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 Incoming links: Possible new effects in superconductive tunnelling by Brian D. Josephson

Josephson effect 2026-10-18

In the ideal sinusoidal Josephson junction, the pair electric current and quantum phase obey

I_{s} = I_{c} sin ϕ, \frac{d ϕ}{d t} = \frac{2 e}{ℏ} V .

Here

e > 0

is the magnitude of the Electron electric charge,

ℏ = h / (2 π)

uses the Planck constant, and

I_{c}

is the junction's superconducting critical current under the specified conditions. Define the signs as follows: positive conventional electric current flows from terminal 2 to terminal 1, and

V

is the voltage of terminal 2 relative to terminal 1. The Gauge-invariant Josephson phase below fixes the matching orientation of

ϕ

. The DC Josephson effect and AC Josephson effect follow from these relations. ^[ref]

Figure 1.
Phase, zero-voltage current branch and voltage-driven oscillations of an ideal Josephson junction
. Original stipulated sinusoidal model, not measured data. The middle panel shows possible static states with adjustable quantum phase, not a uniquely selected electric current under ideal zero-voltage bias. The last panel shows only the pair electric current, with initial phase zero and constant $V = 10 μ V$ ; a quasiparticle contribution is excluded from that panel. Details.

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Josephson junction 2026-10-18

A Josephson junction couples two regions with superconductivity through a weak link. A tunnel barrier is one implementation.

The remarkable possibility is a steady electric current across an insulating barrier at zero electric potential difference. This is the DC Josephson effect, carried by coherent transfer of Cooper pairs. It differs from single-electron superconducting tunneling, which probes the quasiparticle excitation spectrum and produces a dissipative current-voltage characteristic. Both contributions can occur in the same superconducting tunnel device. Brian D. Josephson predicted the pair contribution in 1962; his paper treats transfer that leaves the quasiparticle distribution unchanged. ^[ref]

The Josephson effect turns a difference of quantum phases into a measurable electric current, and an applied electric potential difference into a rate of phase advance. The Giaever gap experiment instead turns an electric potential difference into an excitation energy scale. These complementary measurements expose two aspects of superconductivity: its coherent order parameter and its gapped quasiparticle spectrum. The microscopic pairing calculation belongs to BCS theory and the BCS gap equation. A tunnel diode uses a different device, a semiconductor p-n junction.

Adding capacitance and an external bias makes the Gauge-invariant Josephson phase dynamical. Current-biased Josephson phase dynamics explains how its trapped energy levels and escape can be measured electrically.

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