First-principles study on the electronic structure of Pb10−xCux(PO4)6O (x=0, 1) | Hacker News Reader

First-principles study on the electronic structure of Pb10−xCux(PO4)6O (x=0, 1)

arxiv.org

Looks like the flood gates are open now. I’d expect a lot on the arxiv over the next few days. A priori, theory like this should be supportive (because calculations like these can’t prove the opposite) and experiment should be antagonistic (because the majority of things that you can accidentally make don’t superconduct at room temperature).

> because calculations like these can’t prove the opposite

You meant the calculations can't show it's a superconductor, but can only show that some materials aren't?

On that note, I’d like to see a paper about the failed replication attempts especially from the Indian lab that ended up with a paramagnetic insulator. Not that I’d understand anything, but a comparison of various attempts might lead us to the understanding of what works and what doesn’t.

This and the other theoretical paper that has been linked in another HN thread agree that there are chances of superconductivity only when copper substitutes lead in certain crystal positions and not in the other positions.

If this is correct, then it is expected that it will be very hard to produce good samples, because when impurity atoms are introduced in a crystal it is very difficult to control the final positions of the atoms, when there is little energy difference between alternatives.

Minor differences in heat treatment can cause great differences in the electrical and magnetic properties of the samples.

So it is likely that some time will pass until we will know for sure whether this material can be a superconductor, unless some laboratory gets very lucky.

I suppose that the reason why the Korean team was not really ready to publish their results is because they are not able yet to produce material samples in a reproducible manner.

It may also be that this sort of crystal is impossible to construct with uniformity and in large quantities. But there's still new chemistry here.

I would love to see it too.

Papers about failed experiments are worth a lot more than no papers about failed experiments. Alas, it is rare.

I think this paper is by the Indian lab you're talking about https://arxiv.org/abs/2307.16402

Can’t we work backwards and define a molecular structure for a SC and have software assisted program try to get this?

Looks like someone did exactly that

https://twitter.com/Andercot/status/1686215574177841152

I really appreciate the final line in that post.

> This is insanely bullish for humanity.

:heart:

Parameter space is too large, and the simulations too expensive.

People have been trying to get there for decades.

As I understand it, a quantum computer might help here, but we're not there yet.

It almost feels like we're on the brink of some revolutionary discoveries: quantum computers, room-temperature superconductors, fusion, general artificial intelligence. Unless it's all hype. I'm reluctant to be optimistic.

Maybe the AI can help us develop a quantum computer with which we'll find useful materials to build a fusion reactor!

Well, a real experimental system is a quantum computer that 'calculates' the emerging behavior in real time. Sorry, that was needlessly sarcastic---actually, you have a good point there: it's ironic that we used digital computers to simulate quantum systems, and now we're beginning to use quantum computers to calculate digital properties (like decryption, etc), whereas it would be interesting to actually use quantum computers to calculate quantum systems such as electronic structure of many body systems. It's just that we're nowhere near that yet.

This was actually the original purpose of quantum computing as proposed by Feynman.

How might a quantum computer help? I was under the impression that there are only two quantum algorithms that are concretely known to provide exponential speedups for interesting problems relative to known classical state-of-the-art, and neither of them (Shor's and Grover's) appears to be useful for physics simulations. Was I mistaken?

There's another problem, the original one that quantum computers were conceived to solve: Simulating a quantum system.

It's been a while since college physics, are classic superconductors quantum mechanical effects as well?

Yes. The theory that explains the better understood ones works based on the idea of "cooper pairs", where there are, aiui, entangled pairs of electrons which are in a lower energy state due to how they are entangled, and where in order to get like, bumped around in a way that would produce resistance, they would have to change in energy in a way by an amount that isn't available?

So, very much a quantum mechanical effect.

Cooper pairs are not entangled. They stick together because the first electron causes atoms to clump a little bit, so that they produce a locally higher positive charge, that in turn attracts the other electron.

Are you sure? I mean, not the second part. That part matches my impression of things. But them not being entangled. My understanding is that collectively, the pair of electrons acts like a boson, unlike an individual electron, which allows multiple such pairs to be in the same state, and, I would expect that this would require the electrons in each pair to be entangled?

Because reasoning about the real deal sounds like it would be rather difficult for me (and likely too difficult for me without significant assistance, at least, within any reasonable about of time for me to spend on this), I want to make up a toy model now.

Say I have a single-electron Hilbert space and a single electron Hamiltonian on it (where, I would later maybe add terms for interactions between the electrons, and/or a space for how the surrounding material can change in ways tied to the electrons). Below a certain energy level, I want to say that the eigenspace of the single electron Hamiltonian for each lower energy level, is finite-dimensional, and also the spectrum is discrete. (and, I want to consider the electrons only with energies below this threshold.)

For any wavefunction in the single-electron Hilbert space, there is a corresponding creation operator acting on the Fock space.

Now, I imagine that without any interactions, the concept of a cooper pair is probably inapplicable. But, I am imagining that when we add in the interactions, that, at least at low energies, the Fock space obtained from the single-electron Hilbert space, should work as a Hilbert space for the many-particle system with interactions between electrons (and then, I guess take the tensor-product with another Hilbert space representing how nuclei can change, when handling that part).

Everything in the Fock space can be obtained as a linear combination of applications of some number of creation operators to the vacuum state. As such, a state with a single cooper pair can be expressed as a linear combination of states obtained by applying two creation operators to the vacuum state.

Unless this "linear combination" can be done with only a single term, this would be an entangled state, right?

I would think that there should be creation operators for cooper pairs, consisting of a linear combination of products of two creation operators for electrons?

You don't need them to be entangled to act as a boson.

A Cooper pair is a composite object, and you absolutely need to consider the atomic lattice of the superconductor.

So you end up with your electron being entangled with all the surrounding atoms in the lattice. And all other electrons.

Ah, so it isn't so much that they don't need to be entangled, so much as, describing them as entangled isn't a good way to frame it, because all the electrons (and the rest of the material) will be all entangled with each-other, so, it isn't a distinguishing feature, and misleading to focus on the two in the pair being entangled?

Yes, pretty much.

Is there a known method for doing this, or is it just theoretically possible but no actual algorithm?

as someone who don't know anything about anything I've been bugging GPT4 with the questions about this material, if you are curious to see the conversation https://chat.openai.com/share/50bceb29-7042-40aa-bc13-a97443...

please, issue corrections in the comments if you have a second

I think this conversation demonstrates a misunderstanding of what GPT4 can and cannot do. You can get useful background information about DFT and molecular simulation, but definitely no first-principles reasoning about molecular properties.

good to know, thank you for the note! maybe there can be a prompt that can investigate molecular properties?

GPT can't run simulations or break any new ground.

makes sense

This is not snark, just trying to understand but: why would you expect a text autocompleter to answer questions about cutting edge material science?

just curious and trying to understand better what text autocompletion is capable of

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