Today's society heavily relies on secure communications, which can be guaranteed by Quantum Key Distribution (QKD), the most mature quantum technology. However, achieving long-distance links without relying on trusted nodes is still challenging. An important limitation is the non-ideality of detection systems, where intrinsic dark counts can hinder key extraction. This work proposes using state-of-the-art superconducting nanowire singlephoton detectors (SNSPD) with ultra-low dark count rates (<1 Hz) to reduce the quantum bit error rate (QBER) and achieve a higher secret key rate. Together with a high-rate QKD transmitter and a self-stabilizing receiver, we enabled a key exchange over 55 dB, corresponding to 340 km over an ultra-low-loss optical fiber.