We analyze the interplay of disorder and long-range hopping in a paradigmatic one-dimensional model of quantum transport. While typically the current is expected to decrease as the disorder strength increases due to localization effects, in systems with infinite range hopping, it was shown in Chavez et al. [Phys. Rev. Lett. 126, 153201 (2021)] that the current can increase with disorder in the disorder-enhanced-transport (DET) regime. Here, by analyzing models with variable hopping range decaying as $1/r^{\alpha }$ with the distance $r$ among the sites, we show that the DET regime is a general feature of long-range hopping systems and it occurs, not only in the strong long-range limit $\alpha <1$ but even for weak long range $1\le \alpha \le 3$. Specifically, we show that, after an initial decrease, the current grows with the disorder strength until it reaches a local maximum. Both disorder thresholds at which the DET regime starts and ends are determined. Our results open the path to understand the effect of disorder on transport in many realistic systems where long-range hopping is present.

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• Long-range interactions
• Quantum transport
• Nanowires
• Lattice models in condensed matter
• Quantum master equation