Probing the topological band structure of diffusive multiterminal Josephson junction devices with conductance measurements

The energy of an Andreev bound state in a clean normal metal in contact with two superconductors disperses with the difference $Δϕ$ in the superconducting phase between the superconductors in much the same way as the energies of electrons in a one-dimensional crystal disperse with the crystal momentum k of the electrons. A normal metal with n superconductors maps onto a n − 1 dimensional crystal, each dimension corresponding to the phase difference $Δϕi$ between a specific pair of superconductors. The resulting band structure as a function of the phase differences ${Δϕi}$ in such ballistic devices has been proposed to have a topological nature with gapped regions characterized by different Chern numbers separated by regions where the gap in the quasiparticle spectrum closes. A similar complex evolution of the quasiparticle spectrum with ${Δϕi}$ has also been predicted for diffusive normal metals in contact with multiple superconductors. While the underlying topological description is different in diffusive devices, gapped regions of the band diagram associated with different topological indices are also separated by regions where the gap closes. Here, we show that the variation of the density of states at the Fermi energy of such a system can be directly probed by relatively simple conductance measurements, allowing rapid characterization of the energy spectrum.