Experimental Proposal to Detect Topological Ground State Degeneracy

Understand

One of the most profound features of topologically ordered states of matter, such as the fractional quantum Hall (FQH) states, is that they possess topology-dependent ground state degeneracies that are robust to all local perturbations.

• Here we propose to directly detect these topological degeneracies in an experimentally accessible setup.
• The detection scheme uses electrical conductance measurements in a double layer FQH system with appropriately patterned top and bottom gates.
• We discuss two experimental platforms; in the first, the detection of topologically degenerate states coincides with the detection of $Z_N$ parafermion zero modes.