact specification of your components, but you can play with capacity, an extra pull up resistor and the cathode voltage on the diode.