Josephson effect junctions

The quantum of magnetic flux is only 2.07 x 10-15 Wb, which is approximately equal to the amount of the earth s magnetic field enclosed by a ring of 10p,m in diameter. The Josephson effect is observed when two superconductors are separated by a very thin insulating layer (about 20 nm). Single electrons and Cooper pairs can tunnel through such a layer. The characteristics of the Josephson junction are now used to define the volt and have enabled the uncertainty in the maintained standard to be reduced to 0.1 p,V. 

To analyze the Josephson effects let us consider the current through the insulating layer which separates two superconductors [Fig. 15(a)]. Let T, and T2 be the wave function of the electron pair on either side of the junction. For simplicity, both superconductors are assumed to be similar. Following Feynman et al. [40], we use the following time-dependent Schrodinger equations for T, and T2... 

Equations (27) describe the first two Josephson effects. With the lack of voltage, the junction is traversed by the current which can be equal to any value between + J0 and — J0 depending on what the value of the d0 phase is. When a constant external voltage is applied, the current oscillates with the... 

Summary. We consider the Josephson effect in a ballistic Superconductor/ Quantum Wire/ Superconductor junction. It is shown that the interplay of chiral symmetry breaking generated by Rashba spin-orbit interaction and Zeeman splitting results in the appearance of a Josephson current even in the absence of any phase difference between the superconductors. 

In 1962 a postgraduate student, Brian Josephson, working in the University of Cambridge, and later to win a Nobel Prize, predicted that Cooper pairs should be able to tunnel through a thin (approximately 1 nm) insulating barrier from one superconductor to another with no electrical resistance [46]. This quantum tunnelling was confirmed by experiment and is known as the Josephson effect . The superconducting electronic devices exploit Josephson junctions. 

Josephson110 Effect. If two superconductors are separated by a thin layer (<3 nm for an insulator, several micrometers for a metal), then both a DC Josephson effect and an AC Josephson effect can occur. In the DC Josephson effect, a supercurrent can bridge the layer by quantum-mechanical tunneling, but there is a change in phase, which can be detected. It is very sensitive to magnetic fields indeed the supercurrent has the form f = f0 sin (O/O0)/ 7i(/0), where I0 depends on the temperature and the structure of the junction. If a DC potential V is applied across a Josephson junction, then the AC Josephson effect creates a response at a frequency... 

The RF SQUID is based on the AC Josephson effect, uses only one Josephson junction, and is less sensitive than the DC SQUID, but is cheaper and easier to manufacture its SQUID is inductively coupled to a resonant tank circuit. Depending on the external magnetic field, as the SQUID operates in the resistive mode, the effective inductance of the tank circuit changes, thus changing the resonant frequency of the tank circuit. These frequency measurements can be easily done, and thus the losses that appear as the voltage across the load resistor in the circuit are a periodic function of the applied magnetic flux with a period of 0. 

Josephson junction A superfast, superconducting electronic switch based on the Josephson effect. 

Although quantum mechanics is required to explain the origin of the Josephson effect, we can nevertheless describe the dynamics of Josephson junctions in classical terms. Josephson junctions have been particularly useful for experimental studies of nonlinear dynamics, because the equation governing a single junction is the same as that for a pendulum In this section we will study the dynamics of a single junction in the overdamped limit. In later sections we will discuss underdamped junctions, as well as arrays of enormous numbers of junctions coupled together. 

As a 22-year-old graduate student, Brian Josephson (1962) suggested that it should be possible for a current to pass between the two superconductors, even if there were no voltage difference between them. Although this behavior would be impossible classically, it could occur because of quantum mechanical tunneling of Cooper pairs across the junction. An observation of this Josephson effect was made by Anderson and Rowell in 1963. 

