Breaking the Quantum PIN Code of Atomic Synapses

Atomic synapses represent a special class of memristors whose operation relies on the formation of metallic nanofilaments bridging two electrodes across an insulator. Due to the magnifying effect of this narrowest cross section on the device conductance, a nanometer-scale displacement of a few atoms grants access to various resistive states at ultimately low energy costs, satisfying the fundamental requirements of neuromorphic computing hardware. However, device engineering lacks the complete quantum characterization of such filamentary conductance. Here we analyze multiple Andreev reflection processes emerging at the filament terminals when superconducting electrodes are utilized. Thereby, the quantum PIN code, i.e., the transmission probabilities of each individual conduction channel contributing to the conductance of the nanojunctions, is revealed. Our measurements on Nb2O5 resistive switching junctions provide profound experimental evidence that the onset of the high conductance ON state is manifested via the formation of truly atomic-sized metallic filaments.


■ INTRODUCTION
Recently, incredible progress has been achieved in the hardware implementation of artificial neural networks utilizing resistive switching memory (RRAM) technology relying on the voltage-induced formation and degradation of conducting filaments within an insulator matrix. 1−6 As an example, 128 × 64 memristor crossbar arrays were built and successfully applied for efficient image processing and machine learning tasks. 7−10 Such artif icial synapse devices usually exploit the highly linear current−voltage characteristics and the broad analog tunability of the resistance states in their transition metal oxide memristor units, which are typically operated in the <1000 μS conductance range approaching or spanning the G 0 = 2e 2 /h ≈ 77.5 μS universal conductance quantum. 6−13 In the latter regime, it is tempting to interpret the RRAM device state as an atomic-sized filament (Figure 1a), representing the ultimate smallest memory element. However, it is evident that solely the conductance value cannot supply any information about the cross-sectional area of the active device region: a truly atomic-sized metallic filament may provide exactly the same conductance as a much wider, nanometer-scale filamentary switch with a tunnel junction at the middle (Figure 1b), or an even larger interface-type RRAM device ( Figure 1c). 14 At truly atomic dimensions, the direct microscopic imaging of the active volume of resistive switching devices is extremely challenging. Therefore, the claims on atomic-scale switching typically rely on indirect evidence. For instance, elemental single-atom silver nanowires are known to exhibit a welldefined configuration with a conductance of 2e 2 /h; therefore, the statistically pronounced occurrence of the quantum conductance in silver-based filamentary RRAM units is an indication of atomic switching. 15−17 On the contrary, pure single-atom nanowires made of transition metal elements exhibit very broad conductance distributions, where the conductance quanta are not distinguished in any sense. 18,19 Moreover, the variable oxygen content of the conducting filaments in transition metal oxide-based RRAMs is expected to further increase the conductance variety. As a consequence, it is extremely challenging to identify the physical nature of the conducting filaments in these technologically highly important structures.
Here we employ the powerful method of superconducting subgap spectroscopy developed in the field of mesoscopic physics. 18−23 This method is capable of decomposing all of the τ i transmission probabilities (the so-called quantum PIN code 18,24 ) of the individual quantum conductance channels contributing to filamentary conductance, thus providing substantially more information about the conduction properties than the overall G e h i M i 2 1 2 τ = ∑ = conductance, 25 where M is the number of open quantum conductance channels. This approach was originally implemented in the field of atomic and molecular electronics to reveal the nature of conductance in single-atom nanowires 20 and more recently to identify the distinct atomic states upon reversible current-induced singleatom rearrangements. 26 Here we apply this unique method to study the nature of the conducting filaments in transition metal oxide-based RRAM structures. We focused our studies on Nb/ Nb 2 O 5 /Nb point contacts where the advantageous resistive switching properties 2,7,8,11−13,27−35 are accompanied by the conveniently high superconducting transition temperature (T c = 9.22 K) of the elemental Nb electrodes. Our measurements provide profound experimental evidence that the observed switching takes place due to the structural rearrangement of a truly single-atom-diameter conductance channel. The scheme of our analysis is illustrated in Figure 1d,e. At higher voltage scales, the resistive switching junction exhibits conventional hysteretic I(V) characteristics ( Figure 1d). However, if the I(V) traces are compared in the range of the superconducting gap (Δ), distinct structures are observed due to multiple Andreev reflections (Figure 1e). 