Superconductivity is like an Eldorado for electrons, as they flow without resistance through a conductor. However, it only occurs below a very low critical temperature. Physicists now believe they can enhance superconductivity - the idea is to externally drive its underlying physical phenomena by changing how ions vibrating in the crystal lattice of the conductor material, called phonons, interact with electron flowing in the material. Andreas Komnik from the University of Heidelberg and Michael Thorwart from the University of Hamburg, Germany, adapted the simplest theory of superconductivity to reflect the consequences of externally driving the occurrence of phonons. Their main result, published in *EPJ B*, is a simple formula explaining how it is theoretically possible to raise the critical temperature using phonon driving.

The authors studied the all-important autocorrelation function of phonons in the superconductivity BCS theory, named after John Bardeen, Leon Cooper and John Robert Schrieffer. Superconductivity is induced by phonons cooperating to bring the electrons together in the so-called Cooper pairsâ€”against their spontaneous tendancy to repel each other. In this work, the authors focused on the scenario of an X-ray light field rattling the phonons. They realised that a kind of driving, which controls the frequency of vibration of the lattice sites, can profoundly change the pairing of the electrons.

However, electrons and phonons do not follow the same internal clock. This means that change at what is perceived as a normal pace for phonons comes across as extremely slow to electrons. To eliminate this discrepancy, the author devised a solution based on bringing a clever time-averaging procedure into the BCS equations. This theoretical approach, the authors found, reveals the controlled elevation of the critical temperature. They thus managed to integrate the external phonon drive into the standard BCS theory. The advantge is that the critical temperature can be computed from this simple formula and can, in theory, be considerably elevated using the driving procedure. Suprisingly, the critical temperature was even higher up when further refinment to the equations accounted for phonon-phonon interactions.

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**More information:**
Andreas Komnik et al, BCS theory of driven superconductivity, *The European Physical Journal B* (2016). DOI: 10.1140/epjb/e2016-70528-1

## Macksb

The "crystal vibrations" here are periodic oscillations--phonons.

The "inner clock" of these vibrations is "extremely slow" compared to that of electrons. But "driving the frequency of the vibrations" can "profoundly change the pairing of the electrons." The critical temperature of superconductivity onset can be increased with such phonon "driving."

Moreover, such critical temperature can be increased even higher by "accounting for phonon-phonon interactions." These phonon interactions are also a form of coupled periodic oscillations.

So the highest "super" temp results when (a) phonons couple their oscillations and (b) the periodic oscillation frequency of the phonons more closely matches the periodic oscillation frequency of the electrons.

The product is Cooper pairs. Cooper pairs are two electrons in which the periodic oscillations of the electrons are coupled in two ways.

## Macksb

Cooper pairs are joined perfectly in two ways. Spin up for A and spin down for B. Clockwise orbit for A and counterclockwise orbit for B. In both cases the coupling is exactly anti-synchronous. Exactly 180 degrees apart. So paired, the system is a boson, not a fermion.

At every pairing step in this progress towards superconductivity, the pairing is a pairing of periodic oscillations. In a two oscillator system, pairing can only take one of two forms: exactly anti-synchronous, or exactly synchronous.

Think of Huygens' clocks, where the two pendulums coupled 350 years ago. That was anti-synchronous coupling. Or think of our moon, where two different types of periodic oscillations, orbit and spin, are coupled synchronously. Mercury has a 3:2 period coupling of spin to orbit.

## Macksb