We now give a more quantitative discussion of the Josephson effect. Suppose that a Josephson junction is connected to a de current source (Figure 4.6.2), so that a constant current I >0 is driven through the junction. Using quantum mechanics, one can show that if this current is less than a certain critical current, no voltage will be developed across the junction that is, the junction acts as if it had zero resistance However, the phases of the two superconductors will be driven apart to a constant phase difference 0 = 0 - 0, where 0 satis-... 

If a Josephson junction is irradiated with microwaves of frequency /, the I-V behavior shows a series of steps, called Shapiro steps, as shown in Figure 30.32. These steps correspond to supercurrents across the junction when the condition for the absorption of microwave photons is satisfied (this is called the ac Josephson effect). Similar behavior is seen when we expose the junction to a magnetic field. How Josephson junctions can be used to detect very small magnetic fields is described in Chapter 33. 

Most electronic applications are based on the turmel effect between two superconductors that are separated by a weak (isolating) link that is only a few atomic layers thick. Currently, Nb and A1 are used preferably to build Josephson tunnel junctions (JTJs), whereas ceramic superconductors are stiU less common. However, the situation may soon change following the discovery of coherently emitting tera-Hertz radiation of intrinsic BSCCO JTJs (Ozyuzer et al., 2007). Some aspects of electronic applications are considered in detail at this point. 

In 1962, B. D. Josephson predicted that Cooper pairs in superconductors could tunnel through an insulating barrier without encountering electrical resistance, the Josephson effect. A Josephson junction allows current to flow with no resistance with no apphed field. However, at a critical voltage level, the Cooper pairs split up and normal quantum-mechanical tunneling occurs with resistive losses. The Josephson effect allows the fabrication of microelectronic switches and transistors that operate faster and with lower power loss than semiconductor devices. 

MG Wicks, PR Haycocks, T Hori. AC Josephson effect in superconducting niobium nitride tunnel junctions at up to 2.5 THz. Electron Lett 26 610, 1990. 

Josephson junctions, 23 820, 821 Josephson string, 23 827 Josephson vortex, 23 827 Jost Report, 15 201, 202 Joule-Thompson effect, 12 374 Joule-Thomson expansion, 24 647, 648, 650-651... 

Judd-Hunter color difference scale, 7 321 Juglone, in skin coloring products, 7 847 Juglone derivatives, 21 264-265 Juice softening, 23 463 Junctional heart rhythm, 5 107 Junction capacitance, 22 244 Junction devices, 22 180-181 Junction FETs (JFETs), 22 163, 164. See also Field effect transistors (FETs) physics of, 22 241-245, 249 Junction potentials, 9 582 Junctions, stacking, 23 38-39. See also Josephson junctions p-n junction Just-in-Time technique, 21 172 Jute, 11 287, 288, 292, 293. See also China jute... 

Since the Hamiltonian for atoms in accelerated optical lattices is similar to the Legett Hamiltonian for current-biased Josephson junctions [37], the present theory has been extended to describe effects of current modulations on the rate of macroscopic quanmm tunneling in Josephson junctions in Ref. [11]. 

We have considered here the influence of dispersion asymmetry and Zee-man splitting on the Josephson current through a superconductor/quantum wire/superconductor junction. We showed that the violation of chiral symmetry in a quantum wire results in qualitatively new effects in a weak superconductivity. In particularly, the interplay of Zeeman and Rashba interactions induces a Josephson current through the hybrid ID structure even in the absence of any phase difference between the superconductors. At low temperatures (T critical Josephson current. For a transparent junction with small or moderate dispersion asymmetry (characterized by the dimensionless parameter Aa = (vif — v2f)/(vif + V2f)) it appears, as a function of the Zeeman splitting Az, abruptly at Az hvp/L. In a low transparency (D Josephson current at special (resonance) conditions is of the order of yfD. In zero magnetic field the anomalous supercurrent disappears (as it should) since the spin-orbit interaction itself respects T-symmetry. However, the influence of the spin-orbit interaction on the critical Josephson current through a quasi-ID structure is still anomalous. Contrary to what holds... 

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