Investigating Energy Scales of Fractional Quantum Hall States using Scanning Gate Microscopy

We use the voltage biased tip of a scanning force microscope at a temperature of 35,mK to locally induce the fractional quantum Hall state of $\nu =1\mathrm{/}3$ in a split-gate defined constriction. Different tip positions allow us to vary the potential landscape. From temperature dependence of the conductance plateau at $G=1\mathrm{/}3\times e^2\mathrm{/}h$ we determine the activation energy of this local $\nu =1\mathrm{/}3$ state. We find that at a magnetic field of 6,T the activation energy is between 153,$\mu$eV and 194,$\mu$eV independent of the shape of the confining potential, but about 50% lower than for bulk samples.