20,21,23,36 As a first order process, single electron charges can pass the junction with τ probability, but due to the presence of the superconducting gap, this is only possible at eV > 2Δ. However, an nth order process including the simultaneous transfer of n electron charges with τ n probability becomes available at a reduced voltage of eV > 2Δ/n. In a tunnel junction, all of the transmission probabilities are small (τ i ≪ 1) and therefore all of the higher order processes are negligible. In this case, the current remains zero at eV < 2Δ, whereas at higher voltage a linear I(V) curve is observed with the slope of the G N normal state conductance (see the green curve in Figure 1e). In an atomic-sized metallic filament, however, a single or a few conductance channels are highly transparent (i.e., their transmission probability is close to unity), and thus, the higher order processes also become enabled. This introduces finite subgap current at eV < 2Δ with distinct structures at the 2Δ/n thresholds (red curve in Figure 1e). In the extreme case of τ i = 1, even the n ≫ 1 order processes are available, giving rise to an infinitely steep current rise at zero voltage (blue curve in Figure 1e). By the numerical fitting of the I(V) curve in the gap region, one can, in principle, determine all of the τ i transmission eigenvalues, 36 and thus, one can clearly distinguish physically different device states even if they share the same conductance.

■ RESULTS AND DISCUSSION
Before demonstrating our main result of resolving truly atomicscale resistive switching by subgap spectroscopy, we take the following steps: (i) we demonstrate the operation of Nb 2 O 5 resistive switching junctions close to the quantum conductance unit also highlighting the analog tunability of the resistance states in this regime; (ii) we present reference measurements on pure Nb atomic junctions also demonstrating the proper spectroscopic resolution of our subgap spectroscopy setup; (iii) we analyze how much the applicability of subgap spectroscopy is restricted by the superconducting proximity effect in the niobium oxide region.
Resistive Switching in the Vicinity of the Quantum Conductance Unit. Our measurements were performed on ∼20 nm thick Nb 2 O 5 layers that were grown on the top of an ∼300 nm thick Nb thin films by anodic oxidation. The resistive switching junctions were established in a scanning tunneling microscope (STM) arrangement by touching either a PtIr or a Nb STM tip to the thin film sample. The sample preparation and the scheme of the measurement follow the same protocol as in our previous study on the general resistive switching properties of Nb 2 O 5 . 31 Here we demonstrate that Nb 2 O 5 exhibits room temperature resistive switching in the vicinity of the quantum conductance unit as well ( Figure 2). Furthermore, as the V drive 0 amplitude of the driving triangular signal increases, the resistive switching curves open up, exhibiting a clear multilevel programmability. Accordingly, the device states can be fine-tuned in the ∼1−2.5 G 0 interval, as demonstrated by the V drive 0 dependence of the G ON and G OFF low voltage conductances in the bottom inset of Figure 2. We emphasize that, in spite of the ∼1 G 0 quantum conductance range, no conductance jumps due to distinct atomic rearrangements are observed; the OFF state conductance is rather tunable in a fully continuous fashion. In this case, the ON state conductance remains constant, which we attribute to the interplay of the R S = 3.35 kΩ serial resistance and the strong intrinsic nonlinearity of the I(V) curve 31 restricting the V bias voltage drop on the junction.
To study the superconducting subgap characteristics of such resistive switching junctions, we have performed our further measurements utilizing Nb tips at T = 1.4 K temperature. The low temperature setup is optimized to prevent noise pickups, which would induce a smearing of the spectroscopic Reference Experiments on Pure Nb Atomic Wires. Prior to resistive switching measurements, we characterized our low temperature subgap spectroscopy setup using the wellstudied reference system of pure single-atom Nb nanojunctions 19−21,37 established in a mechanically controllable break junction (MCBJ) arrangement (see Figure 3a). In this case, a macroscopic Nb wire is broken in a three-point bending configuration to form extremely stable single-atom contacts, which are ultraclean due to the freshly broken surfaces. Figure  3c displays the experimental subgap curves of pure atomicsized Nb contacts realized at different displacements of the electrodes. For a better comparison of the subgap curves corresponding to different G N values, the conventional normalization procedure of the current and voltage scales is applied, 21 such that all curves scale to a slope of unity at eV bias / Δ ≫ 2. The bottom, green curve in Figure 3c shows typical tunneling characteristics resembling the green curve in Figure  1e. The numerical derivative of this I(V) curve shows sharp peaks at ±2Δ/e (see the green differential conductance curve in Figure 3d). The Γ MCBJ = 131 μV half-width of these peaks directly tells the voltage resolution of our subgap measurement setup. As our MCBJ and STM setups are exact clones of each other (apart from the mechanical actuation), this voltage resolution can also be considered as an electronic resolution baseline for our resistive switching experiments.
