Cooper-pair current through ultrasmall Josephson junctions

Abstract

The current-voltage characteristics of ultrasmall Josephson junctions sensitively depend on the electromagnetic environment of the junction. When the charging energy exceeds the Josephson coupling energy, the usual supercurrent at zero voltage is completely suppressed. However, for typical environmental impedances, which are small compared to the resistance quantum, stochastic Cooper-pair tunneling leads to a supercurrent peak at a small finite voltage which is proportional to the temperature and the low-frequency resistance of the external circuit. An analytic expression for the form of this universal peak, which is independent of the high-frequency behavior of the environment, is given. With increasing Josephson coupling the peak merges into the usual supercurrent of a Josephson junction. At larger voltages the Cooper-pair current depends on details of the environment. Current peaks are shown to result from resonances in the environmental impedance. Specifically, the case of an LC transmission line of finite length is discussed.

Phase Diffusion in Graphene-Based Josephson Junctions

“…The overall agreement convinces us that the macroscopic behavior of the junction is adequately described by Ref. 17.…”

“…17 we estimate that at T = 1.3 K, I S is close to I (0) C (exceeds 70% for the whole range shown in Figure 1(b)). Therefore, we can use I S in place of I (0) C and plot I S R N vs. 1/R N in Figure 2(d).…”

“…In case of an underdamped junction, R ′ 0 ∼ h e 2 ω P /k B T [9], so that R ′ 0 depends on E J and the junction capacitance C through the plasma frequency ω P ∝ E J /C. Finally, if the junction is underdamped at DC, but overdamped at the plasma frequency, R ′ 0 scales as ∝ Z 0 E J /k B T , where Z 0 is the real part of the environmental impedance at high frequency [17].…”

“…Theoretically, the zero-current differential resistance due to the phase diffusion should depend on temperature as [9,[14][15][16][17] …”

Single-walled carbon nanotube weak links in Kondo regime with zero-field splitting

“…15 In our case, the measured I CM is nearly 1 order of magnitude smaller than the theoretical prediction I 0 = e⌬ / ប Ϸ 30 nA with one resonant spin-degenerate level. 20 Taking into account the phase diffusion in an underdamped voltagebiased Josephson junction, 21 the measured I CM ϰ E J 2 ϰ I C 2 . With the Breit-Wigner model for wide resonance limit h⌫ ӷ⌬ and transmission probability ␣ BW , we have I C = I 0 ͓1 − ͑1−␣ BW ͒ 1/2 ͔ so the I CM − G N relation can be written as…”