Study of topological phases of two-dimensional electron gas by a coplanar resonator

Two‐dimensional electron gases (2DEG) in magnetic field are known for their rich phase diagram comprising integer and fractional quantum Hall states, Wigner, bubble, stripes and skyrmion crystals. Some of these phases, in particular the 5/2 fractional quantum Hall state, are predicted to have topological properties that may be useful for the quantum processing of information. To study theses phases, we propose a new technique that allows the measurement of the reactive and dissipative response of a 2DEG to an alternating electric or magnetic fields. Such measurements are usually very difficult because of the small electronic density in a two‐dimensional system. Recent experiments done at the IQ, however, have shown that the coupling to a coplanar

resonator is strong enough to reach the required sensitivity. Our study of the properties of these phases of the 2DEG, and in particular the 5/2 state, will involve a close collaboration between theory and experiments.