At such resolution, all of the subgap I(V) curves in Figure 3c are well fitted with the theory of multiple Andreev reflections 20,21,23,36 (see the black fitting curves in Figure 3c and the corresponding transmission eigenvalues in the caption). Further details on the fitting procedure are provided in the Methods section.
The transmission eigenvalue decomposition reveals that the transport is dominated by the first conductance channel for all traces, exhibiting increasing τ 1 from the bottom (green) curve toward the top (blue). The τ 1 ≪ 1 value for the green curve confirms that a tunneling junction is concerned, the red curves correspond to partially open channels (τ 1 ≈ 0.3−0.7), whereas the blue curve resembles the blue curve in Figure 1e representing a single dominant channel with nearly perfect transmission (τ 1 ≈ 0.97). Note that the transition from a tunnel junction to a transparent metallic nanowire is not only indicated by the transition from zero current to a steep current rise in the subgap regime (eV bias /Δ < 2). At the same time, the so-called excess current is also increased, i.e., the high-bias (eV bias /Δ ≫ 2) linearly varying part of the curves exhibits an increasing current offset as the channels open up.
Next, we briefly review the well-studied transmission properties of Nb single-atom nanowires, 18−21 which will serve as a comparison basis for our subgap analysis on Nb 2 O 5 resistive switching junctions. In a simple free electron picture, one can argue that the first quantum conductance channel opens in nanowires, where the (2πℏ) 2 /(2λ F 2 m*) kinetic energy of the electrons at the Fermi surface of the electrodes exceeds the transverse confinement energy at the narrowest cross section of the wire. Considering a cylindrical  Nano Letters pubs.acs.org/NanoLett Letter nanowire geometry 18 and the λ F ≈ 0.53 nm Fermi wavelength 38 of niobium, the first quantum conductance channel is expected to open at R ≈ 0.2 nm filament radius; i.e., the first channel indeed opens at truly atomic dimensions. However, it is to be emphasized that the free electron picture is a very rough approximation in transition metal nanowires; 18 more realistic first principle simulations and subgap spectroscopy measurements refine this picture, showing that a single-atomdiameter Nb nanowire has a broad conductance distribution around 2.5 G 0 possessing up to five partially open channels due to the transport through the s and d valence orbitals of the central atoms. 20 The transport through the d orbitals happens through partially open channels, for which τ i are mostly well off from unity, whereas the s channel is usually well transmitting. 39 Furthermore, the transport through the d channels is very sensitive to the precise details of the particular atomic arrangement. As a clear consequence, one should not expect any sign of conductance quantization features; rather, a broad continuum of possible conductance values appears. To illustrate this, we reproduce a typical conductance histogram of Nb in Figure 3e (see refs 18, 19, and 21), demonstrating that any conductance value can be set in the plotted G = 0−4 G 0 range and the quantized values are not enhanced at all. The sample conductance versus electrode separation traces in Figure 3f also illustrate that in Nb (and in various further transition metals) the well-known conductance staircase of noble metal nanowires 18 is replaced by a rather smooth and continuous conductance variation with minor conductance jumps (black curve) or no conductance jumps at all (red curve). According to the above considerations, the atomic configurations behind the subgap curves of Figure 3c are reflecting the smooth disconnection of a single-atom nanowire along the continuous G ≲ 1 G 0 tail region of the conductance traces in Figure 3e. This is illustrated with the inset cartoons in Figure 3c: the blue curve corresponds to a transparent singleatom junction, the red curves are related to junctions, where the central atoms are already slightly disconnected, and the green curve reflects a disconnected tunneling junction.
