Lawrence Berkeley Lab Researchers Optimize Higher Density Copper Doping to Make LK99 Variant into a Superconductor

Lawrence Berkeley National Lab researchers use computational methods to describe an approach for optimizing the LK99 material as a superconductor.

Some will say, hey why is Nextbigfuture still covering LK99. Didn’t some angry scientists say that LK99 was not a superconductor? I have been covering science for over 20 years and there are a lot of angry scientists who believe many things will not work. Scientists going into experiments looking to debunk something will not be the ones who figure out how to make it work.

Lawrence Berkeley National Lab researchers spent time and worked on supercomputers to try to figure out how to make LK99 work. There computational work is showing promise.

Science is Hard

There were AI winters over the decades. In 1969, Marvin Minsky proved that single layer neural networks were very limited. Mainstream research into perceptrons ended partially because the 1969 book Perceptrons by Marvin Minsky and Seymour Papert emphasized the limits of what perceptrons could do. While it was already known that multilayered perceptrons are not subject to the criticism, nobody in the 1960s knew how to train a multilayered perceptrons. Backpropagation was still years away. Major funding for projects neural network approaches was difficult to find in the 1970s and early 1980s. Important theoretical work continued despite the lack of funding. The “winter” of neural network approach came to an end in the middle 1980s, when the work of John Hopfield, David Rumelhart and others revived large scale interest.

Here is a 52 page paper by Nobel Prize winner in Physics, Philip Anderson. Philip wrote a personal history of his engagement with the high-Tc problem of the cuprate superconductors, in rather informal and autobiographical style. As the work proceeded he realized that it was impossible and would have been dishonest to separate out my rather amusing but seminal early fumblings from the complete restructuring of the problem which he have achieved during the past decade. The Nobel Prize in Physics 1977 was awarded jointly to Philip Warren Anderson, Sir Nevill Francis Mott and John Hasbrouck Van Vleck “for their fundamental theoretical investigations of the electronic structure of magnetic and disordered systems.

JANUARY 1987: THE CUPRATES CHANGE MY LIFE, TOO
It is not widely known that John Bardeen produced at least three wrong theories of superconductivity before BCS, the one which got it right. Two of his previous attempts were published, one, in 1951, with great fanfare. The difference between John and the many other brilliant physicists who attempted theories of superconductivity (among them Einstein, Feynman and Heisenberg ) was that he was willing to admit that he had been wrong, go back to the beginning and start over.

At Bell I met my close friend Ted Geballe, past supervisor and collaborator of the charismatic Bernd Matthias, who is rightly considered the father of the field of superconducting materials. Ted, it turned out, had just returned from the Materials Research Society meeting in Boston, the first week of December, where a highly reliable Japanese researcher, Kitazawa, had surprised everyone by confirming unequivocally the results on a new superconductor, (La,Ba)2CuO4, with a transition temperature over 30 degrees, which had been published obscurely six months earlier by Georg Bednorz and Alex Muller. Ted , although a very down-to-earth empiricist, who shares to an extent Bernd’s disdain for theories not his own, is somewhat optimistic on the subject of high-Tc superconductors, and has been known to fall for an occasional USO (unidentified superconducting object); but he convinced me this one was real. Paul Chu of Houston also confirmed the new results at this meeting.

You can see in the descriptions that people can get things completely wrong in science. It can take many tries and many years to work out complex problems and materials. Some very good scientists can have a disdain for theories that are not their own.

Twenty years of talking past each other: The theory of high Tc

In 1988, the outline of an essentially correct theory of the high Tc cuprates was published by two groups, Zhang et al. in Zurich and Kotliar et al. in the US, based on earlier suggestions. The rather startling experimental predictions:
1. that the gap would be real d-wave with nodes;

2. that the gap would greatly increase with underdoping;

3. that Tc would exhibit a dome terminating linearly around x = 30%;

were so bizarre that these papers gathered little attention from others, including myself and at least 8 other Nobel prize-winners, and as they came to be substantiated one by one nobody much noticed that fact until the method was revived a dozen years later by Paramekanti et al. and Sorella et al. I will discuss some recent achievements and generalizations of these methods.

Back the Lawrence Berkeley National Lab Work

The flurry of theoretical and experimental studies following the report of room-temperature superconductivity at ambient pressure in Cu-substituted lead apatite CuxPb10−x(PO4)6O (‘LK99’) have explored whether and how this system might host strongly correlated physics including superconductivity. While first-principles calculations at low doping (x ≈ 1) have indicated a Cu-d9 configuration coordinated with oxygen giving rise to isolated, correlated bands, its other structural, electronic, and magnetic properties diverge significantly from those of other known cuprate systems. Here we find that higher densities of ordered Cu substitutions can result in the formation of contiguous edge-sharing Cu-O chains, akin to those found in some members of the cuprate superconductor family. Interestingly, while such quasi-one-dimensional edge-sharing chains are typically ferromagnetically coupled along the chain, we find an antiferromagnetic ground-state magnetic order for our cuprate fragments which is in proximity to a ferromagnetic quantum critical point. This is a result of the elongated Cu-Cu distance in Cu-substituted apatite that leads to larger Cu-O-Cu angles supporting antiferromagnetism, which we demonstrate to be controllable by strain. Finally, our electronic structure calculations confirm the low-dimensional nature of the system and show that the bandwidth is driven by the Cu-O plaquette connectivity, resulting in an intermediate correlated regime.

The Cu-substituted apatites provide a new system for understanding one-dimensional cuprate chains in a previously inaccessible coupling regime. The large lattice vector (Cu-Cu separation) compared with other edgesharing cuprates leads to a larger Cu-O-Cu angle. In turn, this enabled a stronger effective Cu-Cu nearestneighbor interaction, stabilizing antiferromagnetic ordering, in contrast to typically ferromagnetic edge-sharing cuprates. Calculations show that the Cu-4 structure is very close to a ferromagnetic ground state, indicative of strongly frustrated interactions and proximity to a quantum critical point.

This transition is dependent on the Cu-O-Cu angle, and can be tuned by structural modifications as seen below.

The increased band width of the Cu-dxy states at the Fermi level seen in Cu-2 and Cu-4 over the previously examined x = 1 structure is an expected result of halving the Cu-Cu separation along the c direction. While the Cu-Cu separation is large compared to other edgesharing cuprates, which could be expected to reduce the band width, the researchers find the structures to be in the intermediate coupling regime, favorable for superconductivity.

This is in part due to the distortion to larger Cu-O-Cu bond angles which is also seen to stabilize an antiferromagnetic ground state. The oxygen atoms that constitute the plaquettes are also bound to the PO4 units, the size of which, along with the c lattice constrains the CuO bond lengths and the Cu-O-Cu angle. Substitutions on the B sites may allow for a further tuning of the correlation and antiferromagnetic ordering.

The proposed structure requires substantially higher doping than has been reported experimentally and also with a high degree of site selectivity to facilitate macroscopic cuprate chains. This is not insurmountable as both solid-solution and ordered doping of apatite structures are common. Reported synthesis attempts have been carried out under ambient pressure and using oxygen as the channel species X. Recent theoretical work has identified that pressure, strain, and channel species call all have a strong effect on the site selectivity of the copper dopants.