image: In anti-Klein tunneling, sound waves bounce back as if hitting an invisible wall; in Klein tunneling, they pass through the barrier effortlessly—as if the wall isn’t there at all.
Credit: ©Science China Press
In a groundbreaking experiment, researchers from Tianjin University, Zhejiang University, Northeastern University and University of Science and Technology of China have directly observed anti-Klein tunneling (AKT)—a quantum paradox where chiral particles are entirely reflected instead of passing through an energy barrier. This long-sought quantum-like behavior is realized not with electrons, but with engineered sound waves in a custom-designed bilayer phononic crystal.
Klein tunneling (KT), first proposed in 1929, refers to the paradoxical ability of massless relativistic particles to pass through energy barriers with no reflection, defying classical expectations. Its theoretical counterpart, anti-Klein tunneling, suggests that massive chiral particles—particles whose wave functions carry handedness—can be completely reflected by such barriers due to destructive interference. While KT has been demonstrated in systems such as graphene and photonic crystals, AKT had remained elusive in experimental settings.
To realize AKT, the research team designs a bilayer phononic crystal system that mimics the quantum band structure of bilayer graphene. This system supports the emergence of massive chiral phonons, which act as acoustic analogs of massive Dirac fermions. By carefully tuning the intralayer and interlayer coupling strengths—controlled mechanically through structural parameters—the researchers construct an acoustic potential barrier that allows or blocks phonon transmission.
The experiment uses a pump-probe acoustic setup to measure wave propagation across the barrier. In the bilayer configuration, the sound wave decays exponentially within the barrier region, resulting in vanishing transmission—a clear signature of AKT. When the same structure is adjusted to form a monolayer configuration, the phonons pass through the barrier without reflection, confirming the presence of KT. The team also demonstrates that by varying the layer thickness, they can continuously tune the phonon transport from total reflection (AKT) to perfect transmission (KT), revealing a controllable transition path between these regimes.
“This system mirrors deep quantum phenomena using sound,” says Professor Ying Li of Zhejiang University, co-corresponding author of the study. “It’s an elegant and accessible way to study fundamental physics.”
Phononic crystals offer unique advantages over traditional electronic systems: they operate at macroscopic scales, have low energy loss, and allow real-time structural tuning. These features make them ideal platforms for topological wave manipulation, reconfigurable acoustic devices, and quantum-inspired simulations without relying on electrons or extreme conditions.
The discovery of anti-Klein tunneling in a classical system also opens up new possibilities in wave-based computation, acoustic signal routing, and the design of functional metamaterials that harness quantum analogs for practical applications.
“This research not only confirms a fundamental theoretical prediction, but also provides a versatile experimental platform for future exploration,” adds Professor Qian Ding from Tianjin University, another co-corresponding author of the study.
As advances in microstructure fabrication and high-resolution acoustic detection continue, phononic systems like this one are poised to become powerful tools for probing the quantum–classical boundary and engineering next-generation wave-based technologies.