Quantum Tunneling of the Order Parameter in Superconducting Nanowires

Quantum tunneling of the superconducting order parameter gives rise to the phase slippage process which controls the resistance of ultra-thin superconducting wires at sufficiently low temperatures. If the quantum phase slip rate is high, superconductivity is completely destroyed by quantum fluctuations and the wire resistance never decreases below its normal state value. We present a detailed microscopic theory of quantum phase slips in homogeneous superconducting nanowires. Focusing our attention on relatively short wires we evaluate the quantum tunneling rate for phase slips, both the quasiclassical exponent and the pre-exponential factor. In very thin and dirty metallic wires the effect is shown to be clearly observable even at $T \to 0$. Our results are fully consistent with recent experimental findings [A. Bezryadin, C.N. Lau, and M. Tinkham, Nature {\bf 404}, 971 (2000)] which provide direct evidence for the effect of quantum phase slips.