Capacitive measurements of chemical potential in the fractional quantum Hall regime

We present the design and implementation of a GaAs device for precise measurement of chemical potential in the fractional quantum Hall regime. Precise simultaneous measurements of chemical potential and electron temperature may be combined to study changes in entropy associated with specific fractional quantum Hall states. In particular, the putative non-abelian state at filling factor ν=5/2 is conjectured to possess excess entropy associated with its topological degrees of freedom. Excess entropy may in principle be detected via examination of the temperature dependence of electrochemical potential. Small changes in filling factor away from ν=5/2 will change the density of quasiparticles in the ground state, modifying ground state degeneracy. Current methods of measuring the quantum capacitance of the two-dimensional electron gas (2DEG) formed in an AlGaAs/GaAs heterostructure lack the resolution necessary to quantitatively assess small changes in entropy expected in the fractional quantum Hall regime. Our device addresses this issue by leveraging a heterostructure design that has proven useful for the determination of braiding statistics using a Fabry-Perot interferometer. Using multiple quantum wells, we can increase geometric capacitance without increasing disorder that is known to suppress the formation of fragile fractional quantum Hall states. Preliminary device measurements will be presented.