The first universal theory of strange metals could help explain why they behave so oddly – for example, why they resist the flow of electrons more than ordinary metals such as gold or copper. The new theory, developed by researchers at the Flatiron Institute in New York City and Harvard University, both in the US, takes into account two properties of strange metals: the quantum entanglement of their electrons and the non-uniform arrangement of their atoms. The work could advance our understanding of high-temperature superconductors and other correlated quantum materials.

Strange metals lie somewhere between metals and insulators and get their name from the peculiar behaviour of their electrons. Unlike electrons in ordinary metals, which travel freely with few interactions and little resistance, electrons in strange metals move sluggishly and in a restricted fashion. The electrons in a strange metal also lose the “memory” of their past positions at the fastest possible rate allowed by the fundamental laws of quantum mechanics.

More strangely still, researchers recently learned that cuprate (copper oxide) high-temperature superconductors, which were discovered in 1987, contain a strange metal phase as well as a superconducting phase. The strange phase occurs when the copper oxide layer is highly doped with holes, and it puzzles physicists because it cannot be described by conventional theories that treat electrons as independent quantum particles, and largely ignore any quantum entanglement between them.

Subtle interplay between many-electron entanglement and disorder

“Understanding this strange phase is a necessary ingredient in any theory of high temperature superconductivity, and much effort has been expended in this direction in the last few decades,” says Subir Sachdev of Harvard, who co-led the new study together with Aavishkar Patel of the Flatiron Institute’s Center for Computational Quantum Physics (CCQ). “We propose a new theory in our paper that is consistent with existing observations and highlights the subtle interplay between many-electron entanglement and the disorder that is present in all crystals due to the presence of impurities.”

The irregularity of a strange metal’s layout means that the nature of its electron entanglements strongly depends on where the entanglement takes place within the material, Sachdev adds. This inhomogeneity adds randomness to the electrons’ momentum as they propagate though the material and interact with each other. As a result, instead of the electrons flowing together, they collide with each other in all directions and push each other around, generating electrical resistance. And because the electrons collide more frequently as the material’s temperature increases, the electrical resistance increases proportionally with temperature.

A more realistic model

This interplay of entanglement and nonuniformity has never been experimentally documented before in any material, but Patel notes that it is an extremely simple concept – at least in hindsight.

“The initial idea was my proposal in 1993 in (a variation of) what is now called the Sachdev-Ye-Kitaev model,” Sachdev tells Physics World. “This is a simple, solvable, toy model that allows us to study the interplay between quantum entanglement and disorder in a regime in which current flows in an entangled ‘quantum soup’ and not via individual electrons.”

Since then, the researchers have been looking into ways to make this toy model more realistic via collaborations with both experimentalists and theorists – in particular Flatiron’s Antoine Georges and Olivier Parcollet. “After many wrong turns along the way, we finally hit upon the generalization described in our present study, which we detail in Science, during long discussions with my co-authors during the pandemic period,” Sachdev says.

The theory could serve as a “launching pad” towards understanding the complete phase diagram of the copper-oxide-based high-temperature superconductors and a number of other related quantum materials, he adds.

The Flatiron/Harvard team is now computing many observable properties of its theory, including the noise in current flow and the response to strong laser light and magnetic fields. “We will compare these results with ongoing experiments and hope to arrive at a complete picture of the underlying physics,” Sachdev concludes.

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