Topologically protected subdiffusive transport in two-dimensional fermionic wires

The conductance at the band edges of one-dimensional fermionic wires, with N sites, has been shown to have subdiffusive (1/N²) behavior. We investigate this issue in two-dimensional fermionic wires described by a hopping model on an Nₓ×Ny rectangular lattice comprised of vertical chains with a Hermitian intrachain and interchain hopping matrices given by H₀ and H₁, respectively. We study particle transport using the nonequilibrium Green's function formalism, and we show that the asymptotic behavior of the conductance, T(ω), at the Fermi level ω, is controlled by the spectrum of a dimensionless matrix A(ω)=(-ω+H₀)H₁^-1. This gives three simple conditions on the spectrum of A(ω) for observing ballistic, subdiffusive, and exponentially decaying T(ω) with respect to Nₓ. We show that certain eigenvalues of A(ω) give rise to subdiffusive contributions in the conductance, and correspond to the band edges of the isolated wire. We demonstrate that the condition for observing the subdiffusive behavior can be satisfied if A(ω) has nontrivial topology. In that case, a transition from ballistic behavior to subdiffusive behavior of the conductance is observed as the hopping parameters are tuned within the topological regime. We argue that at the transition point, different behaviors of the conductance can arise as the trivial bulk bands of A(ω) also contribute subdiffusively. We illustrate our findings in a simple model by numerically computing the variation of the conductance with Nₓ. Our numerical results indicate a different subdiffusive behavior (1/Nₓ³) of the conductance at the transition point. We find the numerical results to be in good agreement with the theoretical predictions.