{'fraction_non_alphanumeric': 0.033488171113751755, 'fraction_numerical': 0.015555795614129848, 'mean_word_length': 4.504161712247325, 'pattern_counts': {'":': 0, '<': 3, '<?xml version=': 0, '>': 4, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Superconducting junction of a single-crystalline Au nanowire for an ideal Josephson device

We report on the fabrication and measurements of a superconducting junction of a single-crystalline Au nanowire, connected to Al electrodes. Current-Voltage characteristic curve shows clear supercurrent branch below the superconducting transition temperature of Al and quantized voltage plateaus on application of microwave radiation, as expected from Josephson relations. Highly transparent (0.95) contacts very close to an ideal limit of 1 are formed at the interface between the normal metal (Au) and the superconductor (Al). The very high transparency is ascribed to the single crystallinity of a Au nanowire and the formation of an oxide-free contact between Au and Al. The sub-gap structures of the differential conductance are well explained by coherent multiple Andreev reflections (MAR), the hallmark of mesoscopic Josephson junctions. These observations demonstrate that single crystalline Au nanowires can be employed to develop novel quantum devices utilizing coherent electrical transport.

mesoscopic regime, the measured physical effects exhibit ubiquitous influence of phasecoherent transport of Cooper pairs penetrating the normal system.
The theory of proximity effect was initially investigated by de Gennes. 1, 2 Various theories have since been developed to incorporate the phase-coherent transport of Cooper pairs through SNS junctions, both in the diffusive limit 3-5 and ballistic limit. [6][7][8][9] Underlying these theories is the picture of multiple Andreev reflections (MARs). An electron in a normal system slightly above the Fermi level is reflected back as a hole at one super conductornormal system (NS) interface leaving a Cooper in the superconductor. The hole is reflected again as an electron at the other NS interface, and these processes are repeated coherently, resulting in a resonance-like behaviour. The MAR is the hallmark of phase-coherent transport of Cooper pairs in mesoscopic Josephson junctions.
Even though in his original theory of the proximity effect 1 de Gennes had in mind "metal" as the normal system, MARs and coherent Cooper pair transport have been observed mostly in SNS junctions with semiconductor or semimetal as a normal system. The observation of MARs in an all-metallic system is presumably hindered by the high critical current of the junctions, which results in severe Joule heating, and also by the relatively low transparency of the NS interface. 18 Herein, we report on the very unique features of mesoscopic Josephson junctions comprised of single crystalline Au NWs connected to superconducting Al electrodes, an ideal system that is much closer in spirit to the model considered by de Gennes. The Au NWs, grown by the vapor transport method, 19 are singlecrystalline with no defects and do not form a native oxide layer on their surface, thereby enabling us to form oxide-free and highly transparent contact between Al and Au of the NS interface. We observed supercurrent flow through the Au NW and multiple peaks of dynamic conductance caused by resonant MARs. Single-crystalline Au NWs hold promise as a facile route to realize various quantum devices with -junctions 20 and Andreev qubits. 21 Figure 1(a) displays a scanning electron microscopy (SEM) image of Au NWs and a high-resolution transmission-electron microscopy (TEM) image in the inset. Details of the NW growth and device fabrication have been reported elsewhere. 19,22 A representative SEM image and a schematic view of the device are shown in Fig. 1(b) and the inset, respectively.
The width (w) of the Au NW and the distance (L) between two superconducting electrodes are found to be w = 80 -125 nm and L = 280 -740 nm, respectively. The normal-state resistance (R n ) of the junctions ranges from 4 to 10 , and thus the upper limit of the Au NW resistivity is found to be  Au = 14 ± 8 cm at T = 2 K.
As the temperature decreases, the junction resistance drops sharply at around T = 1.3 K, which corresponds to the superconducting transition temperature (T c ) of the Al electrodes.
