On the possibility of magnetic flux detection by Andreev quantum dot

The charge of subgap state in Andreev quantum dot (AQD) inserted into the superconducting loop is very sensitive to the magnetic flux threading the loop. We studied the sensitivity as a function of AQD parameters in details in $\Delta\to\infty$ limit. We also accounted for a weak Coulomb interaction in AQD. We discuss a possibility of using this setup as a device detecting week magnetic field.