We find that, in the presence of weak incoherent effects from surrounding environments, the low-temperature conductance of nearest-neighbor tight-binding fermionic chains exhibits a counter-intuitive monotonic growth with system length when Fermi energy is near the band edges, indicating a superballistic scaling. This fascinating environment-assisted superballistic scaling of conductance occurs over a finite but extended regime of system lengths. This regime can be systematically expanded by decreasing the coupling to the surrounding environments and by reducing temperature. This behavior is robust against weak disorder and slight shifts from band edge, although the extent of the superballistic scaling regime is affected by them. We give precise predictions of how the superballistic scaling regime depends on coupling to surrounding environments, disorder strength, shifts from band edge, and temperature. There is no corresponding analog of this behavior in isolated systems. The superballistic scaling stems from an intricate interplay of incoherent effects from surrounding environments and exceptional points of the system's transfer matrix that occur at every band edge.

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• Open quantum systems
• Quantum transport
• Landauer formula
• Transfer matrix method