For comparison, I–V tests are carried out for PVA, carbon, pure copper nanowires and Cu-Cu 2 O-C nanocapacitor, respectively, as shown in Figs 6 and 7. The resistance of PVA is ~650 MΩ (Fig. 6a), which is close to that of an insulator. The typical resistance of carbon nanotube and pure copper nanowire are 26.4 KΩ and 19.6 Ω (Fig. 6b,c), respectively. For different carbon nanotube samples, electrical conductivity ranged from 0.2×105 to 3.3×105 S m−1, comparable to that of bulk graphite ~1.2×105 S m−1 (refs 18,19. For the pure copper nanowires, the measured electrical conductivity ranged from 0.7×107 to 1.9×107 S m−1, close to the value of bulk copper ~2.0×108 S m−1. The conductivities of these devices are compared in Fig. 6d. I–V curves of Cu-Cu 2 O-C nanocapacitor are shown in Fig. 7a–d. For most of devices, the working voltage needs to be larger than 1 V. When a voltage less than 1 V is applied, no current could be detected (<2 pA, which can be regarded as background noise, Fig. 7a). Although the voltage is up to 5 V, the cuprous oxide layer showed recoverable electrical breakdown (Fig. 7b, Supplementary Fig. S5). The devices permanently break down if the applied voltage is large than 10 V (Fig. 7c) and therefore maintain a small resistance (~740 Ω, Fig. 7d) in repeated measurements. The corresponding conductivity is ~3×107 S m−1, comparable to the value from pure copper nanowires we discussed above. Such I–V behaviours can be found for most samples we have measured. According to the breakdown voltage and the typical thickness of cuprous oxide (~5–10 nm from TEM results), we estimate that the dielectric field strength of cuprous oxide is more than 100 MV m−1, close to the value of PEFE (Teflon), a widely used insulating material in coaxial cables.

Figure 6: I-V curves and conductivity of different devices. (a) PVA-coated copper nanowire. (b) Carbon-coated copper nanowire (after CVD process). (c) Pure copper nanowire. (d) Conductivity of these devices. Full size image

Figure 7: I-V curves of voltage and frequency response of Cu-Cu 2 O-C cylindrical nanocapacitor (IV). (a) Voltage less than 1 V. (b) Voltage from −5 to 5 V. (c) The device is permanently broken down by applying a 10 V voltage. (d) I-V curve of Cu nanowires after breakdown of the Cu 2 O layer. Resistance is ~740 Ω (e) Frequency response of the device. Inset: corresponding configurations of the electrodes. Full size image

LCR meter and network analyzer are used to study the frequency response of Cu-Cu 2 O-C nanocapacitor as shown in Fig. 7e. They have been calibrated carefully before measurements, and the noise can be suppressed down to 2fF in a wide frequency range (103–106 Hz, Supplementary Fig. S6). Interestingly, for most devices, the capacitance per unit area are 28–143 μF cm−2 (at106 Hz), with magnitudes 10–37 times higher than that predicted by the classical electrostatics (Supplementary Fig. S7). A similar result is also obtained via the radio frequency measurement (Supplementary Fig. S8). These values are higher than various M-I-M capacitors built in sub-microporous templates (from 2.5 to 100 μF cm−2)2,3,4,5,20,21. The measured capacitance is further supported by impedance spectroscopy for Cu-Cu 2 O-C nanowires, shown in Fig. 8a. A semi circle was found in the Nyquist diagram (Z′ versus −Z″, Fig. 8b) with a red line showing the best fit, which is often found in RC circuits and is well explained based on the coaxial structure of the device. The structure of the cylindrical nanocapacitor and its equivalent circuit are illustrated in the inset of Fig. 8b. The resistance of carbon, copper core and the capacitance between them are denoted with R c , R Cu and C, respectively, as shown in the circuit. For d.c. or low frequency, current flows along the outmost graphitic layer. At high frequencies, current passes through both the graphitic layer and inner copper nanowire because the capacitance won't work at such a frequency. According to the best fit of the plot, the resistance of graphitic layer and copper core were R C ~3.2×105 Ω and R Cu ~30 Ω. Also, the same device measured with a DC source exhibited a resistance of ~3.5×105 Ω (Supplementary Fig. S9), close to the fitted value. The resistance of copper nanowire core was found to be of the same order as the value for pure copper nanowires shown in Fig. 6c. The fitted capacitance between graphitic layer and copper core is ~54.9 pF, close to the value in the frequency response measurements (Fig. 7e).

Figure 8: Impedance spectra of Cu-Cu 2 O-C cylindrical nanocapacitors. (a) Impedance spectra of cylindrical nanocapacitor. (b) Z′ versus −Z″ fitting based on traditional cylindrical capacitor geometry. R C , R Cu and C are the resistance of carbon, copper and capacitance between them, respectively. (c) Configuration of Cu-Cu 2 O-C capacitor [3 Cu cells-3 Cu2O cells-2 C cells] for the first-principle calculations. Full size image

We have carried out detailed quantum mechanical calculations to better understand our experimental results (Supplementary Fig. S10 and Supplementary Methods). Figure 8c shows the configuration of Cu-Cu 2 O-C capacitor (3 Cu cells-3 Cu2O cells-2 C cells). The total capacitance of the Cu-Cu 2 O-C nanocapacitor consists of two capacitances added in series : the classical term and a quantum capacitance term. At small sizes, quantum capacitance (which is usually very large) can be the controlling factor and can either significantly decrease the effective capacitance or increase it if the quantum capacitance is negative22,23,24,25. Recent work has illustrated some interesting (and exotic) cases where negative capacitances are found, especially for oxide interfaces. Accounting for both roughness of the metal–dielectric interface and the quantum capacitance (which is indeed found to be negative for this materials system), we find that the capacitance of Cu-Cu 2 O-C capacitor can be up to 40 pF. It is important to note that quantum capacitance has such a significant effect only because of the extremely small dimensions of the dielectric. In the 5-10 nm regime (corresponding to Cu 2 O thickness), C Clas is quite high and becomes comparable to . In case of macroscopic dielectric thickness, C Clas is much smaller than and thus the latter becomes irrelevant. Our experimental process that allows fabrication of the coaxial dielectric layer at such nanoscopic dimensions provides direct experimental evidence of the significant role of quantum capacitance in nanostructures.