Josephson Junction: quick revision, 13 bites

The Josephson Effect: Supercurrent Without Voltage

Two superconductors, one thin barrier.

A **Josephson junction** consists of two **superconductors** separated by a thin **insulator** (or weak link). When the barrier is thin enough, **Cooper pairs** can tunnel through even with **zero applied voltage**, producing a **DC supercurrent**. This is the **DC Josephson effect**.

Takeaway. A Josephson junction allows a supercurrent to flow with no voltage—a purely quantum effect.

What Exactly Is a Josephson Junction?

Superconductor–barrier–superconductor sandwich.

A **Josephson junction** is a device made of two **superconducting electrodes** separated by a **thin insulating barrier** (typically 1–2 nm thick). The barrier is thin enough for **quantum tunneling** of **Cooper pairs**.

Takeaway. It's a quantum tunnel device where superconductors are coupled through a weak link.

DC Josephson Effect: Current–Phase Relation

Current depends on phase difference.

With **no voltage** across the junction, a **DC supercurrent** flows up to $I_c$. The phase difference $\phi$ is constant in time.

Takeaway. Zero voltage still gives current—phase controls its magnitude.

AC Josephson Effect: Voltage Makes Oscillations

Apply voltage, get high-frequency current.

A constant **DC voltage** $V$ causes the phase to evolve linearly, producing an **AC supercurrent** at frequency $f = \frac{2eV}{h}$. This is the **AC Josephson effect**.

Takeaway. Voltage converts to a precise frequency—used for voltage standards.

Critical Current: The Maximum Supercurrent

Exceed it and superconductivity breaks.

The **critical current** $I_c$ is the maximum **DC supercurrent** a junction can carry without developing a voltage. It depends on the **barrier thickness**, **temperature**, and **material properties**.

Takeaway. Critical current sets the limit for zero-voltage operation.

SQUIDs: The Most Sensitive Magnetometers

Detect magnetic fields a billion times weaker.

A **SQUID** (Superconducting Quantum Interference Device) uses **two Josephson junctions** in a superconducting loop. It exploits **quantum interference** to measure extremely small **magnetic fields**—as low as $10^{-15}$ T.

Takeaway. SQUIDs turn Josephson junctions into ultra-sensitive magnetic sensors.

Voltage Standard: The Josephson Constant

The volt is defined by Josephson junctions.

The **AC Josephson effect** gives a precise relation between **voltage** and **frequency**: $V = \frac{h}{2e} f$. Since frequency can be measured with extreme accuracy, this is used to **realize the volt** as a standard.

Takeaway. Josephson junctions define the SI volt via frequency-to-voltage conversion.

How Cooper Pairs Tunnel Through a Barrier

Quantum mechanics lets pairs leak.

Takeaway. Cooper pairs tunnel as a coherent quantum fluid, not individual electrons.

DC vs AC Josephson Effect

Zero voltage vs constant voltage.

Takeaway. DC gives steady current; AC gives oscillations proportional to voltage.

Don't Confuse Josephson Junction with a Tunnel Diode

Both tunnel, but physics differs.

A **tunnel diode** relies on **single-electron tunneling** in a semiconductor. A **Josephson junction** relies on **Cooper pair tunneling** between superconductors. The latter shows **zero-voltage supercurrent** and **phase coherence**—absent in tunnel diodes.

Takeaway. Josephson junctions are superconducting; tunnel diodes are not.

Key Formulas to Memorize

Two equations cover most exam questions.

Takeaway. Remember: current depends on phase; frequency depends on voltage.

Remember 'SIN' for DC Josephson

I equals I_c sine phi.

The DC Josephson relation is $I = I_c \sin\phi$. Think: **S**upercurrent **I**s **N**ow sine of phase. The **AC** effect adds **V** for **V**oltage → frequency.

Takeaway. SIN for DC; V for AC frequency.

Josephson Predicted It at Age 22

Nobel Prize at 33.

**Brian Josephson** predicted the effect in 1962 as a PhD student. He won the **Nobel Prize in Physics** in 1973 at age 33—one of the youngest ever.

Takeaway. A young theorist's insight became a cornerstone of quantum electronics.