The top student must be diligent

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

It has become very critical to crack the mechanism of high-temperature superconductivity!

…

"Local electron density fluctuations enhance the interaction between electrons..."

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

Xiao Yi was thinking deeply about this matter.

"How exactly is the interaction between electrons enhanced?"

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

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

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 some low-temperature superconducting metals.

In the 1950s, physicists such as John Bardeen had proposed that lattice vibrations may produce an attractive force between electrons, which is 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, which refers to the maximum energy boundary of electrons at absolute zero.

"In Cooper's research, he assumed that if the total momentum of two electrons is 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 electron pairs."

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

"... The most important thing is that he proved through quantum mechanical calculations that when the temperature is below a certain critical value, the formation of electron pairs is spontaneous. This spontaneously formed electron pair 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, 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, and the temperature does not reach the threshold of the pairing energy between Cooper pairs, so the interaction between electrons and phonons can form Cooper pairs."

"But in At high temperatures, electrons are excited to higher states, and thermal noise causes random scattering between electrons, so traditional superconductors explained by the BCS theory cannot achieve superconductivity at high temperatures. "

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

"For example, in copper oxide high-temperature superconductors, Cooper pairs are usually considered to have d-wave symmetry rather than s-wave symmetry in traditional 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 also recalled the previous inspirations, until finally, his eyes suddenly burst into a gleam of light.

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

"If the local spin density wave is also substituted..."

"Add the local electron density wave..."

"Combining these two theories to describe the electron strongly correlated system..."

It's feasible!

In any case, this can definitely be regarded as a research angle.

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

"Well... these two cannot be directly substituted in, it is best to start from other directions."

"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+h.c.)+U∑ini↑ni↓]

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

"Then there is the spin density wave... which can be described by a periodic spin arrangement."

[[Szi]=S0cos(QRi)]

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

"But we have to build a model first."

After about two hours, Xiao Yi completed the modeling and input the model into the computer.

"Next, it's connecting to the server."

The server that Xiao Yi bought for hundreds of W is still in HKUST.

So, he quickly connected to the server and put the model on it to run.

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

There is basically no better or more suitable method to analyze his model.

However, in addition to the absolute electronic property calculation, he also used another method called density matrix renormalization group DMRG. DMRG is particularly suitable for processing low-dimensional strongly correlated electronic 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 helps Xiao Yi to deeply study the local electronic state distribution and spin density wave behavior caused by iron vacancies.

Soon, the results came out.

"Sure enough, the local electron density fluctuations and spin density waves caused by iron vacancies produce effective attractive interactions 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 caused by spin density waves."

"Magnetic fluctuations..."

His eyes became brighter and brighter.

"Local electron density fluctuations lead to the rearrangement of electron states, making it easier for some electron states to form pairs in these regions. Spin density waves cause magnetic fluctuations in these local regions, and these fluctuations enhance the attractive interactions between electrons... Wait!"

His expression suddenly became serious, and he re-observed the simulated data.

Until the end, he re-listed 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 considering the coupling of electron density waves and spin density waves, the ground state energy of the system is significantly reduced, 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 am still a little uncomfortable with this way of assuming."

Although he has made many important achievements in physics, he still recognizes his identity as a mathematician psychologically, and some methods in physics are quite difficult to recognize from a mathematical point of view.

It's like a joke: [Maybe mathematicians will be angry when they see this step, but we don't care about him].

He is like this now, first make an assumption, no matter whether the assumption is right or not, just use it.

After using it, go to the control experiment, as long as the experiment is verified, then the assumption 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, while for physics, there is no real infinity. The currently verified series are 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, physicists can use it directly after assuming it, but mathematicians have to consider a lot.

Although Xiao Yi is still a little uncomfortable, once this method is used, it is still very refreshing.

Until the end.

"Done..."

He looked at the seamless model that was finally obtained on the draft paper in surprise.

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

Where x is the coupling constant between electron density and spin density.

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

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

His heart was full of excitement.

It is really a case of mountains and rivers, and there is no way out.

Electron density waves and spin density waves have appeared in front of him countless times, and of course, they have also appeared in front of people in the entire physics community countless times. Probably no one could imagine that there can be coupling between the two!

"This new model... let's call it XSC theory for the time being."

Xiao's superconductivity theory.

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 listed before into it to see if he could explain it.

And the final result was very gratifying.

Because they almost all match!

It's just that there are certain errors.

Of course, Xiao Yi still thinks that it has errors as a mathematician.

This is another joke.

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

Physics Department: [Experimental result 0.999..., calculated result 1, damn, the theory and practice are so perfect, people won't say that I falsified the data? ]

Astrophysics Department: [Observation data 1*10 to the 24th power, calculated result 9*10 to the 24th power, an order of magnitude? There is no problem, this model is perfect. ]

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

"So, I've got it done?"

He was still a little confused.

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