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We theoretically study transport properties in one-dimensional interacting quasiperiodic systems at infinite temperature. We compare and contrast the dynamical transport properties across the many-body localization (MBL) transition in quasiperiodic and random models. Using exact diagonalization we compute the optical conductivity σ(ω) and the return probability R(τ ) and study their average low-frequency and long-time power-law behavior, respectively. We show that the low-energy transport dynamics is markedly distinct in both the thermal and MBL phases in quasiperiodic and random models and find that the diffusive and MBL regimes of the quasiperiodic model are more robust than those in the random system. Using the distribution of the DC conductivity, we quantify the contribution of sample-to-sample and state-to-state fluctuations of σ(ω) across the MBL transition. We find that the activated dynamical scaling ansatz works poorly in the quasiperiodic model but holds in the random model with an estimated activation exponent ψ ≈ 0.9. We argue that near the MBL transition in quasiperiodic systems, critical eigenstates give rise to a subdiffusive crossover regime on finite-size systems.arXiv:1707.02984v2 [cond-mat.dis-nn]

We study the zero-temperature transport properties of one-dimensional normal metalsuperconductor (NS) junctions with topological superconductors across their topological transitions. Working within the Blonder-Tinkham-Klapwijk (BTK) formalism generalized for topological NS junctions, we analytically calculate the differential conductance for tunneling into two models of a topological superconductor: a spinless intrinsic p-wave superconductor and a spin-orbit-coupled s-wave superconductor in a Zeeman field. In both cases we verify that the zero-bias conductance is robustly quantized at 2e 2 /h in the topological regime, while it takes non-universal values in the non-topological phase. The conductance spectra in the topological state develops a peak at zero bias for certain parameter regimes, with the peak width controlled by the strength of spin-orbit coupling and barrier transparency.