## Wednesday, August 21, 2019

### 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 La2-xSrxCuO4 (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.

## Friday, August 16, 2019

### "Seeing" chemistry - another remarkable result

I have written before (here, here) about the IBM Zurich group that has used atomic force microscopy in ultrahigh vacuum to image molecules on surfaces with amazing resolution.  They've done it again.  Starting with an elaborate precursor molecule, the group has been able to use voltage pulses to strip off side groups, so that in the end they leave behind a ring of eighteen carbon atoms, each bound to its neighbor on either side.  The big question was, would it be better to think of this molecule as having double bonds between each carbon, or would it be energetically favorable to break that symmetry and have the bonds alternate between triple and single.  It turns out to be the latter, as the final image shows a nonagon with nine-fold rotational symmetry.  Here is a video where the scientists describe the work themselves (the video is non-embeddable for some reason).  Great stuff.

## Sunday, August 11, 2019

### APS Division of Condensed Matter Physics invited symposium nominations

While I've rotated out of my "member-at-large" spot on the APS DCMP executive committee, I still want to pass this on.  Having helped evaluate invited symposium proposals for the last three years, I can tell you that the March Meeting benefits greatly when there is a rich palette.

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The DCMP invited speaker program at March Meeting 2020 is dependent on the invited sessions that are nominated by DCMP members. All invited speakers that we host must be nominated in advance by a DCMP member.

The deadline to submit a nomination is coming up soon: August 23, 2019.

Please take a moment to submit an invited session nomination.

Notes regarding nominations:
• All nominations must be submitted through ScholarOne by August 23, 2019.
• In ScholarOne, an invited session should be submitted as an "Invited Symposium Nomination".
• An invited session consists of 5 speakers. You may include up to 2 alternate speakers in your nomination, in the event that one of the original 5 does not work out.
• While no invited speakers will be guaranteed placement in the program until after all nominations have been reviewed, please get a tentative confirmation of interest from your nominated speakers. There will be a place in the nomination to indicate this.
• A person cannot give technical invited talks in two consecutive years. A list of people that gave technical invited talks in 2019, and are therefore ineligible for 2020, can be found on this page.
• Nominations of women, members of underrepresented minority groups, and scientists from outside the United States are especially encouraged.
Be sure to select a DCMP Category in your nomination. DCMP categories are:
07.0 TOPOLOGICAL MATERIALS (DCMP)
09.0 SUPERCONDUCTIVITY (DCMP)
11.0 STRONGLY CORRELATED SYSTEMS, INCLUDING QUANTUM FLUIDS AND SOLIDS (DCMP)
12.0 COMPLEX STRUCTURED MATERIALS, INCLUDING GRAPHENE (DCMP)
13.0 SUPERLATTICES, NANOSTRUCTURES, AND OTHER ARTIFICIALLY STRUCTURED MATERIALS (DCMP)
14.0 SURFACES, INTERFACES, AND THIN FILMS (DCMP)
15.0 METALS AND METALLIC ALLOYS (DCMP)

Thank you for your prompt attention to this matter.

Daniel Arovas, DCMP Chair, and Eva Andrei, DCMP Chair-Elect

## Wednesday, July 31, 2019

### More brief items

Writing writing writing.  In the meantime:

## Monday, July 22, 2019

### Ferromagnetic droplets

Ferromagnets are solids, in pretty nearly every instance I can recall (though I suppose it's not impossible to imagine an itinerant Stoner magnet that's a liquid below its Curie temperature, and here is one apparent example). There's a neat paper in Science this week, reporting liquid droplets that act like ferromagnets and can be reshaped.

The physics at work here is actually a bit more interesting than just a single homogeneous material that happens to be liquid below its magnetic ordering temperature.  The liquid in this case is a suspension of magnetite nanoparticles.  Each nanoparticle is magnetic, as the microscopic ordering temperature for Fe3O4 is about 858 K.  However, the individual particles are so small (22 nm in diameter) that they are superparamagnetic at room temperature, meaning that thermal fluctuations are energetic enough to reorient how the little north/south poles of the single-domain particles are pointing.  Now, if the interface at the surface of the suspension droplet confines the nanoparticles sufficiently, they jam together with such small separations that their magnetic interactions are enough to lock their magnetizations, killing the superparamagnetism and leading to a bulk magnetic response from the aggregate.  Pretty cool!  (Extra-long-time readers of this blog will note that this hearkens waaaay back to this post.)

## Saturday, July 13, 2019

### Brief items

I just returned from some travel, and I have quite a bit of writing I need to do, but here are a few items of interest:

• No matter how many times I see them (here I discussed a result from ten years ago), I'm still impressed by images taken of molecular orbitals, as in the work by IBM Zurich that has now appeared in Science.  Here is the relevant video.
• Speaking of good videos, here is a talk by Tadashi Tokieda, presently at Stanford, titled "Science from a Sheet of Paper".  Really nicely done, and it shows a great example of how surprising general behavior can emerge from simple building blocks.
• It's a couple of years old now, but this is a nice overview of the experimental state of the problem of high temperature superconductivity, particularly in the cuprates.
• Along those lines, here is a really nice article from SciAm by Greg Boebinger about achieving the promise of those materials.
• Arguments back and forth continue about the metallization of hydrogen.
• And Sean Carroll shows how remunerative it can be to be a science adviser for a Hollywood production.

## Friday, July 05, 2019

### Science and a nation of immigrants

It was very distressing to read this news article in Nature about the treatment of scientists of Chinese background (from the point of view of those at MIT).  Science is an international enterprise, and an enormous amount of the success that the US has had in science and technology is due to the contributions of immigrants and first-generation children of immigrants.  It would be wrong, tragic, and incredibly self-defeating to take on a posture that sends a message to the international community that they are not welcome to come to the US to study, or that tells immigrants in the US that they are suspect and not trusted.

In any large population, there is always the occasional bad actor - the question is, how does a bureaucracy react to that?  One example:  Clearly some small percentage of medical researchers in the US have behaved unethically, taking money from medical and pharmaceutical companies in ways that set up conflicts of interest which they have hidden.  That's wrong, we should try to prevent it from happening, and those who misbehave should be punished.  The bureaucratic response to this has been that basically nearly every faculty member at a research university in the US now has to fill out annual disclosure and conflict of interest forms.   The number of people affected by the response dwarfs the number of miscreants by probably a factor of 1000, though in this case the response is only at the level of an inconvenience, so the consequences have not been dire.

Reacting to the bad behavior of a tiny number of people by taking wholesale measures that make an entire population feel threatened, unwelcome, and presumed guilty, is wrong and lazy.  The risk of long term negative impacts far beyond the scale of any original bad behavior is very real.