A new breakthrough may help scientists solve some of the mysteries of the quantum realm.
For the first time, physicists have been able to measure the geometrical 'shape' a lone electron adopts as it moves through a solid. It's an achievement that will unlock a whole new way of studying how crystalline solids behave on a quantum level.
"We've essentially developed a blueprint for obtaining some completely new information that couldn't be obtained before," says physicist Riccardo Comin of the Massachusetts Institute of Technology (MIT).
The research was led by physicists Mingu Kang – formerly of MIT and now at Cornell University – and Sunjie Kim of Seoul National University.
Within the physical Universe, matter behaves in ways that are well described by classical physics.
However, on a more fundamental level of particle interactions and methods of measurement, things can get a little weird. On the finest of scales, precision must give way to a more fuzzy description represented by waves of possibility known as quantum mechanics.
We refer to objects like electrons as particles, and that conveys the impression that they are like teeny tiny little balls. Given their size, the properties and behaviors of electrons are far more accurately described by their wave-like quantum nature.
To describe the wave aspect of electrons, physicists use wave functions: mathematical models that describe the properties of the wave as evolving possibilities of finding the particle in a specific place with specific features.
Some of these features we can think of as a kind of geometry, often not unlike a curve or sphere that rotates in an infinite number of directions. Other forms of quantum geometry, like those of electrons in a lattice of atoms, are as complicated as a Klein bottle or a Möbius strip.
Determining some aspects of the messy quantum geometry of an electron in a solid has previously involved a lot of guesswork based on properties that physicists can measure.
To measure the quantum geometry of electrons, Kang, Jie, and their colleagues sought the measurement of a property known as the quantum geometric tensor, or QGT. This is a physical quantity that encodes the entire geometric information of a quantum state, similar to the way a two-dimensional hologram encodes information about a three-dimensional space.
The technique they used is called angle-resolved photoemission spectroscopy, in which photons are fired at a material to dislodge electrons and measure their properties, such as polarization, spin, and angle.
This was directed at single crystals of a cobalt-tin alloy, a material known as a kagome metal – a quantum material whose properties the team had previously investigated using the same technique.
The results provided the researchers with the first measurement of the QGT in a solid, and from this, they were able to infer the rest of the quantum geometry of the electrons in the metal.
The team compared this to theoretically derived quantum geometry for the same material, allowing them to determine the usefulness of estimating the geometry compared to measuring it directly.
And, they say, their technique will be applicable to a broad range of materials, not just the cobalt-tin alloy used for this study. It's a result that will have some interesting implications. For example, quantum geometry could be leveraged to discover superconductivity in materials where it is not usually found.
"The geometric interpretation of quantum mechanics underpins many recent advances in condensed-matter physics," an anonymous expert told Nature Physics.
"These authors have pioneered a methodology to experimentally access the quantum geometric tensor, which fundamentally characterizes the geometric properties of quantum states. The developed methodology is straightforward, applicable to various solid-state materials, and has great potential for boosting experimental activity in pursuit of geometric understanding of novel quantum phenomena."
The team's research has been published in Nature Physics.