Preconditions of Subgap Spectroscopy on Resistive Switching Junctions. The application of superconducting subgap spectroscopy on the ON and OFF states of resistive switching Nb/Nb 2 O 5 /Nb junctions relies on three obvious preconditions: (i) resistive switching should work with a compositionally symmetric electrode arrangement, i.e., using Nb electrodes on both sides; (ii) operation at cryogenic temperatures; (iii) the presence of the oxide layer should not result in an untolerable reduction of the subgap spectroscopy's resolution. In the following, these requirements are analyzed.
(i) Most works apply a compositionally asymmetric junction design to grant a well-defined bipolar resistive switching; however, in our case, subgap spectroscopy necessitates Nb electrodes on both sides. In our previous work, 40 we have demonstrated that the tip−sample geometrical asymmetry alone is enough to enable bipolar resistive switching. This was justified on our specific Nb 2 O 5 resistive switching junctions as well, as demonstrated by the similar room temperature switching I(V) traces using PtIr(tip)/Nb 2 O 5 /Nb(thin film) junctions (Figure 2) or Nb(tip)/Nb 2 O 5 /Nb(thin film) junctions (Figure 4a). Based on the statistical analysis of 100 independent junctions, we generally find that in spite of the symmetric electrode material arrangement the Nb(tip)/ Nb 2 O 5 /Nb(thin film) junctions exhibit a dominant switching voltage polarity: in >80% of the cases, the set transition happens when the thin film sample is positively biased with respect to the tip. In the remaining cases, the local geometrical asymmetry of the filament center is presumably reversed compared to the larger-scale tip−sample asymmetry.
(ii) Our low temperature measurements (T = 1.4 K) have routinely yielded resistive switching curves, which are similar to the room temperature switching characteristics (see a typical low temperature switching curve of Nb/Nb 2 O 5 /Nb junctions in Figure 4b). The low temperature operation of the switching is attributed to the extremely large electric fields at the narrowest part of the junction as well as to the self-heating effect of the active junction area. 41 (iii) The superconducting features are clearly observed in the I(V) curves of the SmS junctions. However, according to the differential conductance curve of a Nb/Nb 2 O 5 /Nb tunnel junction (brown curve in Figure 3d), the width of the superconducting coherence peak is increased (Γ ox. = 565 μV), whereas the gap value determined from the peak position (Δ ox. = 0.866 mV) is reduced with respect to the clean Nb MCBJ junctions. This Γ-broadening results in a smearing of all subgap traces, and thus, the spectroscopic resolution is reduced. In the following, we discuss the possible background of the resolution loss, emphasizing that our subgap data are still suitable to draw Nano Letters pubs.acs.org/NanoLett Letter the conclusions of our study. As the STM and the MCBJ setups share the same electromagnetic environment thanks to the same sample holder structure and measurement circuits, including identical filter stages, we exclude the possibility of enhanced noise pickups in the former case. According to the XPS analysis carried out in our earlier study, 31 our Nb 2 O 5 /Nb thin film samples contain an ∼10 nm thick interface region of inhomogeneous oxygen content between the Nb 2 O 5 layer and the bulk Nb. We argue that this suboxide region forms a conducting but intrinsically non-superconducting volume, 42,43 which is made superconducting by the proximity effect of the nearby superconducting Nb electrode. Such proximity superconducting structures are known to exhibit a reduced gap value and a smeared superconducting density of states, 44−47 as was also demonstrated along the subgap spectroscopy of Al/Au/Al atomic contacts. 48 As a rough estimate based on the theoretical model described in refs 48 and 49, the presence of a 10 nm wide proximity superconducting region would induce the observed Δ ox. /Δ MCBJ ≈ 0.67 reduction of the measured gap value in our oxide samples (see Figure 3d) if a superconducting coherence length of ∼22 nm is assumed. The latter value is reasonable in a highly disordered oxide layer 50 in comparison with the 39 nm bulk coherence length of niobium. 51 Quantum PIN Code Decomposition of the ON and OFF Resistance States. Having the basic requirements of subgap spectroscopy satisfied, we wish to classify our resistive switching junctions via their quantummechanical PIN code decomposition. If a larger area tunneling junction ( Figure  1b,c) is concerned, the green tunneling characteristic of Figure  1e should be measured. However, the Γ-broadening yields a smearing of this curve, as demonstrated by the brown lines in Figure 4c,d showing an experimentally measured tunneling trace with G N ≈ 0.01 G 0 conductance. Note that, if the τ i ≪ 1 condition is satisfied, the tunneling I(V) curves scale to the same universal dimensionless trace on the eI/(G N Δ) vs eV bias / Δ plane of Figure 4c,d. This means that the brown curves in panels c and d are expected to look similar for any tunnel junction with arbitrary conductance. Due to the Γ-broadening, the light brown area under these brown tunneling characteristics is experimentally unaccessible; however, any subgap trace growing above this brown background should be related to a device state which is definitely not a tunneling junction.
