Physicists trying to understand a bizarre quantum phenomenon called a “pseudo-gap” believe their research could lead to room-temperature superconductivity – a holy grail for condensed matter physics.

Superconductors can be used for lossless power transmission, faster MRI machines and superfast levitating transport.

The drawback is that most superconductors require temperatures close to absolute zero (–273°C) to work. The highest temperature superconductors experiments still require frigid conditions of –134°C.

## Mind the pseudo-gap

At even higher temperatures, these materials fall into a pseudo-gap state. In this state, the material can sometimes act like a normal metal, and sometimes like a semiconductor.

Quantum pseudo-gap states occur as a material is cooled. A gap appears in the energies of electrons in the system before the material reaches the critical temperature at which it becomes a superconductor.

Why this happens and its relevance to superconductivity have been mysteries.

Computer simulations of electrons can be used to study pseudo-gap states. But quantum entanglement – where the electrons become linked and can’t be treated individually even after being separated – makes this more complicated. Simulating the behaviour of more than a few dozen electrons is impossible.

A new paper published in the journal *Science* provides a clever workaround to solving the puzzle of the quantum pseudo-gap.

“There is a class of methods which work very well at 0 temperature, and there is another class of methods which work very well at finite temperatures,” says lead author Fedor Šimkovic IV, team lead at IQM Quantum Computers in Germany. “These two worlds don’t usually speak to each other because, in between them, at very low but finite temperatures, actually lies the computationally hardest regime.”

It’s in this in-between area where pseudo-gaps live.

## Computing the pseudo-gap

“Computing the properties of these materials is extraordinarily challenging – you can’t simulate them exactly on even the most powerful computer you can think of,” says co-author Antoine Georges, director of the Flatiron Institute’s Center for Computational Quantum Physics (CCQ) in the US.

“You have to resort to clever algorithms and simplified models.”

One is the Hubbard model. The material is treated like a chessboard. Electrons can move to adjacent spaces (energy values) like a rook. Electrons can be spin up or spin down. Electrons can share a space only if they have opposite spins – and they do so at an energy cost.

The team then applied an algorithm called a diagrammatic Monte Carlo.

Quantum Monte Carlo algorithms have been extremely helpful in studying quantum systems by using randomness to examine small areas of a model then piece them together.

But the diagrammatic Monte Carlo looks at the whole chessboard. In principle, it could simulate an infinite number of particles.

## Showing the true quantum stripes

The team found that materials in a pseudo-gap state cooling toward absolute zero developed into rows of electrons with matching spins separated by rows of empty squares (continuing with the chessboard analogy).

However, adding diagonal moves – like a bishop – leads to the material evolving into a superconductor as it cools.

“It was debated if the pseudo-gap always evolves into the stripe state,” Georges says. “Our paper answers this prominent question in the field and closes that window.”