National Physical Laboratory

Quantum Phase-Slip

A current standard based on quantum phase-slip

To perform the metrological triangle experiment, a quantum current standard delivering at least 1 nA is needed.  Since the early 1990s, efforts have focussed on devices based on Single Electron Transport. An alternative approach is to use a phase-slip junction, formed from an extremely narrow superconducting wire. Theoretical predictions show that a phase-slip junction will behave as the exact dual of a Josephson junction. Since Josephson junctions are accurate standards of voltage, this is an attractive prospect. However, making the wires poses a major nano-fabrication challenge.

What is quantum phase-slip (QPS)?

The amplitude of the wavefunction in superconductors is subject to constant quantum fluctuations, even at very low temperatures. In bulk superconductors, these fluctuations average out and do not affect the electrical properties.  However, if a superconducting wire is made narrower than the coherence length (around 100 nm in aluminium), it can be treated as one-dimensional (1D). Then, if the amplitude of the order parameter fluctuates to zero, a small region of the wire goes into the normal state, and momentarily blocks the flow of supercurrent along the wire. This allows the phase of the wavefunction to slip by 2π.

Phase Slip Centre

Figure 1: Phase slip occurs when the amplitude of the superconducting wavefunction fluctuates to zero at some point along the nanowire

Properties of a phase-slip junction

The properties of a phase-slip junction are identical to those of a Josephson Junction, but with current and voltage exchanged.  For example, a Josephson junction biased at a low current is a perfect conductor, and a phase-slip junction biased at low voltage is a perfect insulator (Fig. 2).

Phase Slip IV
Figure 2: Left: IV characteristic of a Josephson junction.  Right: IV characteristic of a phase-slip junction

Under microwave irradiation, a current-biased Josephson junction exhibits flat voltage plateaux. This is the basis for its use as a voltage standard. Exchanging current and voltage, we see that a voltage-biased phase-slip junction could function as a current standard (Fig. 3).

Phase Slip Plateaux
Figure 3: Current plateaux in the IV characteristic of a phase-slip junction under microwave irradiation

At a deeper theoretical level, the complementary behaviour of Josephson- and phase-slip junctions is explained by the dual role of charge and phase. In quantum electrical circuits, charge and phase are conjugate variables, subject to the uncertainty relation [n, φ] = i, where n is the number of Cooper pairs, each of which have charge 2e.  In a Josephson junction, phase is a good quantum number and charge is poorly defined.  In a phase slip junction, the reverse is true. This means that, while the phase difference between the ends can fluctuate, the charge stored in the junction remains fixed.

Under what conditions can QPS be observed?

There are several conditions that must be met before we can make a current standard based on quantum phase-slip.

  1. The superconducting nanowire should have a width of order 10 nm.  This is to ensure that the wire behaves as a 1D conductor.
  2. The wire must have a large series resistance R > RQ = h/4e2 to provide damping.  The resistance must be maintained up to high frequencies of order 100 GHz.
  3. The wire must be maintained at a temperature well below the superconducting transition temperature TC to suppress thermal fluctuations.

It is only recently that fabrication technology has developed to the level of realising conditions (1) and (2). We are now collaborating with research groups at Surrey University in the UK, La Trobe University in Australia and PTB in Germany to investigate QPS phenonena.

This area has close links with the research in superconducting devices.

Last Updated: 25 Mar 2010
Created: 8 Jun 2007


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