Electron Waves Trapped in a Metal for the First Time, Columbia Physicists Report in Science

Physicists at Columbia University have trapped waves of electrons inside a metal, something quantum mechanics has allowed on paper for about a century but that nobody had seen in a metal until now. The team reports the result in the journal Science.

Quantum theory describes electrons as waves, not tiny balls. In a metal, those waves normally spread freely through the crystal, which is why metals conduct electricity. "Quantum mechanics predicts that an electron wave can, theoretically, remain trapped even when there are infinitely many paths for it to escape," said Raquel Queiroz, a theoretical physicist at Columbia. "This effect is known from light waves, but it has never been seen before for electrons."

The material is a metal called Pd5AlI2. Chemist Xavier Roy's lab at Columbia made it a few years ago, and it can be peeled into two-dimensional layers while staying metallic. Its electrons moved more slowly than expected. Working with Queiroz and experimental physicists Cory Dean and Aravind Devarakonda, the team concluded that the electrons are frustrated: the arrangement of the atoms and their orbitals gives electrons competing paths to hop from atom to atom, and those paths cancel each other out, holding many electrons back. They published that result in Nature Physics last year.

The new finding came when the group worked with physicist Abhay Pasupathy, whose lab has instruments that can image materials with atom-scale accuracy. Early scans showed unexpected patterns. A closer look showed electron waves bound in place near atomic defects in the crystal lattice. "Bound electrons shouldn't occur in a metal, but they do in Pd5AlI2," Queiroz said. "What we have observed is the first clear evidence of quantum interference trapping a state in a metal."

The explanation is wave interference. Waves can add together to make a path more likely, or cancel to suppress it. With enough destructive interference, an electron wave cannot leave its starting point and is held in place within a larger sea of moving waves. Physicists call this a bound state in the continuum. It has been seen before with light, where researchers learned over the past decade to etch materials with tiny patterns that trap individual photons.

"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," Roy said. "We have now realized it with electrons in a material. And if you trap a particle, you can manipulate it." Optical versions of the effect have already advanced lasers, sensing and nonlinear optics. Electronic versions could eventually lead to very sensitive quantum sensors, better information transfer and processing in quantum computers, and advances in quantum chemistry.

There is a limit for now. Optical bound states can be designed into materials on purpose, but the electronic ones in Pd5AlI2 are random, produced by defects that arise when the crystal is grown. Roy and Pasupathy are working on ways to place defects at chosen spots so they can tune the interference patterns.

In a metal, the only way to localize an electron is through this kind of bound state, and it can only occur in materials with frustrated lattices like Pd5AlI2. That suggests other classes of metals with similar structures could host the same effect, and the team now has a recipe for finding them. The paper, by Morgan Thinel and colleagues, is titled "Electronic bound states in the continuum in a two-dimensional metal."