Electron teleportation and fractional conductance in Multimode Majorana Systems

Majorana Zero Modes (MZMs) are non-Abelian excitations appearing in pairs in topological superconductors and provide a platform for quantum computation. In previous seminal work, non-local electron teleportation via 2-MZM system is established, causing a maximal conductance of e 2/h. To investigate further on how conductance changes with different parameters and whether fractional conductance emerges in multimode networks, we analyze both 2 and 4 MZMs on a superconducting island, using Landauer-Buttiker theory and nonequilibrium Green's functions. Crucially, two principle quantization signatures for 4-MZM system are predicted: (i) a half-quantized conductance e^2/(2h) when each output lead is under symmetric lead-Majorana coupling Γ_j = Γ and eV_Leads = δ/2 (where δ is the energy difference between a TLS, this condition includes the Zero-bias Peak eV_Leads = δ/2=0). (ii) double quantized conductance 2e^2/h when only two leads are active (e.g. Γ_1,2 = Γ, Γ_3,4 = 0) and eV_Lead = δ/2. More generally, under same condition as (ii), we show that systems with 2n MZMs exhibit quantized conductance scaling as 2^(n−1)e^2/h. The half-quantized signature serves as a clear experimental benchmark for confirming 4-MZM existence in topological qubits, while the double-quantized conductance measures the multiplicity of teleportation paths. Our findings confirm that fractional conductance is a hallmark of multimode teleportation, providing a method to verify engineered MZM networks.