FIGURE 53.3 A real Josephson tunnel junction can be modeled deal lumped circuit elements. IcR FIGURE 53. 4 The i-v curves for a Josephson junction: (a)B>>1, and (b)B<<1. 2πⅠRC (53.17) R where p is known as the Stewart-McCumber parameter Clearly, if B>> 1, the capacitive time constant R; Ci dominates the dynamics of the circuit. Thus, as the bias current is raised from zero, no time-average voltage is created until the critical current I is exceeded. At this point, the junciton switches to a voltage consistent with the breaking of the Cooper pairs, 2A/e, with a time constant L C. Once the junction has latched in the voltage state, however, the capacitor has charged up and the only way for it to discharge is to lower the bias current to zero again. As a result, a device with B >>1 will have a hysteretic current-voltage curve as shown in Fig. 53.4a. Conversely, B < 1 implies that the capacitance of the device is unimportant and so the current- voltage curve is not hysteretic(see Fig. 53.4b). In fact, the time-averaged voltage(v)for such an RS] device is iR. 1 ori>I (53.18) In other words, once the supercurrent channel carries its maximum amount of current, the rest of the current is carried through the normal channel Just as the correlated motion of the superelectrons creates the frequency-independent Meissner effect in a bulk superconductor through Faraday's law, so too the macroscopic quantum nature of superconductivity c2000 by CRC Press LLC© 2000 by CRC Press LLC (53.17) where b is known as the Stewart-McCumber parameter. Clearly, if b >> 1, the capacitive time constant RjCj dominates the dynamics of the circuit. Thus, as the bias current is raised from zero, no time-average voltage is created until the critical current Ic is exceeded. At this point, the junciton switches to a voltage consistent with the breaking of the Cooper pairs, 2D/e, with a time constant . Once the junction has latched in the voltage state, however, the capacitor has charged up and the only way for it to discharge is to lower the bias current to zero again. As a result, a device with b >>1 will have a hysteretic current-voltage curve as shown in Fig. 53.4a. Conversely, b << 1 implies that the capacitance of the device is unimportant and so the current￾voltage curve is not hysteretic (see Fig. 53.4b). In fact, the time-averaged voltage ·nÒ for such an RSJ device is (53.18) In other words, once the supercurrent channel carries its maximum amount of current, the rest of the current is carried through the normal channel. Just as the correlated motion of the superelectrons creates the frequency-independent Meissner effect in a bulk superconductor through Faraday’s law, so too the macroscopic quantum nature of superconductivity FIGURE 53.3 A real Josephson tunnel junction can be modeled using ideal lumped circuit elements. FIGURE 53.4 The i-v curves for a Josephson junction: (a) b >> 1, and (b) b << 1. Q R C L R j j I R C j j cjj o 2 2 2 = = º p b F L Cj j v iR I i i I j c c = - Ê Ë Á ˆ ¯ 1 ˜ > 2 for