Fundamental quantum model recreated from nanographenes

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The smallest unit of information in a computer is the bit: on or off, 1 or 0. Today, the world's entire computing power is built on the combination and interconnection of countless ones and zeros. Quantum computers have their own version of the bit: the qubit. It, too, has two basic states. The main difference: Quantum effects allow a superposition of the two states, so that the qubit is not either 1 or 0, but both at the same time. With different proportions of 0 and 1, the qubit can theoretically assume an infinite number of states.

This ambiguity should give quantum computers true "superpowers." At least in theory, quantum-based computers can perform calculations in fractions of a second that stump today's best supercomputers. However, quantum computing is not yet fully developed. One of the biggest challenges is linking the qubits—since one single (qu)bit is not much of a computer.

One way to realize the 0 and the 1 of the qubit is via the alignment of the so-called electron spin. The spin is a fundamental quantum mechanical property of electrons and other particles, a kind of torque that, put simply, can point "up" (1) or "down" (0).

When two or more spins are quantum-mechanically linked, they influence each other's states: Change the orientation of one, and it will also change for all the others. This is therefore a good way to make qubits "talk" to each other. However, like so much in quantum physics, this "language," i.e. the interaction between the spins, is enormously complex.

Although it can be described mathematically, the relevant equations can hardly be solved exactly even for relatively simple chains of just a few spins. Not exactly the best conditions for putting theory into practice...

A model becomes reality

Researchers at Empa's nanotech@surfaces laboratory have now developed a method that allows many spins to "talk" to each other in a controlled manner—and that also enables the researchers to "listen" to them, i.e. to understand their interactions.

Together with scientists from the International Iberian Nanotechnology Laboratory and the Technical University of Dresden, they were able to precisely create an archetypal chain of electron spins and measure its properties in detail. Their results have now been published in the journal Nature Nanotechnology.

The theory behind the chain is familiar to all physics students: Take a linear chain of spins in which each spin interacts strongly with one of its neighbors and weakly with the other. This so-called one-dimensional alternating Heisenberg model was described almost 100 years ago by physicist and later Nobel Prize laureate Werner Heisenberg, one of the founders of quantum mechanics. Although there are materials in nature that contain such spin chains, it has not yet been possible to deliberately incorporate the chains into a material.

"Real materials are always much more complex than a theoretical model," explains Roman Fasel, head of Empa's nanotech@surfaces laboratory and co-author of the study.

A 'goblet' made of carbon

To create such an artificial quantum material, the Empa researchers used tiny pieces of the two-dimensional carbon material graphene. The shape of these nanographene molecules influences their physical properties, in particular their spin—a kind of nano-sized quantum Lego brick from which the scientists can assemble longer chains.

For their Heisenberg model, the researchers used the so-called Clar's Goblet molecule. This special nanographene molecule consists of eleven carbon rings arranged in an hourglass-like shape. Due to this shape, there is an unpaired electron at each end—each with an associated spin. Although predicted by chemist Erich Clar as early as 1972, Clar's Goblet was only produced in 2019 by Fasel's team at the nanotech@surfaces laboratory.

The researchers have now linked the goblets on a gold surface to form chains. The two spins within a molecule are weakly linked, while the spins from molecule to molecule are strongly linked—a perfect realization of the alternating Heisenberg chain. The researchers were able to precisely manipulate the length of the chains, selectively switch individual spins on and off and "flip" them from one state to another, allowing them to investigate the complex physics of this novel quantum material in great detail.

From theory to practice

Fasel is convinced that, just as the synthesis of Clar's Goblet enabled the production of Heisenberg chains, this study will in turn open new doors in quantum research.

"We have shown that theoretical models of quantum physics can be realized with nanographenes in order to test their predictions experimentally," says the researcher. "Nanographenes with other spin configurations can be linked to form other types of chains or even more complex systems."

The Empa researchers are leading by example: In a second study, which is about to be published, they were able to recreate a different type of Heisenberg chain in which all spins are equally linked.

To be at the forefront of applied quantum physics, theoretical and experimental scientists from different disciplines need to work together. Chemists at Dresden University of Technology provided Empa researchers with the starting molecules for their synthesis of Clar's Goblets. And researchers from the International Iberian Nanotechnology Laboratory in Portugal contributed their theoretical expertise to the project.

The theory needed for such breakthroughs is not (just) what you find in physics textbooks, Fasel emphasizes, but a sophisticated transfer between the quantum physics model and the experimental measurements.

More information: Chenxiao Zhao et al, Tunable topological phases in nanographene-based spin-1/2 alternating-exchange Heisenberg chains, Nature Nanotechnology (2024). DOI: 10.1038/s41565-024-01805-z

Journal information: Nature Nanotechnology

Provided by Swiss Federal Laboratories for Materials Science and Technology