The blue and red lines in Figure 4c and d, respectively, show the subgap I(V) curves of the ON and OFF states demonstrated in Figure 4b. The subgap curve of the ON state with close to 1 G 0 conductance (Figure 4c) clearly separates from the brown background exhibiting a steep current rise around zero bias similarly to the blue curves in Figure 1e and Figure 3c. For this curve, the fitting procedure unambiguously concludes a dominant channel with close to unity transmission, which is extended by a further channel with smaller transmission (see the thick black fitting curve and the corresponding PIN code). This result provides clear evidence that the ON state corresponds to a highly transmitting filament with a single atom at the narrowest cross section (see the illustration in Figure 1a). If the same conductance would be shared between a larger number of less transmitting channels, the I(V) curve would strongly deviate from the measured curve, as illustrated by the thin black theoretical subgap traces owing the total conductance of the ON state shared between different numbers of equally transmitting channels. On the other hand, a highly transmitting filament with several atoms in the narrowest cross section would correspond to a filament diameter significantly exceeding the λ F = 0.53 nm Fermi wavelength, and therefore, it is expected to exhibit a larger conductance with more than one highly transmitting channel. 18,22 The subgap trace of the OFF state (Figure 4d) is best fitted with a single conductance channel, as demonstrated by the thick black line and the corresponding set of transmission eigenvalues. However, this subgap curve only slightly grows above the brown background, indicating that the G N = 0.321 G 0 conductance of the OFF state is already close to the border, where subgap spectroscopy provides a less conclusive classification between a single-channel conductor or a multichannel tunnel junction. In spite of this uncertainty, we argue that a single-atom diameter ON state is expected to switch to a single-atom diameter OFF state such that a narrow barrier forms between the central atoms due to a voltageinduced atomic displacement at the junction center.
Statistical Analysis of the Transmission Eigenvalues. Next, we investigate the transmission properties of a larger ensemble of Nb/Nb 2 O 5 /Nb resistive switching junctions (see Figure 5). To precisely define the validity range of our analysis, Figure 5. Evolution of the conductance channels. (a, b, c, d, e) The distribution of the τ 1 , τ 2 , τ 3 , τ 4 , and τ 5 transmission eigenvalues numerically evaluated in various independent Nb(tip)/Nb 2 O 5 / Nb(thin film) resistive switching junctions measured at T = 1.4 K. The blue (red) circles correspond to the ON (OFF) states, respectively. As a comparison, the gray squares display the transmission eigenvalues of pure Nb single-atom nanowires also including the data shown in Figure 3c. As a further reference taken from ref 19, the black data points and error bars represent the mean transmission values and their standard deviations acquired on 30 + 30 independent pure Nb atomic junctions measured at G ≈ 1 G 0 and G ≈ 0.3 G 0 conductances. The shaded area in panel a highlights the region in the τ 1 −G N plane where our analysis is not conclusive due to the Γ-broadening (see text). The inset in panel a illustrates an atomicsized filament. Nano Letters pubs.acs.org/NanoLett Letter we linearly rescale the brown tunneling curve of Figure 4c,d to various normal state conductances, G̃N. We fit these scaled tunneling curves and extract τ1, the leading transmission probability values (brown dots in Figure 5a). Due to the G N ≈ 0.01 G 0 conductance and the corresponding τ 1 ≤ 0.01 transmission probability of the original tunneling curve, the rescaled curves should exhibit similarly small τ 1 values with M ≥ G̃N/G N conductance channels. The fitting procedure, however, provides only a few channels with significantly larger τ̃1 values due to the smearing of the tunneling curves. As a general tendency, at G̃N < 0.3 G 0 , the fitting yields a single channel with τ̃1 ≈ G̃N/G 0 , whereas, at G̃N > 0.3 G 0 , the leading transmission saturates at τ̃1 ≈ 0.3, and the remaining conductance is filled with further channels. Accordingly, the light brown area under these τ̃1 values defines the range, where