The top student must be diligent.

Chapter 181 Xiao's Superconductivity Theory, Physics and Mathematics Jokes
Time passed quickly, and in the following period, Xiao Yi began to participate in the design of the Science Island laboratory.

For example, site selection, and how to design the overall structure of the laboratory based on the site selection, etc.

To this end, Xiao Yi spent several days studying laboratory design and related books on architectural design.

After all, this laboratory was built specifically for him, and as the future director of the Science Island Laboratory, he had to think about where he would probably work for a long time in the future.

After a few days of simple research, he was able to say with confidence that even if he was not a master architect, he could be called a top design expert.

Architectural design is basically about playing around with structural mechanics, which also requires considering the relevant properties of various building materials.

Considering that a building is often quite large, the entire design becomes more complicated.

But for Xiao Yi, if it was just complicated, it would not be a big deal at all.

It's nothing more than a lot of calculations, and calculations are the least of his problems.

Asking him to participate in the Brain or something like that is basically a dimensionality reduction attack.

He had actually received an invitation to participate in the show "The Brain" before, but of course he was not interested in this kind of show.

In short, after returning from his studies, the suggestions he made from time to time surprised the design team responsible for designing the Science Island laboratory.

Their team has taken over many laboratory-related designs, such as a bunch of research institute laboratories on Science Island, in which they have participated. In addition, they have also undertaken design tasks for many national key laboratories and even national laboratories. Even for foreign laboratories, they have participated in the design. They can be regarded as one of the top teams in the world.

But almost every suggestion Xiao Yi made was able to bring them some inspiration, or was better than their original designs, which made them wonder, is it possible that someone with a high IQ could be proficient in even this kind of architectural design?
Fortunately, Xiao Yi is not a full-time designer, otherwise how could they make a living?

In this way, with Xiao Yi's help, their design speed was accelerated.

In addition to laboratory design, another important point is the purchase of various experimental equipment, instruments and other supplies.

These things are the key to a laboratory. After all, a laboratory is used to conduct experiments. Only sufficiently advanced experimental equipment can help a laboratory continuously make more excellent conclusions.

Therefore, Xiao Yi and his team have already contacted the world's top manufacturers of experimental instruments and equipment, and started to place orders for related experimental instruments and equipment.

Xiao Yi had already thought about which experimental instruments to order, mainly to serve the purpose of mastering the materials.

For example, for some experimental instruments of the same price, some have many additional functions, but their resolution and clarity are slightly weaker, while some have not many additional functions, but their resolution and clarity are high enough.

As for Xiao Yi, what he needs is the latter with high resolution and clarity.

No matter how powerful the additional functions of the experimental equipment are, can they compare to the additional functions that come with his plug-in?
joke!

Do you know what a plug-in is?
Of course, considering that he now has sufficient funding, both of these can be satisfied.

Anyway, out of the 5 million, 4 million can be used to purchase experimental instruments, and the remaining 1 million is for the cost of building materials. After all, the building materials needed to construct a laboratory must be relatively advanced. For example, to maintain the internal temperature and other properties, the impact of temperature is often very large for experiments.

Considering Xiao Yi's high requirements, the cost of 1 million is relatively reasonable.

As for the land price, that doesn't exist. The Science Island Laboratory has a total of more than 10 acres of land, which was completely donated by the Feicheng Municipal Government. According to the land price on Science Island, it is almost equivalent to to million yuan.

This is considered an investment by the Feicheng Municipal Government in this laboratory, but it is not included in the provincial-level funding.

In this way, the construction of the Science Island Laboratory began to get on track. The construction time is about one year, mainly the design, and the design acceptance time is expected to take three months. The remaining 9 months are the actual construction and subsequent decoration time.

Apart from paying attention from time to time, Xiao Yi was also busy the rest of the time.

Cracking the mechanism of high-temperature superconductivity has reached a very critical point!

……

"The local electron density fluctuates, enhancing the interactions between electrons..."

"Local electron density fluctuations... local electron density fluctuations..."

Xiao Yi was thinking deeply about this matter in his mind.

"How exactly is the electron interaction enhanced?"

In his mind, he began to review the history of physics, the discovery process of BCS theory, and especially the discovery process of Cooper pairs.

Cooper pairs are a phenomenon of electron correlation, but they are not a strong electron correlation system.

However, in complex material systems such as high-temperature superconductors, the concepts of strong electron correlation and Cooper pairs may work together. Therefore, reviewing this process may also help him reveal the mechanism of high-temperature superconductivity.

The BCS theory explains the superconductivity mechanism of certain low-temperature superconducting metals.