Below T c , the resistance diminishes to zero near T = 1.2 K due to supercurrent flow through the NW. Figure 2 The evolution of dynamic conductance curves with temperature is shown in Fig. 3 where multiple peaks persist even near T c . This robustness of MARs against temperature is in striking contrast to the exponentially decaying Josephson coupling, as revealed in the I c (T) curve. Since each peak value V n is scaled with  BCS , the temperature dependence of  BCS can be extracted from V n (T). Shown in Fig. 3(b) are measured peak values V n with n = 2, 3, and 4 at different temperatures, which are in good agreement with the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. 25 A highly transparent NS interface is required to explain our observation of multiple peaks in the differential conductance curves. For our device with a single-crystalline Au NW, the transparency of the NS interface surpasses that of conventional NS interfaces fabricated by a top-down approach such as the shadow evaporation technique. 18 The interface transparency (T int ) can be estimated from the excess current (I exc ), 26 which is the current at the crossing point of the extrapolated line of the I-V curve from the high bias (eV > 2 BCS ) region to the zero V-axis. 27 In our experiment, eI exc R n / BCS ranges from 0.36 to 1.98, resulting in T int = 0.55 -0.95, which is among the highest values observed in superconducting proximity junctions. 14 Such high transparency is attributed to the single crystalline Au NW with a chemically inert surface. It is also worth noting that T int is proportional to the I c R n product in our experimental range [see Fig. 3 One of the unique features observed in our devices is the occurrence of hysteresis at both low-(near I c ) and high-(> I c ) bias currents. We first discuss the lower-bias hysteresis.
When the current is swept down, reversed switching from resistive to supercurrent branch occurs at a retrapping current I r (<I c ), giving a low-bias hysteretic to the I-V curve. The hysteresis is predominant at temperatures lower than 0.5 K, as shown in Fig. 3(d). Similar behaviour has been observed in the weak links of semiconductor NWs, 13, 14 carbon nanotubes, 15,16 graphene, 17 and normal metals. 28 where ħ is the Planck constant, is estimated to be about 2.8. This is comparable to the observed value.
A self-heating effect may be induced by the Joule power. The power density just above I c is roughly 230 nW/m, 3 which is at least two orders of magnitude larger than the typical value necessary for electron heating, 31 implying that the Joule heating is not negligible.
However, considering the high thermal conductivity of Au NW, it cannot be conclusively stated that a self-heating effect is the primary origin of the low-bias hysteresis in our system.
Finally, the conductance enhancement due to the MARs can give rise to hysteresis in the I-V curve. 4 If the transparency of the NS interface is adequate and the inelastic mean-free path (phase breaking length, L  ) is sufficiently larger than L, then each Andreev reflection process gives rise to an increase of the conductance and, consequently, low-bias hysteresis.
Though plausible, there is no direct evidence of this scenario yet.
Another interesting feature of a long diffusive SNS junction is the temperature dependence of the critical current, I c (T), shown in Fig. 3 technique, even at lower temperatures. 29,30 Theoretically, eI c R n = 10.8 E Th was predicted at zero temperature in the long-junction limit (E Th / BCS << 1), 32 and eI c R n = 2.08  BCS in the short-junction regime (E Th / BCS >> 1). 33 In the present experiment, E Th / BCS ranges from 0.02 to 0.11, which indicates that our Au NW junctions belong to a crossover regime between two extreme limits and thus give rise to relatively high I c R n values.
To gain further insight into the Au NW SNS junctions, we investigated the effect of an In summary, we have fabricated mesoscopic Josephson junctions using single crystalline Au NWs contacted with superconducting Al electrodes. A highly pronounced I c R n product and high-order (n = 17) sub-gap structures of dI/dV imply that the coherent MARs are the dominant electronic transport mechanism over the whole system, which differs significantly from previous studies on conventional SNS junctions. We anticipate that the single crystalline Au nanowires will provide an ideal platform for SNS mesoscopic Josephson junctions for future applications involving quantum information devices.

Methods
Au NWs were synthesized on a c-cut sapphire substrate in a horizontal quartz tube furnace system by using a vapor transport method. The sapphire substrate was placed a few cm downstream from an alumina boat that was filled with 0.03 g of pure Au powder as a precursor. The Ar gas flowed at a rate of 100 sccm, keeping the chamber pressure at 1 ~ 5  Fig. 1(b) and the inset, respectively. The normal-state resistance (R n ) of the Au NW junctions ranges from 4 to 10 , from which the upper limit of the Au NW resistivity can be estimated to be  Au = 14 ± 8 cm at T = 2 K.