Microwave activation studies of fractional quantum Hall effect

Fractional quantum Hall states are characterised by gap energies for quasiparticle-quasihole excitations and these gaps are typically measured from the temperature (T) dependence of the FQHE R_xx minima in the thermally activated regime. Here, we examine the possibility of determining these gaps by measuring the microwave power (P) variation of the R_xx minima with the specimen at base temperature, followed by a calibrated conversion of P to T. We note, that from the experimental point of view, there are some definite experimental advantages to such microwave based measurements over the conventional temperature dependent measurements: i) The applied microwave power can be controlled with great precision at the microwave source and, therefore, very small incremental changes in temperature appear possible at the sample with small power changes at the source, ii) The source microwave power (and therefore, in principle, the temperature) can be varied smoothly at the desired rate. iii) Since microwave induced heating occurs very locally at the specimen, rapid heating and cooling with small time constants can be realized very easily. In sum, it is a lot easier to measure, change, and control the microwave power than it is to change, actively control, and measure the temperature inside a dilution refrigerator. Thus, we examine the activation characteristics for a number of readily observable electronic FQHE states in GaAa/AlGaAs heterostructures characterized by n = 2 x 10¹¹cm^-2 and μ = 10⁷cm²/Vs and report associated results.