Table 1.

Nanowire sample properties. Fab method = fabrication method, Cut-out = cut-out using PMMA resist and EBL, HSQ = fabrication by EBL using hydrogen silsesquioxane (HSQ) resist, Ne-FIB = nanowires defined by neon FIB, sc = standard superconducting behaviour, PSCs = phase-slip centres, IQPS = successful fit of $I\left(V\right)$ to a model based on incoherent quantum phase-slips (see the main text). $R_{\square }$ is the sheet resistance above $T_{\mathrm{c}}$. Indicated $T_{\mathrm{c}}$ values are defined as $R\left(T_{\mathrm{c}}\right)=0.5R_{\max }$, where $R_{\max }$ is the maximum resistance and $\Delta T_{\mathrm{c}}=T(R=0.9R_{\max })-T(R=0.1R_{\max })$. ‘Circuit elements’ indicate thin-film components included in series in the circuit; nanowires NbN80/1 and NbN81/2 have series resistance of 148 kΩ and series inductance with a length of 400 μm and a width of 200 nm. Nanowires 100414 and the films for which $R\left(T\right)$ is shown in Figure 1 were deposited on silicon substrates and were not measured below 4.2 K; all other samples were deposited on sapphire substrates.

Sample	Fab Method	Circuit Elements	l (μm)	w (nm)	${\mathit{R}}_{\square }$ (kΩ)	${\mathit{T}}_{\mathbf{c}}$ (K)	$\mathbf{\Delta }{\mathit{T}}_{\mathbf{c}}$ (K)	Behaviour Summary
100414/D2	Cut-out	none	1	250	∼2	≈7.5	≈2	sc
100414/D1	Cut-out	none	1	100	∼2	≈7.5	≈2.5	sc
100414/C2	Cut-out	none	1	75	∼2	≈7.1	≈3	sc
100414/C1	Cut-out	none	1	50	∼2	≈6.7	≈3	sc
100414/B2	Cut-out	none	1	25	∼2	≈7.2	≈4	sc
NbN25/A1	HSQ	none	18	50	≈5	5.5	5	$V_{\mathrm{c}}\sim$300 μV
NbN65/1	Ne-FIB	none	0.22	40	∼9	4	1	sc, PSCs
NbN80/1	HSQ	L,R	10.5	≈60	≈10	5.5	2–3	$V_{\mathrm{c}}\sim$5 mV
NbN81/2	HSQ	L,R	10.5	≈60	≈1	8.5	2	sc, IQPS