“The noise is greatly suppressed compared to ordinary wires,” said Rice’s Douglas Natelson, the study’s corresponding author. “Maybe this is evidence that quasiparticles are not well-defined things or that they’re just not there and charge moves in more complicated ways. We have to find the right vocabulary to talk about how charge can move collectively.”

The experiments were performed on nanoscale wires of a quantum critical material with a precise 1-2-2 ratio of ytterbium, rhodium and silicon (YbRh2Si2), which has been studied in great depth during the past two decades by Silke Paschen, a solid-state physicist at the Vienna University of Technology (TU Wien). The material contains a high degree of quantum entanglement that produces a very unusual (“strange”) temperature-dependent behavior that is very different from the one in normal metals such as silver or gold.

In such normal metals, each quasiparticle, or discrete unit, of charge is the product of incalculable tiny interactions between countless electrons. First put forward 67 years ago, the quasiparticle is a concept physicists use to represent the combined effect of those interactions as a single quantum object for the purposes of quantum mechanical calculations.

Some prior theoretical studies have suggested that the charge in a strange metal might not be carried by such quasiparticles, and shot noise experiments allowed Natelson, study lead author Liyang Chen, a former student in Natelson’s lab, and other Rice and TU Wien co-authors to gather the first direct empirical evidence to test the idea.

“The shot noise measurement is basically a way of seeing how granular the charge is as it goes through something,” Natelson said. “The idea is that if I’m driving a current, it consists of a bunch of discrete charge carriers. Those arrive at an average rate, but sometimes they happen to be closer together in time, and sometimes they’re farther apart.”

Applying the technique in YbRh2Si2 crystals presented significant technical challenges. Shot noise experiments cannot be performed on single macroscopic crystals but, rather, require samples of nanoscopic dimensions. Thus, the growth of extremely thin but nevertheless perfectly crystalline films had to be achieved, something that Paschen, Maxwell Andrews and their collaborators at TU Wien managed after almost a decade of hard work. Next, Chen had to find a way to maintain that level of perfection while fashioning wires from these thin films that were about 5,000 times narrower than a human hair.

Rice co-author Qimiao Si, the lead theorist on the study and the Harry C. and Olga K. Wiess Professor of Physics and Astronomy, said he, Natelson and Paschen first discussed the idea for the experiments while Paschen was a visiting scholar at Rice in 2016. Si said the results are consistent with a theory of quantum criticality he published in 2001 that he has continued to explore in a nearly two-decade collaboration with Paschen.

“The low shot noise brought about fresh new insights into how the charge-current carriers entwine with the other agents of the quantum criticality that underlies the strange metallicity,” said Si, whose group performed calculations that ruled out the quasiparticle picture. “In this theory of quantum criticality, the electrons are pushed to the verge of localization, and the quasiparticles are lost everywhere on the Fermi surface.”

Natelson said the larger question is whether similar behavior might arise in any or all of the dozens of other compounds that exhibit strange metal behavior.

“Sometimes you kind of feel like nature is telling you something,” Natelson said. “This ‘strange metallicity’ shows up in many different physical systems, despite the fact that the microscopic, underlying physics is very different. In copper-oxide superconductors, for example, the microscopic physics is very, very different than in the heavy-fermion system we’re looking at. They all seem to have this linear-in-temperature resistivity that’s characteristic of strange metals, and you have to wonder is there something generic going on that is independent of whatever the microscopic building blocks are inside them.”

The research was supported by the Department of Energy’s Basic Energy Sciences program (DE-FG02-06ER46337), the National Science Foundation (1704264, 2220603), the European Research Council (101055088), the Austrian Science Fund (FWF I4047, FWF SFB F 86), the Austrian Research Promotion Agency (FFG 2156529, FFG 883941), the European Union’s Horizon 2020 program (824109-EMP), the Air Force Office of Scientific Research (FA8665-22-1-7170), the Welch Foundation (C-1411) and the Vannevar Bush Faculty Fellowship (ONR-VB-N00014-23-1-2870).

The Telescope Array has since observed more than 30 ultra-high-energy cosmic rays, though none approaching the Oh-My-God-level energy. No observations have yet revealed their origin or how they are able to travel to the Earth.

On May 27, 2021, the Telescope Array experiment detected the second-highest extreme-energy cosmic ray. At 2.4 x 10²⁰eV, the energy of this single subatomic particle is equivalent to dropping a brick on your toe from waist height. Led by the University of Utah (the U) and the University of Tokyo, the Telescope Array consists of 507 surface detector stations arranged in a square grid that covers 700 km² (~270 miles²) outside of Delta, Utah in the state’s West Desert. The event triggered 23 detectors at the north-west region of the Telescope Array, splashing across 48 km² (18.5 mi²). Its arrival direction appeared to be from the Local Void, an empty area of space bordering the Milky Way galaxy.

