Can I install a 120V mat on one leg of a double pole breaker?
NO. You cannot install a 120V mat on one leg of a double pole breaker.
There is no neutral leg on a double pole breaker and the polarity between the two sides does not match. This will cause the thermostat to trip and/or it will send too much voltage into a 120V heater.
Please refer to the thermostat Installation Manual for more wiring instructions.