In the 20s, physicists such as John Bardeen had proposed that lattice vibrations might produce an attractive force between electrons, different from the usual Coulomb repulsion between electrons.

Then, Leon Cooper, who proposed the Cooper pair, began to study the behavior of electrons near the Fermi surface. The Fermi surface refers to the maximum energy boundary of electrons at absolute zero.

"In Cooper's study, he hypothesized that if two electrons have a total momentum of zero, that is, the momentum is the same but in opposite directions, and they interact by exchanging phonons, then this interaction can lead to the formation of an electron pair."

Xiao Yi simulated Cooper's original derivation process on the draft paper.

"…Most importantly, he proved through quantum mechanical calculations that when the temperature is below a certain critical value, the formation of electron pairs is spontaneous. Such spontaneously formed electron pairs can reduce the total energy of the system, making the entire system more stable at low temperatures. Even weak electron-phonon interactions can lead to the formation of Cooper pairs."

"Well... this is the key point. Because the temperature is low enough, there is an energy gap between the electronic states near the Fermi surface, so a single electron cannot be easily excited to a higher energy state. At the same time, the temperature does not reach the threshold that exceeds the pairing energy between Cooper pairs, so the interaction between electrons and phonons can allow Cooper pairs to form."

"But at high temperatures, electrons are excited to a higher state, and thermal noise causes random scattering between electrons. Therefore, for these traditional superconductors explained by the BCS theory, superconductivity cannot be achieved at high temperatures."

"For lanthanum-barium-copper oxides such as yttrium-barium-copper oxide, as well as some iron-based superconductors, at higher temperatures, they exhibit strongly correlated electron systems, thus achieving superconductivity."

"For example, in cuprate high-temperature superconductors, Cooper pairs are usually considered to have d-wave symmetry rather than the s-wave symmetry found in conventional superconductors..."

"Local electron density fluctuations... local electron density fluctuations..."

Xiao Yi took out a pen and listed various relevant information on the draft paper.

Looking at all this information, his mind recalled the previous inspirations, until finally, a gleam of light suddenly burst out in his eyes.

"Spin density wave! No, it should be local spin density wave!"

"If we also take the local spin density wave into account..."

"Coupled with local electron density waves..."

"If we combine these two theories to describe the electron-strongly correlated system..."

feasible!
Regardless, this can definitely be considered a research perspective.

Without further ado, he took out a new piece of draft paper.

"Well... we can't directly substitute these two into the equation. It would be best to start from other directions."

"That's right! Hubbard model!"

His eyes lit up and the pen in his hand continued to move.

[Hamiltonian is expressed as: H = t∑[i, j], σ(ciσcjσ+hc)+U∑ini↑ni↓]

[Where t is the amplitude of the electron transition, and U is the energy of the electrons interacting at the same lattice point. ]

"Then there are spin density waves... which can be described by a periodic arrangement of spins."

[Szi] = S0cos(QRi)

"Well... Next, let's simulate the behavior of electrons in iron-based superconductors."

“But we have to build a model first.”

After about two hours, Xiao Yi completed the modeling and input it into the computer. "The next step is to connect to the server."

Xiao Yi spent several hundred thousand to buy the server, but it is still in HKUST.

So, I quickly connected to the server, put the model on it and started running.

The method used in the model is the absolute electronic property calculation. The model he developed has now been widely used in many fields such as materials science and condensed matter.

There is basically no better or more appropriate model for analyzing his model.

However, in addition to the calculation of absolute electronicity, he also used another method called density matrix renormalization group DMRG. DMRG is particularly suitable for dealing with low-dimensional strongly correlated electron systems, especially in one-dimensional and quasi-one-dimensional systems.

Although FeSe/SrTiO3 is a two-dimensional material, in some cases it can be simplified to a quasi-one-dimensional chain to study local phenomena, which helped Xiao Yi to deeply study the local electronic state distribution and the behavior of spin density waves caused by iron vacancies.

Soon, the results came out.

"Sure enough, the local electron density fluctuations and spin density waves induced by the iron vacancy generate an effective attractive interaction near the Fermi surface...Looking at this numerical result, this interaction is similar to the phonon-mediated attraction in the traditional Cooper pair formation mechanism, but its source is the local magnetic fluctuations induced by the spin density waves."

"Magnetic fluctuations..."

His eyes became brighter and brighter.

“Local electron density fluctuations cause rearrangements of electron states that make it easier for certain electron states to pair up in these regions. Spin density waves induce magnetic fluctuations in these local regions. These fluctuations enhance the attractive interactions between electrons… and so on!”