“The particles are so high energy, they shouldn’t be affected by galactic and extra-galactic magnetic fields. You should be able to point to where they come from in the sky,” said John Matthews, Telescope Array co-spokesperson at the U and co-author of the study. “But in the case of the Oh-My-God particle and this new particle, you trace its trajectory to its source and there’s nothing high energy enough to have produced it. That’s the mystery of this — what the heck is going on?”

In their observation that published on Nov. 24, 2023, in the journal Science, an international collaboration of researchers describe the ultra-high-energy cosmic ray, evaluate its characteristics, and conclude that the rare phenomena might follow particle physics unknown to science. The researchers named it the Amaterasu particle after the sun goddess in Japanese mythology. The Oh-My-God and the Amaterasu particles were detected using different observation techniques, confirming that while rare, these ultra-high energy events are real.

“These events seem like they’re coming from completely different places in the sky. It’s not like there’s one mysterious source,” said John Belz, professor at the U and co-author of the study. “It could be defects in the structure of spacetime, colliding cosmic strings. I mean, I’m just spit-balling crazy ideas that people are coming up with because there’s not a conventional explanation.”

Natural particle accelerators

Cosmic rays are echoes of violent celestial events that have stripped matter to its subatomic structures and hurled it through universe at nearly the speed of light. Essentially cosmic rays are charged particles with a wide range of energies consisting of positive protons, negative electrons, or entire atomic nuclei that travel through space and rain down onto Earth nearly constantly.

Cosmic rays hit Earth’s upper atmosphere and blasts apart the nucleus of oxygen and nitrogen gas, generating many secondary particles. These travel a short distance in the atmosphere and repeat the process, building a shower of billions of secondary particles that scatter to the surface. The footprint of this secondary shower is massive and requires that detectors cover an area as large as the Telescope Array. The surface detectors utilize a suite of instrumentation that gives researchers information about each cosmic ray; the timing of the signal shows its trajectory and the amount of charged particles hitting each detector reveals the primary particle’s energy.

Because particles have a charge, their flight path resembles a ball in a pinball machine as they zigzag against the electromagnetic fields through the cosmic microwave background. It’s nearly impossible to trace the trajectory of most cosmic rays, which lie on the low- to middle-end of the energy spectrum. Even high-energy cosmic rays are distorted by the microwave background. Particles with Oh-My-God and Amaterasuenergy blast through intergalactic space relatively unbent. Only the most powerful of celestial events can produce them.

“Things that people think of as energetic, like supernova, are nowhere near energetic enough for this. You need huge amounts of energy, really high magnetic fields to confine the particle while it gets accelerated,” said Matthews.

Ultra-high-energy cosmic rays must exceed 5 x 10¹⁹ eV. This means that a single subatomic particle carries the same kinetic energy as a major league pitcher’s fast ball and has tens of millions of times more energy than any human-made particle accelerator can achieve. Astrophysicists calculated this theoretical limit, known as the Greisen-Zatsepin-Kuzmin (GZK) cutoff, as the maximum energy a proton can hold traveling over long distances before the effect of interactions of the microwave background radiation take their energy. Known source candidates, such as active galactic nuclei or black holes with accretion disks emitting particle jets, tend to be more than 160 million light years away from Earth. The new particle’s 2.4 x 10²⁰ eV and the Oh-My-God particle’s 3.2 x 10²⁰ eV easily surpass the cutoff.

Researchers also analyze cosmic ray composition for clues of its origins. A heavier particle, like iron nuclei, are heavier, have more charge and are more susceptible to bending in a magnetic field than a lighter particle made of protons from a hydrogen atom. The new particle is likely a proton. Particle physics dictates that a cosmic ray with energy beyond the GZK cutoff is too powerful for the microwave background to distort its path, but back tracing its trajectory points towards empty space.

“Maybe magnetic fields are stronger than we thought, but that disagrees with other observations that show they’re not strong enough to produce significant curvature at these ten-to-the-twentieth electron volt energies,” said Belz. “It’s a real mystery.”

Expanding the footprint

The Telescope Array is uniquely positioned to detect ultra-high-energy cosmic rays. It sits at about 1,200 m (4,000 ft), the elevation sweet-spot that allows secondary particles maximum development, but before they start to decay. Its location in Utah’s West Desert provides ideal atmospheric conditions in two ways: the dry air is crucial because humidity will absorb the ultraviolet light necessary for detection; and the region’s dark skies are essential, as light pollution will create too much noise and obscure the cosmic rays.

Astrophysicists are still baffled by the mysterious phenomena. The Telescope Array is in the middle of an expansion that that they hope will help crack the case. Once completed, 500 new scintillator detectors will expand the Telescope Array will sample cosmic ray-induced particle showers across 2,900 km² (1,100 mi² ), an area nearly the size of Rhode Island. The larger footprint will hopefully capture more events that will shed light on what’s going on.