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julia> using ProgressMeter -julia> T₂₁ = transmission(g[2,1]); T₃₁ = transmission(g[3,1]); ωs = subdiv(0, 4, 200); +julia> T₂₁ = transmission(g[2,1]); T₃₁ = transmission(g[3,1]); ωs = subdiv(0, 8, 200); julia> T₂₁ω = @showprogress [T₂₁(ω) for ω in ωs]; T₃₁ω = @showprogress [T₃₁(ω) for ω in ωs]; -Progress: 100%|██████████████████████████████████████████████████████████████| Time: 0:01:05 -Progress: 100%|██████████████████████████████████████████████████████████████| Time: 0:01:04 +Progress: 100%|██████████████████████████████████████████████████████████████| Time: 0:01:02 +Progress: 100%|██████████████████████████████████████████████████████████████| Time: 0:01:00 julia> f = Figure(); a = Axis(f[1,1], xlabel = "ω/t", ylabel = "T(ω)"); lines!(a, ωs, T₂₁ω, label = L"T_{2,1}"); lines!(a, ωs, T₃₁ω, label = L"T_{3,1}"); axislegend("Transmission", position = :lt); f ``` ```@raw html Total transmission from right contact ``` + So we indeed find that the 90-degree transmission `T₃₁` is indeed larger than the forward transmission `T₂₁` for all energies. The rapid oscillations are due to mesoscopic fluctuations. !!! note "Total transmission vs transmission probability" @@ -100,4 +101,23 @@ So we indeed find that the 90-degree transmission `T₃₁` is indeed larger tha ## Conductance +Local and non-local differential conductance $$G_{ij} = dI_i/dV_j$$ can be computed with `G = conductance(g[i,j])`. Calling `G(ω)` returns the conductance at bias $$eV = \omega$$ in units of $$e^2/h$$. Let's look at the local differential conductance into the right contact in the previous example +```julia +julia> G₁₁ = conductance(g[1,1]) +Conductance{Float64}: Zero-temperature conductance dIᵢ/dVⱼ from contacts i,j, in units of e^2/h + Current contact : 1 + Bias contact : 1 + +julia> Gω = @showprogress [G₁₁(ω) for ω in ωs]; +Progress: 100%|██████████████████████████████████████████████████████████████| Time: 0:01:01 + +julia> f = Figure(); a = Axis(f[1,1], xlabel = "eV/t", ylabel = "G [e²/h]"); lines!(a, ωs, Gω); f +``` +```@raw html +Local conductance from right contact +``` + +!! warning "Sign of non-local conductance" + If you compute a non-local conductance such as `conductance(g[2,1])(ω)` in this example you will note it is negative. This is actually expected. It means that the current flowing **into** the system through the right contact when you **increase** the bias in a different contact is negative, because the current is actually flowing out into the right reservoir. + ## Josephson