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Thermal physics

Quantum interference heats up

A thermal effect predicted more than 40 years ago was nearly forgotten, while a related phenomenon stole the limelight. Now experimentally verified, the effect could spur the development of heat-controlling devices. See Letter p.401

Wouldn't it be strange to have a material whose thermal conductivity could be changed by a magnetic field? Imagine holding the end of a rod made of this material with the other end placed in a hot fire. As long as a friend keeps a bar magnet away from the rod, you wouldn't burn your hand, but as soon as they apply a magnetic field — ouch! As odd as this seems, the rules of quantum mechanics predict this type of situation for heat transported across a pair of Josephson junctions (devices that consist of two superconductors separated by a thin insulating gap). Writing on page 401, Giazotto and Martínez-Pérez1 report experiments confirming that this strange phenomenon can actually occur.

In 1962, Brian Josephson made a remarkable discovery2 as a graduate student, while investigating what would happen if two superconducting metals were placed very close together without touching. He found that the 'Cooper pairs' of electrons that make up the supercurrent (a current that flows without resistance) in superconductors could miraculously jump, or 'tunnel', across the gap without needing an applied electric voltage.

The size of the supercurrent flowing through this 'tunnel barrier' depends on whether the superconductors at either edge of the gap have the same or a different phase — a property of the quantum-mechanical wavefunction that describes the behaviour of Cooper pairs. In a bulk superconductor, any phase changes in the wavefunction between local regions gives rise to supercurrent flow. Alternatively, forcing a supercurrent to flow produces phase differences, even across a thin non-conducting or insulating barrier.

Consider also what happens when superconductors form closed circuits, such as loops. Now the total phase that accumulates around the loop when supercurrent flows must be an integer multiple of 2π, to maintain the continuity of the wavefunction. This causes magnetic flux in the system to be quantized. The Josephson effect can be combined with this flux quantization to produce a superconducting direct-current quantum interference device3 (d.c.-SQUID). In these devices, a split superconducting path with two Josephson junctions can sustain a maximum supercurrent, the amplitude of which can be modulated by the amount of magnetic flux piercing the loop (Fig. 1). Such d.c.-SQUIDs are among the most sensitive detectors of magnetic flux ever created and have found many practical applications3.

Figure 1: A direct-current superconducting quantum interference device (d.c.-SQUID).

a, In d.c.-SQUIDs, a superconducting loop contains two Josephson junctions — thin insulating barriers (yellow) sandwiched between the two superconductors (red and blue). b, The maximum electrical current (I, black, left axis) flowing through the device from left to right can be fully modulated by the amount of magnetic flux (Φ) passing through the loop. I0 is the maximum current that can flow through the d.c.-SQUID; Φ0 is the magnetic flux quantum, 2.07 × 10−15 webers. Giazotto and Martínez-Pérez1 have observed an interference effect for heat flow (, red, right axis; 0 is the maximum total heat-flow current) through a d.c.-SQUID: the total amount of heat passing through the device can also be modulated by an applied magnetic flux.

In addition to the phase-dependent supercurrent, Josephson discovered2 two other currents that are present when a finite voltage difference exists across a junction. These currents were caused by the tunnelling of quasiparticles (lone electrons from broken Cooper pairs) or of quasiparticles with Cooper pairs. The first type was similar to the flow of electrons through normal metal–metal junctions, but the second type of current was rather odd: it involved a dynamic process in which the tunnelling occurred in conjunction with processes for breaking and recombining Cooper pairs. Because Cooper pairs are involved, this current should exhibit interference effects analogous to those seen in d.c.-SQUIDs (in which differences in the wavefunction's accumulated phase along the two paths of a loop create constructive or destructive interference). But electrical experiments that clearly quantify the behaviour of this 'interference current' have remained elusive4.

What does all this talk of electrical currents have to do with thermal properties? Well, according to the Wiedemann–Franz law, a metal's thermal conductivity is proportional to its electrical conductivity (and to temperature). This is because electrons can transport some of the heat in a metal. Only three years after Josephson's seminal work, it was proposed5 that thermal conduction through a Josephson junction should involve both quasiparticle flow and the strange interference current that is influenced by the phase across the junction. Most of Josephson's predictions were demonstrated experimentally during the decade following his discovery, but this prediction has lain dormant for many years6.

Giazotto and Martínez-Pérez have now observed the interference effect of heat flow in a study that uses essentially the same d.c.-SQUID arrangement as that used for the electrical experiments. By heating one side of the d.c.-SQUID (the red side in Fig. 1) and monitoring the temperature difference across it, the authors verified that the total heat flux through the device can be modulated by an applied magnetic flux, just as predicted7. The interference heat current has the interesting property of being able to conduct energy in the opposite direction to the temperature drop across a junction. This allowed the researchers to reduce the quasiparticle heat conductance by tuning the phase difference across each junction using magnetic flux, while maintaining net heat conductance in the direction of the temperature drop, in agreement with the second law of thermodynamics.

The quantum interference of heat currents measured by Giazotto and Martínez-Pérez is unique — it is unlike the standard thermoelectric effects discovered in the early 1800s (in which temperature differences are converted into voltage, and vice versa) and the related, more exotic effects that involve applied magnetic fields. It resembles the interference effects resulting from 'Andreev reflection' within loops formed from junctions between normal metals and superconductors8, but those effects are still thermoelectric in nature.

Systems that have interdependent thermal, electric and magnetic properties are immensely important for making practical heat-controlling devices. Exploring superconducting, atomic and molecular junctions, or other nanoscale systems, could lead (and in some cases has already led) to the development of chip-scale heat engines or refrigerators, and energy-harvesting machines9. A limitation of superconducting devices is that they need low temperatures to operate, but there are applications for which cryogenic conditions are an advantage. One example is the transition-edge sensor — a device for detecting photons that has made a huge impact on radioastronomy10. These sensors, and other devices that measure the power of incident electromagnetic radiation, could benefit from Giazotto and Martínez-Pérez's discovery. A device in which thermal conductance can be rapidly tuned using magnetic flux could help to eliminate the heat from a radio telescope's camera pixels, increasing the frame rate for acquiring images and reducing the total time required to map the sky.


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Correspondence to Raymond W. Simmonds.

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Simmonds, R. Quantum interference heats up. Nature 492, 358–359 (2012).

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