Pairs in the cuprates at higher energies than superconductivity

I've been asked by student readers over the years about how scientists come up with research ideas.  Sometimes you make an unanticipated observation or discovery, and that can launch a research direction that proves fruitful.  One example of that is the work our group has done on photothermoelectric effects in plasmonic nanostructures - we started trying to understand laser-induced heating in some of our plasmonic devices, found that the thermoelectric response of comparatively simple metal nanostructures was surprisingly complicated, and that's led to some surprising (to us) insights and multiple papers including a couple in preparation.

In contrast, sometimes you have a specific physics experiment in mind for a long time, aimed at a long-standing problem or question, and getting there takes a while.  That's the case with our recent publication in Nature.

I've written a bit about high temperature superconductivity over the years (here, here, here, here).  For non-experts, it's hard to convey the long historical arc of the problem of high temperature superconductivity in the copper oxides.

Superconductivity was first discovered in 1911 in elemental mercury, after the liquefaction of helium made it possible to reach very low temperatures.  Over the years, many more superconductors were discovered, metallic elements and compounds.  Superconductivity is a remarkable state of matter and it took decades of study and contributions by many brilliant people before Bardeen, Cooper, and Schrieffer produced the BCS theory, which does a good job of explaining superconductivity in many systems.  Briefly and overly simplified, the idea is that the ordinary metallic state (a Fermi liquid) is often not stable.  In ordinary BCS, electrons interact with phonons, the quantized vibrations of the lattice - imagine an electron zipping along, and leaving behind in its wake a lattice vibration that creates a slight excess of positive ionic charge, so that a second electron feels some effective attraction to the first one.  Below some critical temperature \(T_{c}\), electrons of opposite spin and momenta pair up.   As they pair up, the paired electrons essentially condense into a single collective quantum state.  There is some energy gap \(\Delta\) and a phase angle \(\phi\) that together make up the "order parameter" that describes the superconducting state.  The gap is the energy cost to rip apart a pair; it's the existence of this gap, and the resulting suppression of scattering of individual carriers, that leads to zero electrical resistance.  The collective response of the condensed state leads to the expulsion of magnetic flux from the material (Meissner effect) and other remarkable properties of superconductors.  In a clean, homogeneous traditional superconductor, pairing of carriers and condensation into the superconducting state are basically coincident.

In 1986, Bednorz and Muller discovered a new family of materials, the copper oxide superconductors.  These materials are ceramics rather than traditional metals, and they show superconductivity often at much higher temperatures than what had been seen before.  The excitement of the discovery is hard to overstate, because it was a surprise and because the prospect of room temperature superconductivity loomed large.  Practically overnight, "high-Tc" became the hottest problem in condensed matter physics, with many competing teams jumping into action on the experimental side, and many theorists offering competing possible mechanisms.  Competition was fierce, and emotions ran high.  There are stories about authors deliberately mis-stating chemical formulas in submitted manuscripts and then correcting at the proof stage to avoid being scooped by referees.   The level of passion involved has been substantial.   Compared to the cozy, friendly confines of the ultralow temperature physics community of my grad days, the high Tc world did not have a reputation for being warm and inviting.

As I'd mentioned in the posts linked above, the cuprates are complicated.  They're based on chemically (by doping) adding charge to or removing charge from materials that are Mott insulators, in which electron-electron interactions are very important.  The cuprates have a very rich phase diagram with a lot going on as a function of temperature and doping.  Since the earliest days, one of the big mysteries in these materials is the pseudogap (and here), and also from the earliest days, it has been suggested (by people like Anderson) that there may be pairs of charge carriers even in the normal state - so-called "preformed pairs".  That is, perhaps pairing and global superconductivity have different associated energy and temperature scales, with pair-like correlations being more robust than the superconducting state.  An analogy:  Superconductivity requires partners to pair up and for the pairs to dance in synch with each other.  In conventional superconductors, the dancing starts as soon as the dancers pair up, while in the cuprates perhaps there are pairs, but they don't dance in synch.

Moreover, the normal state of the cuprates is the mysterious "strange metal".  Some argue that it's not even clear that there are well-defined quasiparticles in the strange metal - pushing the analogy too far, perhaps it doesn't make sense to even think about individual dancers at all, and instead the dance floor is more like a mosh pit, a strongly interacting blob.

I've been thinking for a long while about how one might test for this.  One natural approach is to look at shot noise (see here).  When charge comes in discrete amounts, this can lead to fluctuations in the current.  Imagine rain falling on your rooftop.  There is some average arrival rate of water, but the fluctuations about that average rate are larger if the rain comes down in big droplets than if the rain comes falls as a fine mist.  Mathematically, when charges of magnitude \(e\) arrive at some average rate via a Poisson process (the present charge doesn't know when the last one came or when the next one is coming, but there is just some average rate), the mean square current fluctuations per unit bandwidth are flat in frequency and are given by \(S_{I} = 2 e I\), where \(I\) is the average current.  For electrons tunneling from one metal to another, accounting for finite temperature, the expectation is \(S_{I} = 2 e I \coth (eV/(2 k_{\mathrm{B}}T) )\), which reduces to \(2 e I\) in the limit \(eV >> k_{\mathrm{B}}T\), and reduces (assuming an Ohmic system) to Johnson-Nyquist noise \(4 k_{\mathrm{B}}T/R\)  in the \(V \rightarrow 0\) limit, where \(R = V/I\).

TLDR:  Shot noise is a way to infer the magnitude of the effective charge of the carriers.

In our paper, we use tunnel junctions made from La_2-xSr_xCuO₄ (LSCO), an archetypal cuprate superconductor (superconducting transition around 39 K for x near 0.15), with the tunneling barrier between the LSCO layers being 2 nm of the undoped, Mott-insulating parent compound, La₂CuO₄.   We could only do these measurements because of the fantastic material quality, the result of many years of effort by our collaborators.   We looked at shot noise in the tunneling from LSCO through LCO and into LSCO, over a broad temperature and voltage range.

The main result we found was that the noise in the tunneling current exceeded what you'd expect for just individual charges, both at temperatures well above the superconducting transition, and at bias voltages (energy scales) large compared to the superconducting gap energy scale.  This strongly suggests that some of the tunneling current involves the transport of two electrons at a time, rather than only individual charges.  (I'm trying to be very careful about wording this, because there are different processes whereby charges could move two at a time.)  While there have been experimental hints of pairing above Tc for a while, this result really seems to show that pairing happens at a higher energy scale than superconductivity.  Understanding how that relates to other observations people have made about the pseudogap and about other kinds of ordered states will be fun.   This work has been a great educational experience for me, and hopefully it opens the way to a lot of further progress, by us and others.