Ever since quantum mechanics first described particles, like electrons, as rippling waves, researchers have wondered if those waves could be trapped in place. Writing today in Science a century later, a team of Columbia University researchers reports waves of electrons becoming trapped for the first time in a metal called Pd5AlI2.
"Quantum mechanics predicts that an electron wave can, theoretically, remain trapped even when there are infinitely many paths for it to escape. This effect is known from light waves, but it has never been seen before for electrons," said Raquel Queiroz , a theoretical physicist at Columbia. It was a surprising discovery, and one that opens new possibilities for manipulating quantum states in metals.
Metals, classically, conduct electricity because their electrons are free to spread around a material. A few years ago, researchers in Xavier Roy 's chemistry lab at Columbia made a new metal, Pd5AlI2, that can be peeled into two-dimensional layers while retaining its metallic characteristics. Its electrons, however, moved more slowly than they expected.
Working with Queiroz and experimental physicists Cory Dean and Aravind Devarakonda (a former Columbia postdoc who is now an assistant professor of applied physics at Columbia), they determined that electrons in Pd5AlI2 experience frustration. The way Pd5AlI2's atoms and their orbitals are arranged gives its electrons competing paths to "hop" from atom to atom. These paths cancel each other out, holding many of the electrons back. The team published their results on frustrated electron hopping in Nature Physics last year.
The team was also working with Columbia physicist Abhay Pasupathy , whose lab has specialized scanning and spectroscopy instruments that can image materials with atom-scale accuracy. During initial scans, they noticed unexpected patterns. Upon closer look, these turned out to be electron waves bound in place near atomic defects in the material's crystal lattice.
"Bound electrons shouldn't occur in a metal, but they do in Pd5AlI2. What we have observed is the first clear evidence of quantum interference trapping a state in a metal," said Queiroz, who developed the models that now explain the team's physical observations.
The classical view of metals describes their conducting electrons as discrete ping-pong balls carrying current from place to place. A classical electron will take a well-defined path from point A to point B, but in quantum mechanics, electron motion is described as waves, which can take all possible paths at once. But a consequence of wave mechanics is interference: Waves can interfere with each other in a constructive way that increases their chances of making it from point A to point B, or in a destructive way that suppresses their movement. If there is enough destructive interference, it can completely stop an electron wave from leaving point A, effectively binding it in place among a larger continuous sea of waves. This is known as a bound state in the continuum (BIC).
While this is the first time a BIC has been observed in a metal, it has been observed before in another quantum-mechanical sea: that of light. Over the past decade, researchers figured out how to etch materials with tiny patterns that can trap individual photons of light.
"Trapping a wave is an idea as old as quantum mechanics itself, but it took almost a century to figure out how to do it with light. We have now realized it with electrons in a material," said Roy. "And if you trap a particle, you can manipulate it." Optical BICs have helped advance lasing, sensing, and nonlinear optics. Electronic BICs could one day lead to new kinds of extremely sensitive quantum sensors, improve information transfer and processing in quantum computers, and help advance quantum chemistry.
But while optical BICs can be intentionally designed into materials, their electronic analogs are currently random, the result of defects arising during the growth of Pd5AlI2 in the lab. To that end, Roy and Pasupathy are exploring ways to deliberately introduce defects into specific places in the metal, which would allow them to fine-tune the resulting interference patterns.
Electrons can be bound in place in insulating and semiconducting materials through several methods. In semiconductors, these bound states are intimately connected to the process of doping by which we get current to flow in a controlled manner—the basis of all chips used in computing devices today. In a metal, the only way to localize an electron is via a BIC, which can only occur in materials, like Pd5AlI2 with frustrated crystal lattice structures. That means there should be other classes of metals with similar structures that could host electronic BICs. Now that Queiroz and her colleagues have confirmed that electron waves can be trapped in metals, and how, they have a new quantum mechanical recipe for finding them in additional materials.