His expression suddenly became serious and he looked at the simulation data again.

Until the end, he re-listed the two models on the draft paper next to him.

One of them is the local electron density wave model, and the other is the local spin density wave model.

After observing the two models for a long time, he started to work.

"Now I directly assume that when the coupling of electron density waves and spin density waves is considered, the ground state energy of the system is significantly lowered, and at the same time a stronger electron pairing interaction is formed near the Fermi surface..."

After completing the hypothesis, he shook his head with a little emotion: "Tsk, no matter what, I'm still a little uncomfortable with this way of hypothesis."

Although he made many important achievements in physics, psychologically he still recognized his identity as a mathematician. However, some methods in physics were quite difficult to accept from a mathematical point of view.

It’s like a joke: [Mathematicians may be angry when they see this step, but we don’t care].

This is what he does now. He makes an assumption first, and then uses it regardless of whether the assumption is correct or not.

After use, conduct a control experiment. As long as the experiment verifies that it is correct, then the hypothesis is correct.

For mathematicians, it is like directly assuming that the Riemann hypothesis is correct. Of course, physicists sometimes really assume that the Riemann hypothesis is correct. This is mainly because mathematics can be infinite, but for physics, there is no real infinity. The range of series that have been verified so far is enough for physicists to use. Therefore, the Riemann hypothesis has been used in many theories of physics, such as quantum chaos theory, statistical mechanics, random matrix theory, etc.

In short, mathematicians are like this, while physicists can use their assumptions directly after making them, but mathematicians have to consider a lot more.

Although Xiao Yi was still a little uncomfortable with it, this method was very enjoyable once he started using it.

till the end.

"Done..."

He looked in amazement at the seamless model that finally appeared on the draft paper.

Its Hamiltonian is described as: [H = t∑[i, j], σ(ciσcjσ+hc)+∑iVini+J∑[i, j]SiSj+∑ihiSiz+x∑iniSiz]

Here, x is the coupling constant between the electron density and the spin density.

Probably, no one could have imagined that these two theories, which were treated separately in the past, actually have such a connection. Electron density waves and spin density waves can be coupled through interaction, thus forming a mechanism to enhance electron pairing.

And this model can roughly describe the mechanism of high-temperature superconductivity!

His heart was filled with excitement.

It is true that there is no way out despite the mountains and rivers, and there is another village with dark flowers and bright flowers.

Electron density waves and spin density waves have appeared before his eyes countless times, and of course, they have also appeared before the eyes of people in the entire physics community countless times. Probably no one could imagine that the two could be coupled!

"This new model... let's call it XSC theory for now."

Xiao's theory of superconductivity.

With a slightly excited mood, he began to carefully examine the theory in front of him, and began to substitute the various phenomena of high-temperature superconductivity he had listed before into it to see if he could find an explanation.

And the final result is very gratifying.

Because they almost all match up!

But there are certain errors.

Of course, Xiao Yi still thinks that it has errors from the perspective of a mathematician.

That's another joke.

Department of Mathematics: [0.9999... is not equal to 1. ]

Department of Physics: [Experimental result 0.999..., calculated result 1. Damn, the theory and practice match so perfectly. Will people accuse me of falsifying the data?]

天体物理系：【观测数据1*10的24次方，计算结果9*10的24次方，一个数量级的？那没啥问题了，这个模型非常完美。】

Therefore, in fact, from the perspective of physics, Xiao Yi's result has almost perfectly explained high-temperature superconductors.

"So, I've got it done?"

He was still a little dazed.

It is probably just like when Cooper accidentally discovered Cooper pairs after assuming that the total momentum of two electrons was zero.

"Just get used to it. That's how physics works."

Sighed slightly.

However, he was clear that this model could be further optimized, because although physics does not care much about a certain degree of error, in fact, according to his previous calculations, the errors between the calculation results and those specific phenomena are still relatively large.

Among them, the main reason may be x, the coupling constant between electron density and spin density, which can now also be called Xiao Yi constant or superconducting constant.

Similar to Einstein's constant and Planck's constant.

According to Xiao Yi's calculation results, this x≈1.271851 is obviously still somewhat inaccurate.

As for how to optimize, there is a very simple method for him.

"Experiments! Data!"

With more experiments and more data, he could easily get a more accurate value for x.

When he thought of this, he wished he could travel back to one year later and go to the already built Science Island laboratory to conduct experiments.

But in the end, he shook his head.

"Forget it, let's not think too much about it."

"Let's go to the School of Materials Science and borrow Sun Lina's laboratory... well, it should be Luo Mingya's laboratory."

……

(End of this chapter)