What is the suggested circuit?
A switching buck regulator like the LT3741: -

It's a bit close to the input supply limit you specified so try looking for a device with an input range from 13 volts to 15 volts using the Analog Device's web-page: -

The LT3741 was found using 13 to 15 volts on the input selection and 11 volts and 20 amps on the output selection boxes so, it might work. But, as with all these things, you should spend maybe a couple of hours investigating. I spent 5 minutes and there may be better devices.
Currently I have an RJP30E2DPK IGBT and IRL3713 and IRFZ44 N-MOSFETs.
Can I use them in the circuit?
Not the IGBT and probably not the IRFZ44 but, the IRL3713 might be in with a shot.