our analysis is not conclusive. Again, the leading transmissions of the OFF states (red circles) are close to the validity border; however, the τ 1 values of the ON states (blue circles) are all well above the light brown area with τ 1 ≈ 0.6−0.9, indicating that all of the investigated resistive switching junctions exhibit a single-atom-wide filamentary ON state (see the inset in Figure 5a). Finally, we compare the transmission properties of atomicsized niobium-oxide resistive switching filaments and pure niobium atomic wires. Our previous study has already demonstrated the mean transmission probabilities and their variances at 0.3 G 0 and 1 G 0 conductances 19 (black data points with error bars in Figure 5a). Here we extend these data with the evolution of pure Nb transmission probabilities covering the whole conductance range, where the resistive switching was analyzed (see gray squares in Figure 5). The presence of oxygen in the filament may alter the transmission eigenvalues of clean Nb atomic wires in either direction: (i) It may induce a barrier at the narrowest cross section (see the illustration in Figure 1b), yielding reduced τ i values for the channels with higher transmission. This effect would be especially remarkable in the reduction of τ 1 . (ii) Similarly to oxygen decorated Ni atomic wires, 52 the presence of oxygen may block the transport through the d orbitals and enhance the role of the s channel, which would result in an increased τ 1 value accompanied by the suppression of the further transmission eigenvalues. In spite of these two possibilities, the data show that the evolution of all transmission probabilities with the total conductance is very similar for resistive switching filaments and pure Nb atomic wires. This again underlines that the transport in the ∼1 G 0 ON state of the resistive switching niobium-oxide filaments highly resembles the transport through single-atom Nb nanowires.

■ CONCLUSIONS
Concluding our analysis, we have investigated resistive switching junctions operated close to the universal quantum conductance unit. This conductance regime offers a unique possibility to establish truly atomic-sized memory devices. However, in transition metal oxide-based resistive switching filaments, the actual determination of the junction diameter is an especially challenging task, as the analog tunability of the conductance states is enabled even at atomic dimensions instead of displaying discrete conductance steps and quantized conductance features characteristic to noble metal atomic wires.
Here, we have shown that superconducting subgap spectroscopy is a powerful method to gain direct insight into the transmission properties of resistive switching junctions. Close to the quantum conductance, this method is especially sensitive to the fine details of the junction's quantum PIN code, providing highly conclusive information about the nature of the conducting filaments. Our measurements on Nb 2 O 5 memristor junctions provide the first direct and well-founded experimental evidence that the switching takes place due to the structural rearrangement of a truly single-atom diameter conductance channel in a transition metal oxide resistive switching device. The method of transmission channel decomposition can be extended to further resistive switching devices including those composed of superconducting metals (Nb, Ta, V, etc.), or even further compounds contacted with auxiliary superconducting electrodes. Furthermore, subgap spectroscopy is also adaptable for crossbar junctions utilizing superconducting electrodes, once a thin enough switching region is fabricated compared to the superconducting coherence length.

Preparation of Atomic Nb Junctions.
Prior to the study of memristive junctions, reference subgap measurements were carried out by establishing pure atomic Nb break junctions at cryogenic temperatures. For this purpose, 99.99% purity Nb wires of 0.25 mm diameter were notched with a sharp razor in a preliminary step, followed by the insertion of the wire into a three-point bending MCBJ arrangement (see Figure 3a). A combined use of a stepper motor and a piezoelectric actuator allows broad range actuation and precise control over breaking the wire; thus, various atomic configurations (see Figure 3c, inset) with stable normal conductance were routinely achieved.
