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Unraveling the mystery of high-temperature superconductors from first principles

Ever since their discovery almost four decades ago, high-temperature superconductors have fascinated scientists and engineers alike. These materials, primarily cuprates, defy classical understanding because they conduct electricity without resistance at temperatures far higher than traditional superconductors. Yet despite decades of research, we still don't have a clear, comprehensive microscopic picture of how superconductivity emerges in these complex materials.

During my Ph.D. at Caltech, I was intrigued by the profound puzzle presented by high-temperature superconductors: Can we directly compute their superconducting properties from fundamental quantum mechanics without relying on simplified models or approximations? With this question, I embarked on a challenging but rewarding scientific journey.

Why cuprates are special, and challenging

Cuprates are layered compounds composed primarily of copper-oxygen planes. In their undoped parent state, they are insulators and antiferromagnets, meaning that the electron spins align antiparallel in adjacent copper atoms. Introducing a small number of holes or electrons dramatically transforms them, causing superconductivity to appear. However, capturing this transition and the detailed pairing mechanism at the atomic scale has proven notoriously challenging for theorists.

Our recent study tackles this long-standing challenge. Together with collaborators from Caltech, Columbia, and Berkeley, we developed an advanced computational framework to simulate and predict superconductivity from first principles—meaning our calculations start directly from atomic positions without simplifications. The work is in Nature Communications.

Pressure, layers, and superconductivity—decoding the clues

We focused specifically on two intriguing and widely observed phenomena in cuprate superconductors:

• The pressure effect: When pressure is applied to cuprate planes, their superconducting temperatures typically rise.
• The layer effect: Cuprate superconductors with different numbers of copper-oxygen layers exhibit different superconducting temperatures (first increase with the number of layers and then decrease).

Remarkably, our ab initio simulations successfully reproduced these well-known experimental observations without pre-adjusting parameters or using fitted data. In fact, we could directly observe the pairing order—the essential quantum property behind superconductivity—and calculate pairing gaps, which relate closely to superconducting temperatures.

Deep dive: Spin and charge fluctuations drive pairing

What makes superconductivity happen at microscopic scales? Our calculations revealed the key lies in two critical types of quantum fluctuations:

• Spin fluctuations: Short-range magnetic interactions primarily among copper atoms.
• Charge fluctuations: Movements and rearrangements of electron density among copper and oxygen atoms.

These fluctuations, which occur at short distances—just a few atoms apart—act together to enable superconductivity. Interestingly, it turned out that spin fluctuations are crucial for pairing, while charge fluctuations set the stage by tuning the electronic environment around copper atoms.

Identifying the fingerprints of superconductivity

Can we quickly estimate how superconductive a material might be from simpler properties? Our simulations identified two straightforward "descriptors":

• Magnetic exchange coupling (J): A measure of how strongly neighboring spins interact.
• Cu–O covalency: The extent to which electrons are shared between copper and oxygen atoms.

These descriptors correlated strongly with computed superconducting properties, giving valuable hints on how structural changes or chemical substitutions might affect superconductivity.

The way forward—bridging theory and experiment

The ability to reliably simulate high-temperature superconductors from first principles represents a significant step forward. While our calculations do not yet capture all complexities—like phonons (atomic vibrations), structural disorder, and explicit dopant effects—they illustrate clearly that a complete microscopic description of high-temperature superconductivity is achievable.

Our hope is that this ab initio approach will allow researchers to more quickly identify promising superconducting materials and better understand existing ones. Perhaps most excitingly, the methods we developed could guide experimentalists toward new materials with even higher superconducting temperatures, bringing us closer to practical applications in energy transmission, transportation, and quantum technology.

The mysteries of high-temperature superconductivity have not been fully solved—but we are now closer than ever to understanding them at their most fundamental level. This journey is just beginning, and I'm excited to see where it takes us next.

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