Minimum current of a sensitive gate SCR
2N5064 is a sensitive-gate SCR. It triggers with a maximum of 200uA at room temperature (Tj = 25°C). 

No minimum is specified in the official data, as you can see. 

Edit: In order to keep it "off" guaranteed, you should keep the gate voltage to less than 100mV, which is guaranteed to not trigger up to Tj = 125°C or so, depending on the manufacturer. In practice that may mean that you'll have to put a resistor from cathode to gate to decrease the sensitivity. 

If you really want something sensitive, play with the gate on a MOSFET such as a 2N7000. pA are more than enough typically.