Preparation and Characterization of Nb 2 O 5 /Nb Thin Films. Studying STM point contacts is a powerful experimental tool to characterize and optimize memristive materials in order to achieve reliable operation of future onchip RRAM devices. For the study of STM type point contacts, the Nb 2 O 5 /Nb(thin film) samples were created with anodic oxidation of a Nb thin film in a 1% aqueous solution of H 3 PO 4 , maintaining 1 mA/cm 2 current density throughout the process. First a 300 nm thick Nb thin film was sputtered on the top of a standard Si wafer. X-ray photoelectron spectroscopy (XPS) with subsequent Ar + milling steps was performed on Nb 2 O 5 / Nb(thin film) samples, uncovering the depth profile of the Nb:O stoichiometric composition. The presence of Nb 2 O 5 was confirmed at the top of the ∼20 nm thick oxide layer. For further details on the anodic oxidation and the structural characterization of Nb 2 O 5 /Nb(thin film) samples, see ref 31.
Electric Circuitry for Resistive Switching and Subgap Measurements. The diagram of the electric circuit identically utilized in the low temperature STM and MCBJ measurement setups is shown in Figure 6. Three main stages were utilized for noise filtering, established in a symmetric arrangement: long cryogenic coaxial cables operating as an RC filter at their full length; commercially available MiniCircuits VLFX-80 low pass filters with f c = 145 MHz cutoff frequency and 40 dB insertion loss up to 20 GHz; and custom-built RC filters made of SMD elements (R = 100 Ω, C = 2 nF at T = 1.4 K). Originating from these filtering elements and the input impedance of the current amplifier, an R S = 300 Ω total serial resistance was connected to the sample. The I(V) characteristics are displayed throughout the paper as a function of the voltage drop on the nanojunction (V bias , bias voltage), while triangular signals with f drive = 2.5 Hz frequency and V drive 0 amplitude are applied Nano Letters pubs.acs.org/NanoLett Letter (taking the optional 1:100 division into account) by the DAQ unit. The low temperature STM point contact measurements were performed at 1.4 K in a Janis Research SVT200T-5 liquid helium cryostat. Measurement Protocol. The distant voltage ranges of resistive switching (∼V) and subgap characteristics (∼mV) require an automated measurement technique capable of controlling the voltage division and the gain of the current amplifier simultaneously. While recording I(V) characteristics in the subgap regime, a 1:100 division was applied to the drive voltage, controlled by a relay. In order to prevent degradation of the nanojunctions due to transient voltage spikes, another relay was used to ground the circuit while switching the gain of the current amplifier.
Fitting Procedure of Subgap I(V) Traces. The fitting of subgap I(V) characteristics was performed with a type of simulated annealing algorithm using the Monte Carlo method written by G. Rubio-Bollinger and co-workers. 36 This algorithm inputs I(V) traces normalized with Δ and G 0 , as demonstrated in Figure 1e. The Δ value is determined form the I(V) traces of the OFF states, which show a tunneling-like characteristic for all of the investigated junctions. In our analysis, the fitting is performed in the 0 < eV < 6Δ interval using M = 5 independent conductance channels. This is already enough to resolve the full compexity of the s and d channels in atomic-sized wires, 20 but the resolution of more channels would require better voltage resolution. It is emphasized that, in the vicinity of G N = 1 G 0 conductance, the subgap traces significantly differ if the transport is dominated by a single channel, or if the same conductance is shared between multiple, partially reflecting channels (see the black curves in Figure 4c). Therefore, the fitting very clearly identifies single-atom nanowires even in the presence of the discussed Γ-broadening.   showing the main filtering elements: LakeShore SS-CC-100 coaxial cables (operating as an RC filter), MiniCircuits VLFX-80 low pass filters, and custom-built RC filters. The red parts refer to the automated control used for switching between the high-bias I(V) data acquisition and subgap spectroscopy modes via two relays. The analog outputs (AO) and inputs (AI) of a National Instruments USB-6363 data acquisition card were utilized to bias the nanojunctions and to record the current, respectively. The latter was measured through a Femto DLPCA200 current amplifier. During subgap measurements, the gain of the current amplifier was set to a higher value (typically 10 6 −10 9 ) and a 1:100 voltage division was applied to increase the signal-to-noise ratio of the voltage bias. The resistive switching I(V) curves were measured at 10 4 gain bypassing the voltage divider. Nano Letters pubs.acs.org/NanoLett Letter