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As far I've understood, channel formation takes place because of the induced negative charge on the semiconductor side of the gate capacitance. So shouldn't the charge concentration increase linearly with the gate voltage from the very beginning. If that is so the current should increase linearly as gate potential is increased from zero. Instead why does the current increase abruptly from zero when a threshold voltage is hit. Why is the sudden increase in carrier concentration?

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Instead why does the current increase abruptly from zero when a threshold voltage is hit?

It doesn't. It is (very near) zero below threshold, but it only starts increasing gradually from zero as it goes above threshold. Here's a "typical" characteristic for a low-voltage MOSFET:

enter image description here

Why is the sudden increase in carrier concentration?

It's not the carrier concentration that changes at threshold. It's the availability of the channel.

Below threshold, the channel is "pinched off" so that no current can flow, even though there are charge carriers available.

Imagine you use your fingers to pinch a drinking straw closed. If you slowly release the pressure of your fingers, you see no current flow until you get to some "threshold" pressure and water starts flowing. It's not because the amount of available water changed, it's because you allowed a path to open so that the water that was there all along could flow. The channel of the MOSFET behaves similar to that.

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