Dissipative tunnelling in 2DEG: effect of magnetic field, impurity and temperature

I have studied the transport process in the two dimensional electron gas (2DEG) in the presence of a magnetic field and a dissipative environment at finite temperature T. By means of the imaginary time series functional integral method I calculate the decay rates at finite temperature in the presence of dissipation, impurity and magnetic field. I have studied decay rates for a wide range of temperatures - from the thermally activated region to the very low temperature region where the system decays by quantum tunnelling. I have shown that tunnelling is strongly affected by the magnetic field. Both dissipation and impurity subdue the effect of magnetic field and enhance the tunnelling rate. I have demonstrated analytical results of quantum tunnelling for different experimentally accessible limits. My results are relevant in the context of quantum tunnelling in SQUIDs or current biased Josephson junctions.