nction not only of temperature but also of frequency. The familiar L/R time constant, here equal to Ao delineates the frequency regimes where most of the total current is carried by J. (if Ad. >>1)or J,(if oAo < 1). This same result can also be obtained by comparing the skin depth associated with the normal channel,8=/2/((. 0,), to the penetration depth to see which channel provides more field screeningIn addition, it is straightforward to use Eq.(53.12)to rederive Poynting's theorem for systems that involve V(EX H)dv= d +=l (T) dv o Using this expression, it is possible to apply the usual electromagnetic analysis to find the inductance(Lo), capacitance(Co), and resistance(R,) per unit length along a parallel plate transmission line. The results of such analysis for typical cases are summarized in Table 53.1 53.3 Superconducting electronics The macroscopic quantum nature of superconductivity can be usefully exploited to create a new type of lectronic device. Because all the superelectrons exhibit correlated motion, the usual wave-particle duality normally associated with a single quantum particle can now be applied to the entire ensemble of superelectrons Thus, there is a spatiotemporal phase associated with the ensemble that characterizes the supercurrent flowing If the overall electron correlation is broken, this phase is lost and the material is no longer a superconductor. There is a broad class of structures, however, known as weak links, where the correlation is merely perturbed locally in space rather than outright destroyed. Coloquially, we say that the phase"slips"across the weak link acknowledge the perturbation The unusual properties of this phase slippage were first investigated by Brian Josephson and constitute the central principles behind onducting electronics Josephson found that the phase slippage could be defined as the difference between the macroscopic phases on either side of the weak link. This phase difference, denoted as d, determined the supercurrent, i,, through and voltage, v, across the weak link according to the Josephson (53.14) Φ。 2πdt where I is the critical(maximum) current of the junction and p, is the quantum unit of flux.(The flux quantum has a precise definition in terms of Planck's constant, h, and the electron charge, e: d= h/(2e) 2. x 10-5 Wb). As in the previous section, the correlated motion of the electrons, here represented by the superelectron phase, manifests itself through an inductance. This is straightforwardly demonstrated by taking the time derivative of Eq.(53. 14)and combining this expression with Eq. (53. 15). Although the resulting inductance is nonlinear(it depends on cos ) its relative scale is determined by (53.16) 2πI c2000 by CRC Press LLC© 2000 by CRC Press LLC function not only of temperature but also of frequency. The familiar L/R time constant, here equal to Ls~ o , delineates the frequency regimes where most of the total current is carried by Jn (if vLs~ o >> 1) or Js (if vLs~ o<< 1). This same result can also be obtained by comparing the skin depth associated with the normal channel, d = , to the penetration depth to see which channel provides more field screening. In addition, it is straightforward to use Eq. (53.12) to rederive Poynting’s theorem for systems that involve superconducting materials: (53.13) Using this expression, it is possible to apply the usual electromagnetic analysis to find the inductance (Lo), capacitance (Co), and resistance (Ro) per unit length along a parallel plate transmission line. The results of such analysis for typical cases are summarized in Table 53.1. 53.3 Superconducting Electronics The macroscopic quantum nature of superconductivity can be usefully exploited to create a new type of electronic device. Because all the superelectrons exhibit correlated motion, the usual wave–particle duality normally associated with a single quantum particle can now be applied to the entire ensemble of superelectrons. Thus, there is a spatiotemporal phase associated with the ensemble that characterizes the supercurrent flowing in the material. If the overall electron correlation is broken, this phase is lost and the material is no longer a superconductor. There is a broad class of structures, however, known as weak links, where the correlation is merely perturbed locally in space rather than outright destroyed. Coloquially, we say that the phase “slips” across the weak link to acknowledge the perturbation. The unusual properties of this phase slippage were first investigated by Brian Josephson and constitute the central principles behind superconducting electronics.Josephson found that the phase slippage could be defined as the difference between the macroscopic phases on either side of the weak link. This phase difference, denoted as f, determined the supercurrent, is, through and voltage, v, across the weak link according to the Josephson equations, (53.14) and (53.15) where Ic is the critical (maximum) current of the junction and Fo is the quantum unit of flux. (The flux quantum has a precise definition in terms of Planck’s constant, h, and the electron charge, e: Fo [ h/(2e) ª 2.068 ¥ 10–15 Wb). As in the previous section, the correlated motion of the electrons, here represented by the superelectron phase, manifests itself through an inductance. This is straightforwardly demonstrated by taking the time derivative of Eq. (53.14) and combining this expression with Eq. (53.15). Although the resulting inductance is nonlinear (it depends on cos f), its relative scale is determined by (53.16) 2 wmos˜ o § ( ) - — × ( ¥ ) = + m + ( ) Ê Ë Á ˆ ¯ ˜ + ( ) Ú Ú Ú E H E H J J 2 2 dv d dt T dv T dv V o s V o n V 1 2 1 2 1 2 1 2 2 e s L ˜ i I s c = sin f v d dt o = F 2p f L I j o c = F 2p